Institute of Fundamental Technological Research

This paper proposes a computationally effective framework for load‐dependent optimal sensor placement in large‐scale civil engineering structures subjected to moving loads. Two common problems are addressed: selection of modes to be monitored and computational effectiveness. Typical sensor placement methods assume that the set of modes to be monitored is known. In practice, determination of such modes of interest is not straightforward. A practical approach is proposed that facilitates the selection of modes in a quasi‐automatic way based on the structural response at the candidate sensor locations to typical operational loads. The criterion used to assess sensor placement is based on Kammer's Effective Independence (EFI). However, in contrast to typical implementations of EFI, which treat the problem as a computationally demanding discrete problem and use greedy optimization, an approach based on convex relaxation is proposed. A notion of sensor density is applied, which converts the original combinatorial problem into a computationally tractable continuous optimization problem. The proposed framework is tested in application to a real tied‐arch railway bridge located in central Poland.

optimal sensor placement, effective independence method, Fisher information matrix

This work is an effort to join, for the first-time, multifractal analysis and damage detection in civil structures subjected to strong ground seismic motions. Specifically, based on the singularity spectrum quantitative and qualitative criteria are proposed. The qualitative criteria are based on the concave of singularity spectrum of damage and undamaged structure. The proposed quantitative criterion is based on calculation of damage index taken the parameters of singularity spectrum. In order to achieve the above goal, a robust signal processing method, which is known as multifractal wavelet leader (MFWL) is used. The multifractal analysis is a tool to calculate fractal properties as well as scaling behavior of the structural response excited by an earthquake. The singularity spectrum is obtained from the Legendre-transformation to Holder exponents. In this paper, a parameter which is based on the shape of singularity spectrum and can identify the damage in the structure is proposed. The proposed method is an output-only approach for damage detection. Considering that the dynamic behavior of an inelastic system subjected to strong ground motion appears to be a non-stationary process, the above procedure of multifractal wavelet leader is suitable to retrieve the simulation response data. The findings from the analysis show that the MFWL is an appropriate scheme for structural damage detection.

multifractal wavelet leader, damage detection, singularity spectrum, earthquake engineering, structural safety

This study is devoted to a novel method for topology optimization of elastoplastic structures subjected to stress constraints. It should be noted that in spite of the classical solutions of the different type of elastoplastic topology problems are more than 70 years old, the integration of the Prandtl-Reuss constitutive equations into the topology optimization process is not very often investigated in the last three decades. In the presented methodology where the classical variational principles of plasticity and the functor-oriented programming technique are applied in topology design, the aim is to find a minimum weight structure which is able to carry a given load, fulfills the allowable stress limit, and is made of a linearly elastic, perfectly plastic material. The optimal structure is found in an iterative way using only a stress intensity distribution and a return mapping algorithm. The method determines representative stresses at every Gaussian point, averages them inside every finite element using the von Mises yield criterion, and removes material proportionally to the stress intensities in individual finite elements. The procedure is repeated until the limit load capacity is exceeded under a given loading. The effectiveness of the methodology is illustrated with three numerical examples. Additionally, different topologies are presented for a purely elastic and an elastoplastic material, respectively. It is also demonstrated that the proposed method is able to find the optimal elastoplastic topology for a problem with a computational mesh of the order of tens of thousands of finite elements.

topology optimization, elastoplastic structures, minimum-weight design, stress constraints

This paper describes a semi-active control strategy that allows to transfer the vibration energy from an arbitrarily induced to a selected structural mode. The intended aim of the proposed control strategy is energy harvesting from structural vibrations. Another potential application is related to structural safety. In the paper, a mathematical model is first introduced to describe the phenomenon of vibrational energy transfer, and then, based on this model, an efficient semi-active control strategy is proposed. Finally, some problems related to measurement techniques are discussed. The effectiveness of the proposed methodology is demonstrated in an example of energy transfer between vibrational modes of a three-bar planar frame structure.

vibration energy, modal control, lockable joint, modal coupling

The success of virtually all structural health monitoring (SHM) methods depends on the information content of the measurements, and thus on the placement of the available sensors. This paper presents an efficient method for finding optimal sensor distribution over structural system with many degrees of freedom (DOFs). The objective function is based on the classical Fisher information matrix. Originally, this yields a computationally hard discrete optimization problem. However, the proposed numerical solution method is based on a concept taken from structural topology optimization, where a discrete optimization problem is replaced with a continuous one. Two numerical examples demonstrate the effectiveness of the proposed methodology. These are a 5-bay truss with 24 DOFs and a two-story frame structure whose finite element model has been condensed to 14 DOFs.

optimal sensor placement, structural damage identification, topology optimization

The paper deals with a novel approach to development of optimality criteria based finite element code for topology optimization of elasto-plastic structures. The novelty of this work is related to the concept of function object called functor and its application to efficient FE code development. First, the general problem of topology optimization under stress constraints is briefly formulated. Then, the programming aspects of topology optimization using traditional object-oriented and functor based programming are discussed. The advantages of the functor based approach are related to simplicity of designing the FE code architecture and reusability of this code. In particular the metric known as 'Lack of cohesion of methods' is useful in comparing these two different paradigms. Finally, the paper is also illustrated with numerical examples of topology optimization using the proposed methodology.

topology optimization, function object, functor programming, optimal design, elasto-plastic structures, finite element programming

Damage identification forms a key objective in structural health monitoring. Several state-of-the-art review papers regarding progress in this field up to 2011 have been published. This paper summarizes the recent progress between 2011 and 2017 in the area of damage identification methods for bridge structures. This paper is organized based on the classification of bridge infrastructure in terms of fundamental structural systems, namely, beam bridges, truss bridges, arch bridges, cable-stayed bridges, and suspension bridges. The overview includes theoretical developments, enhanced simulation attempts, laboratory-scale implementations, full-scale validation, and the summary for each type of bridges. Based on the offered review, some challenges, suggestions, and future trends in damage identification are proposed. The work can be served as a basis for both academics and practitioners, who seek to implement damage identification methods in next-generation structural health monitoring systems.

arch bridge, beam bridge, cable‐stayed bridge, damage identification, suspension bridge, truss bridge

The present study deals with a comprehensive approach for damage identification of spatial truss structures. The novelty of the proposed approach consists of a three-level analysis. First, sensitivity of assumed modal characteristics is calculated. Second, natural frequency sensitivity is used to determine hardly identifiable structural parameters and mode shape sensitivity is applied to select damage-sensitive locations of sensors. Third, two sparsity constrained optimization algorithms are tested towards efficient identification of applied damage scenarios. These two algorithms are based on ℓ1-norm minimization and non-negative least square (NNLS) solution. Performances of both proposed algorithms have been compared in two realistic case studies: the first one concerned a three-dimensional truss girder with 61 structural parameters and the second one was devoted to an upper-deck arch bridge composed of 416 steel members.

sensor placement, damage identification, ℓ1-norm minimization, sparsity constrained optimization

This study proposes a neural network based vibration control system designed to attenuate structural vibrations induced by an earthquake. Classical feedback control algorithms are susceptible to parameter changes. For structures with uncertain parameters they can even cause instability problems. The proposed neural network based control system can identify the structural properties of the system and avoids the above mentioned problems. In the present study it is assumed that a full state of the structure is known, which means the at each floor horizontal displacements and rotations about the vertical axis are measured. Additionally, it is assumed the acceleration signal coming from the earthquake is also available. The proposed neural control strategy is compared with the classical linear quadratic regulator (LQR) not only in terms of displacement responses, but also required control forces. Moreover, the influence of different weighting matrices on performance of the proposed control strategy has been presented.
The effectiveness of the neuro-controller has been demonstrated on two numerical examples: a simple single degree of freedom (DOF) structure and a multi-DOF structure representing a twelve story building. Both structures under consideration have been excited with El Centro acceleration signal. The results of numerical simulations on the SDOF system indicate that using neuro-controller it would be possible to obtain smaller amplitudes as compared with the LQ regulator, but it would require higher control effort.

vibration control, artificial neural networks, seismic excitation

This work proposes an efficient and reliable method for damage localization in truss structures. The damage is localized on the basis of measured acceleration signals of the structure followed by simple statistical signal processing. It has three main advantages over many existing methods. Firstly, it can be directly applied to real engineering structures without the need of identifying modal parameters or solving any global optimization problem. Secondly, the proposed method has higher sensitivity to damage than some other frequently used methods and allows to localize damage as small as a few percents. Thirdly, it is a model-free method, which does not require precise finite element model development or updating. Validation of the method has been conducted on numerical examples and laboratory-scale trusses. Two types of frequently used trusses have been selected for this study, namely Howe and Bailey trusses. The presented experimental validation of the method shows its efficiency and robustness for damage localization in truss structures.

structural health monitoring, truss structures, damage detection

The purpose of this work is the development of an efficient and high-sensitive damage localization technique for truss structures, based on the rank-revealing QR decomposition (RRQR) of the difference-of-flexibility matrix. The method is an enhancement of the existing techniques of damage detection, which rely on the set of so-called damage locating vector (DLV). The advantages of the RRQR decomposition-based DLV (RRQR-DLV) method are its less computational effort and high sensitivity to damage. Compared with the frequently used stochastic DLV (SDLV) method, RRQR-DLV offers higher sensitivity to damage, which has been validated based on the presented numerical simulation. The effectiveness of the proposed RRQR-DLV method is also illustrated with the experimental validation based on a laboratory-scale Bailey truss bridge model. The proposed method works under ambient excitation such as traffic excitation and wind excitation; therefore, it is promising for real-time damage monitoring of truss structures.

damage localization, rank-revealing QR decomposition, damage sensitivity, truss structure, structural health monitoring

The purpose of this study is to present an optimal design procedure for elasto-plastic structures subjected to impact loading. The proposed method is based on mode approximation of the displacement field and assumption of constant acceleration of impacted structure during whole time of deformation process until the plastic displacement limit is reached. Derivation of the method begins with the application of the principle of conservation of linear momentum, followed by determination of inertial forces. The final stage of the method utilizes an optimization technique in order to find a minimum weight structure. Eventually, effectiveness and usefulness of the proposed method is demonstrated on the example of a planar truss structure subjected to dynamic loading caused by a mass impacting the structure with a given initial velocity.

structural dynamics, optimal design, elasto-plastic structures, short-time dynamic loading

The paper deals with non-linear analysis of a telecommunication tower with circular flange-bolted connections (CFBCs). They are composed of two flanges, welded to the structural tubes, and then connected together with pre-tensioned bolts. A rigorous FEM analysis is performed for finding the connection stiffness in two cases. One deals with all bolts undamaged and the second one with one or more bolts broken.

The analysis, which includes contact and friction forces, shows that when joints are under tension, the bolts are not only subjected to axial forces, but also to bending moments due the prying effect. The value of stresses caused by bending depends strongly on the bolt pre-tension and flange thickness. Removing one of the six connection bolts significantly increases stresses in the remaining bolts. Knowing the behaviour of the connection, it is possible to study the behaviour of the whole structure. This is achieved by applying the multilevel substructuring approach. The first levels is related to the flanges and bolts, whereby the connection model is simplified, and compared with the rigorous one, the second level is related to the assembly of the whole tower.

The paper is illustrated with several examples of connections of different thicknesses, and different bolt pre-tensions. The considered tower comes from a real design.

Bolted flange connection, Contact forces, Friction forces, Non-linear FEM analysis, Substructuring, Telecommunication tower, Structural connection damage, Structural health monitoring

We present an efficient and robust damage localization method. Its applications therefore include defect location in shear buildings and beam structures. The proposed method is based on the knowledge of the difference of curvatures, computed for a structure before and after damage occurs. However, instead of using modal shapes for this purpose, as is frequently performed, the present method computes the curvature directly from acceleration signals, without identifying modal shapes of the structure. Additionally, the accelerations are subjected to averaging, which reduces measurement noise, and logarithm extraction, which renders the method independent of the amplitude of the loading impulse used for damage location. Another important feature of the method is that it does not require any calibration of numerical models, because it is solely based on measurement data. The presented method of damage location is illustrated with two examples, which involve experimental tests on laboratory-scale structures. The first example concerns defect location in a shear-building structure, and the second one in a spatially excited simply supported steel beam. Both cases confirm the effectiveness of the method, and its robustness to measurement noise.

degree of dispersion, transient response-based damage detection, robust damage localization, shear buildings, beam structures

This paper describes an application of wavelet analysis for damage detection of a steel frame structure with bolted connections. The wavelet coefficients of the acceleration response for the healthy and loosened connection structure were calculated at each measurement point. The difference of the wavelet coefficients of the response of the healthy and loosened connection structure is selected as an indicator of the damage. At each node of structure the norm of the difference of the wavelet coefficients matrix is then calculated. The point for which the norm has the higher value is a candidate for location of the damage. The above procedure was experimentally verified on a laboratory-scale 2-meter-long steel frame. The structure consists of 11 steel beams forming a four-bay frame, which is subjected to impact loads using a modal hammer. The accelerations are measured at 20 different locations on the frame, including joints and beam elements. Two states of the structure are considered: healthy and damaged one. The damage is introduced by means of loosening two out of three bolts at one of the frame connections. Calculating the norm of the difference of the wavelet coefficients matrix at each node the higher value was found to be at the same location where the bolts were loosened. The presented experiment showed the effectiveness of the wavelet approach to damage detection of frame structures assembled using bolted connections.

complex bolted lap connection, frame structure, wavelet analysis, damage detection

An experimental and analytical study of the relation between local defect, in a steel structure, and its higher frequencies and higher modes is discussed. The structure is a plane steel frame, assembled of beams, joined together with bolted connections. Removing some bolts from a given connection simulates the damage. In the experiment, an impulse force induced structural vibrations. Effects of vibrations were shown by data from gages, measuring accelerations with a high accuracy. From the data, it could be observed, that mode shapes, for the healthy and damaged structures didn’t show any differences for low frequencies. Only modes around thirteen showed significant gap between picks of Frequency Response Functions, for healthy and damaged frame. Moreover, looking at mode shapes, it could be observed that structural configuration may have some influence on defects to be observable. This aspect is discussed in a separate section. The experiment performed on the whole structure allows finding the place where the defect is localized. However, it can’t give detailed information on the defect itself, here defect of a bolt. For finding it, an ultrasonic measurement of pre-tensioning forces in bolts was applied. It allowed not only to determine stresses in the bolt, but also to verify, if in the process of assembling the structure was not pre-stressed.

Detectable damages, Bolted connections, Experimental modal analysis, Ultrasonic measurements, Steel frames, Analytical dynamics

In this study, a relatively simple method of discrete structural optimization with dynamic loads is presented. It is based on a tree graph, representing discrete values of the structural weight. In practical design, the number of such values may be very large. This is because they are equal to the combination numbers, arising from numbers of structural members and prefabricated elements. The starting point of the method is the weight obtained from continuous optimization, which is assumed to be the lower bound of all possible discrete weights. Applying the graph, it is possible to find a set of weights close to the continuous solution. The smallest of these values, fulfilling constraints, is assumed to be the discrete minimum weight solution. Constraints can be imposed on stresses, displacements and accelerations. The short outline of the method is presented in Sec. 2. The idea of discrete structural optimization by means of graphs. The knowledge needed to apply the method is limited to the FEM and graph representation.

discrete structural optimization, combinatorial optimization, structural dynamics, stochastic loading, problem oriented optimization, graphs

The paper is concerned with a minimum weight design of composite floors subjected to dynamic loading, deriving from the rhythmic activity of a group of people. The floor structure consists of concrete slab cast, on thick trapezoidal deck, which is supported by a grid of steel beams. The structure is vibration-prone and exhibits a number of natural frequencies, which are within a range of loading function. Minimum weight design consists in assigning, from catalogues of prefabricated plates and beams appropriate elements assuring fulfillment of imposed constraints on displacements and accelerations. Applied, practical discrete optimization method is based on graph theory and finite element analysis. Efficiency of the proposed design is demonstrated in an example of real-world engineering structure.

structural optimization, discrete optimization, structural vibrations, omposite floor structure

Many optimum structural designs are based on searching for the best of all combinations, arising from the number of structural members, and parameters of listed rolled profiles. Even, in a relatively simple design, the number of such combinations is of an order higher than ten. All known methods of finding discrete minimum of structural weight require very large number of analyses often of an order of four. In this study, are relatively simple method of solving such problems is presented. It is based on a tree graph, representing discrete values of the structural volume. The structure can be subjected to multi static loadings with constraints imposed on displacements and stresses. The number of analyses, in the proposed algorithm, is limited to the order of two. The knowledge needed to apply the method is limited to FEM and graph representation. The paper is illustrated with two examples with numbers of combinations up to 42 to the power 38.

Structural optimization, Problem oriented optimization, Discrete optimization, Combinatorial optimization, Graphs

A very simple method for finding the minimum weight of a structure designed from a list of available parameters is presented. The structure can be subjected to multiple loading conditions with constraints imposed on displacements, stresses and eigenfrequency. The method consists of a recursive removal of redundant material, starting from the heaviest structure. The number of analyses required is a factor of 10 to the power 2 less than for most stochastic methods. The knowledge needed for application of the method is limited to the finite-element method.

structural optimization, combinatorial optimization, structural dynamics

A very simple discrete optimization algorithm for minimum structural weight is presented. The main idea consists in assigning initial cross-sections to a given structure, and then searching for its least stressed elements. In the second stage of the algorithm, the cross-section of the element with minimum stress is reduced to the next catalogue entry. Such reduction of cross-sections is continued until imposed bounds are met. The presented algorithm was positively tested on example configurations with complexity of 10 to the power 10 and 30 to the power 8 combinations.

discrete optimization, truss structures

The purpose of this work is to present an algorithm for optimal vibration control of guyed masts and an example of its application to a numerical simulation. The objective of the proposed control system is to minimize amplitudes of transverse vibrations of the top of a mast induced by wind pressure acting on the structure. Control forces are assumed to be physically realized through changes of tension in guy cables, supporting the mast. The only required measurements are velocities of guy cables at the anchor-points. On the basis of those, a complete state of deformation of the structure is obtained by using the Kalman filter. The Davenport spectral density function is adopted as a model of the stochastic action of the wind.

structural vibrations, vibration control, guyed masts, wind fluctuations

In the paper two methods of real-time load identification are proposed. The first one is based on information about frequency characteristics of loading, while the second one uses only information about deformation of structure. Theoretical considerations are illustrated by numerical calculations on a example of simply supported beam.

load identification, limited number of sensors

This paper deals with the application of wavelet analysis on damage detection in mixed concrete/steel frame structures subjected to earthquake excitation. Such buildings are typically the result of a building initially constructed as a reinforced concrete building and, at a later time, more storeys were added as steel moment resisting frames. These structures consist of rein-forced concrete frames at the lower storeys and steel frames at the upper storeys. They are characterized by the material inconsistency in height. The proposed method of wavelet analysis of structural response is an output-only damage detection method. Non-linear dynamic analysis has been performed and response data at each story are obtained which are used as simulation data. Damage in the frame is due to hysteretic behaviour of columns and beams. Since the dynamic behaviour of an inelastic structure subjected to an earthquake excitation is a non-stationary process, discrete and continuous wavelet analysis were performed in order to re-trieve the simulation response data. The proposed method is based on the assumption that there is a correlation between structural damage, due to non-linear behaviour of structural elements and spikes that can be clearly detected in the wavelet details. This is supported by the fact that at the time when the spikes are recorded, structural damage occurs as well. The numerical results indicate that the discrete wavelet analysis is a promising method for the detection of damage in structures without the need for visual inspection.

Mixed concrete/steel frame, Damage detection, Discrete wavelet analysis, Continues wavelet analysis, Structural dynamics, Earthquake engineering

Recent progress in sensing technology and measurement techniques allows a growing number of critical infrastructures to be equipped with Structural Health Monitoring (SHM) systems. Sensors in such SHM systems should be placed in a proper way to facilitate extracting valuable information from the structure under investigation. In the case of relatively simple spatial truss structures, sensors can be located with the aid of classical methods such as Effective Independence (EI) method proposed by Kammer. However, in the case of large structures, which are intended to be equipped with hundreds if not thousands of sensors, other sensor placement methods may be needed.
The goal of this study is to extend a topology optimization based approach for sensor placement (proposed originally by Mariani and co-workers) to the case of real bridge structures represented by finite element models with a few thousand degrees of freedom. Structural topology optimization aims to find the optimum material distribution in order to minimize the mass of the structure while maintaining mechanical properties (load capacity, displacements, etc.). A similar concept can be used to determine the optimal placement of sensors in a structure to identify its dynamic characteristics. The sensor positions are determined in such a way that estimation error of modal coordinates is minimized. The effectiveness of the proposed methodology is demonstrated on an example of a detailed FE model of a tied-arch bridge.

Optimal sensor placement, Structural parameter identification, Topology optimization

This contribution proposes a semi-active control approach for a directed energy transfer between structural vibrational modes. The motivation is the intended localization of the vibration energy in a selected mode for the purpose of energy harvesting and mitigation of structural vibrations. The proposed control strategy aims at the instantaneous maximization of the energy transfer to the target mode. It is based on an untypical approach of dynamic structural reconfiguration and implemented using a semi-actively controllable node: a lockable joint. Such a joint, depending on the control signal, can act as a hinge or as a typical frame node. Effectively, it provides thus an on/off ability to control the transfer of bending moments between the adjacent structural elements. The effectiveness of the approach is demonstrated in a numerical example of a plane frame structure.

Modal control, Semi-active control, Lockable joints, Energy harvesting

This paper present elasto-plastic topology optimization with reliability constraint. It recalls fundamental concepts from first order reliability analysis and introduces an algorithm for topology optimization of elasto-plastic structures. The presented numerical example shows dependence of the volume fraction on probability of failure.

Structural topology optimization, Elastoplastic analysis, Reliability based optimization

The paper presents a novel method for sensor placement optimized towards effective identification of structural damages. The derivation of the method is based on the concept of virtual distortions together with information provided by a set of strain gauges. Then, a gradient oriented optimization is applied to identify sensor locations, which are the most sensitive to potential damage scenarios. Steepest descent method is utilized to determine the optimal values of the objective function. Additionally, dependence of the method on the applied excitation signal is discussed. Finally, effectiveness of the proposed methodology is demonstrated on an example of optimal search for sensor placement on a 6-bay planar truss structure.

optimal sensor placement, virtual distortion method, damage identification

Optimal topologies obtained for structures subjected to deterministic loading can be sensitive to loading variations in terms of both magnitude and direction. Therefore, in this study we consider problem of topology optimization for structures subjected to probabilistic loading. The proposed method applies basic findings from probability theory, which allow to transform the original problem of topology optimization under single probabilistic loading into analogous problem of topology optimization under multiple deterministic loading cases. After recalling the theoretical background of the method,' its effectiveness is demonstrated on an examples of cantilever structure subjected to horizontally oriented load with randomly varying angle of action.

Topology optimization, Stochastic load, Elastoplastic FE analysis

The purpose of this study is a practical engineering formulation of the topology optimization problem for three dimensional elastoplastic structures. The present study constitutes a comprehensive approach to topology optimization of elastoplastic structures, including both the mechanical problem statement and its efficient computer implementation. Instead of the traditional approach based on compliance minimization the aim of this work is to find a minimum weight structure, which is able to carry a given load while satisfying the condition that the corresponding stresses do not exceed an allowable limit. The general form of the problem is based on the classical limit design formulations of plasticity. The proposed method finds the optimal structure in an iterative way using only stress intensity distribution and does not require from the User explicit knowledge of any gradients or sensitivities. The effectiveness of the proposed methodology has been illustrated on two representative examples including simply supported and cantilever beams.

topology optimization, computational morphogenesis, elastoplastic FE analysis

This paper presents the measurement and model updating of a pedestrian's center of mass trajectory. A mathematical model proposed by the authors is updated using the actual trajectory of a pedestrian. The mathematical model is based on the principle that a human's control capability tries to maintain balance with respect to the pedestrian's center of mass (CoM), independently of the surface type. In this research, the human is considered as a mass point concentrated at CoM. The parameters of the models are updated using experimental identification of the human walking trajectory on a rigid surface. The proposed measurement technique uses a depth sensor, which enable skeletal tracking of the pedestrian walking on rigid or flexible structures. Experiments were performed using a mobile platform with the time-of-flight commercial camera Microsoft Kinect for Windows 2.0. The velocity of the mobile platform is set to maintain a 1 m separation from the pedestrian in order to provide high resolution. The results of the measurement technique allowed the identification of the human's CoM trajectory. The results of the model updating process present the probability density function of the parameters which could be used for modeling the CoM's trajectory of the pedestrian.

Human-structure interaction, Pedestrian's trajectory, Human-induced vibrations, MS Kinect sensor

We present a new human-structure interaction (HSI) model of walking on a flexible surface. A human is considered as a mass point, located at the body’s center of mass (COM). The mass moves along a predefined trajectory, which deforms together with the surface on which the human walks. The forces of motion, equal to the sum of inertial and gravitational forces acting on the mass, are transfered to the surface at prescribed foot positions. The motion of the surface is described using a few selected mode shapes, corresponding damping ratios, and natural frequencies. The equations of motion of the system are time-dependent and discontinuous. They can be written in the form of the second order differential equations of structural dynamics, but with the right-hand forcing dependent on the deformation of the surface. We present a numerical example of a human walking on a long beam structure. The motion of the beam is described by three mode shapes, representing its vertical, lateral, and torsional deflections.

Human induced vibrations, Dynamics of bridges, Human walking model

The purpose of this study is to introduce a new method of damage quantification for truss structures. Its advantage is that it can be directly applied to engineering structures without identifying modal parameters or solving a global optimization problem. The damage is localized and quantified based only on measured acceleration signals, distributed across the structure. Moreover, the method is implemented in a decentralized way rather than a centralized one; that is, for quantification of damage in a given substructure, only a small subset of sensors is considered. The method possesses higher sensitivity to damage than other frequently used methods such as Damage Locating Vectors. Validation of the method has been conducted on a numerical example and a laboratory-scale model of a truss bridge, showing its efficiency and robustness.

structural health monitoring, damage detection, truss structures

This work is focused on experimental verification of existing techniques for localization of a loosened bolted connection. To this end, a laboratory-scale 2-meter-long steel frame is used. The structure consists of 11 steel beams forming a four-bay frame, which is subjected to impact loads using a modal hammer. The accelerations are measured at 20 different locations on the frame, including joints and beam elements. Two states of the structure are considered: a healthy and a damaged one. The damage is introduced by means of loosening two out of three bolts at one of the frame connections. Experimental modal analysis reveals that the loosened bolts in the connection cause a shift only in some of the frame’s natural frequencies, while the others remain insensitive to the damage.

bolted lap connection, frame structure, experimental modal analysis, damage location

The paper deals with a nonlinear analysis of a tall tower, with Circular Flange Bolted Connections (CFBC), in which friction and contact effects are taken into account. Due to these nonlinearities, a detailed dynamic model of the whole structure would lead to very complex computational problem, unable for practical solutions. To overcome these difficulties a reduced order model of CFBC is proposed. Such a model enables the simulation of the whole tower including nonlinearities in connections. The paper is illustrated with an example of model reduction and dynamic calculations for a contemporary telecommunication tower. The tower is assembled of 4 truss segments, of triangular cross section, interconnected with CFBCs. Finally, the influence of the number of modes, included in the reduced order model, on the accuracy and computational effect, is discussed.

Reduced order modeling, Circular flange-bolted connections, Dynamic substructuring, Nonlinear contact and friction effects, Telecommunication towers

Real-time structural health monitoring is very important for truss structures especially those having large-spans. In recent years, many methods have been proposed for damage monitoring of truss structures. However, damage sensitivity of these methods is still required to be improved. In this work an efficient damage localization technique for truss structures is proposed, which is based on the LDLT decomposition of the flexibility difference matrix and the Damage Locating Vectors (DLV) method. Compared with the present Stochastic DLV (SDLV) method, the proposed method is modified in two ways. First of all, the way of calculating the damage locating vectors is modified by using LDLT decomposition instead of Singular Value Decomposition. Secondly, in order to compute the flexibility, the mass matrix which is obtained from the finite element model is used to mass-normalize mode shapes identified from ambient excitations. As a result, the proposed LDLT-DLV method has a higher sensitivity to damage for different types of truss members. The effectiveness of the proposed LDLTDLV method is validated with the numerical example of a laboratory-scale Bailey truss bridge.

Damage localization, damage localization, LDLT-DLV method, truss structure, structural health monitoring

This article presents the implementation of wireless sensors in obtaining modal parameters. The Imote2 platform is used. This is an open platform developed by Intel. The application example is a simply supported wooden plate. It explains how to use the Imote2 sensor and how to extract modal information from the raw data.

wireless sensors, modal analysis

A successful structural monitoring and control systems should be able to discern critical events, scan frequencies and dynamic ranges. This, in turn, requires that models, applied in these systems, are as close as possible to real structural behavior. Many structures, among them, electricity transmission towers, windmills, radio and TV masts, bridges and parabolic dishes, concentrating solar energy, are build as trusses. All of them are subjected dynamic loadings coming, mostly from wind gusts, water waves and thermal activity of sun. The paper is revising assumptions, commonly made for trusses. The main assumption made is that systems of rods are pin joint. Such structures don’t exist, in real engineering design. All, above, mentioned structures are made with rigid or flexible joints. The “pin joint” assumption was made for static analyses. It stated that if joint displacements caused by rod bending can be neglected, comparing with displacements caused by rod elongations, the structural system can be considered as pin joint. As it is commonly known, such cases occur when some necessary conditions joining number of joints and hinges are fulfilled. The “pin joint”, static assumptions has been, without any formal justification, taken for granted in dynamics. Simple examples presented in the paper show that “pin joint” assumption can lead to considerable errors. The paper is illustrated with two numerical examples (simple 2 bar structure and 25 bar transmission tower). Presented examples allowing to compare results of different assumptions applied for structural elements connections.

lattice structures, monitoring, control, structural dynamics

Topics considered in this paper include: dynamic properties of the mast and nonlinearities present in the problem, linearized equations governing guyed mast motion, conditions of stability, contollability and observability. Control forces are exerted by an anchored mechanism in such a way, that they change tension in guy cables. A control algorithm ensuring robust optimal control is also proposed. Finally, the paper is verified by a numerical simulation of a vibration control process.

guyed mast, vibration control

Structural safety is a critical aspect in modern engineering practice. One of the factors leading to the risk of failure is the variability of design parameters. To be able to estimate the risk of failure, this variability should be taken into account in design process. One way to tackle this issue is to assume a random nature of selected design parameters. These parameters can represent: loads acting on a structure, material properties or shape parameters. Minimizing the structural mass in the process of topology optimization is equivalent to removing the material from the initial, usually regular design space. This process can lead also to a reduction of the structural safety. Therefore, apart from deterministic constraints (such as stresses, displacements or load capacity), it is also worth to control the probabilistic ones. The purpose of this work is to introduce in topology optimization of elastoplastic structures an additional constraint on the probability of failure. Deterministic constraints, in the form of constraints on stresses, are imposed on elastoplastic analysis and utilized by the return mapping algorithm. One of the difficulties coming from the application of these random effects in the process topology optimization is its numerical complexity. Topological optimization itself is a complex issue. Adding a structural safety estimation can extend this process significantly. Fortunately, in the field of reliability analysis, which deals with determining reliability, there are methods that allow for relatively fast estimation of the probability of failure. These are First and Second Order Reliability Methods (FORM, SORM). Only several finite element iterations are sufficient to determine the probability of failure. These methods are based on the concept of the design point or the most probable point. This is the point on the limit state surface that lies closest to the mean point, and represents the most probable failure scenario. Moreover, approximation of limit state surface is linear (FORM) or quadratic (SORM). This allows to estimate quite accurately low probabilities of failure. Such a low probability of failure should characterized a safe structure. The search for a design point is based on the iterative formula developed by Rackwitz and Fiesler. The paper will present the formulation of the elasto-plastic problem of structural analysis as well as the detailed description of the algorithm for topology optimization under reliability constraint. The paper will be illustrated by examples, in which we will demonstrate, how probability of failure changes in the topological optimization process.

topology optimization, elasto-plastic structures, reliability analysis, probabilistic design

Damage identification attracted a lot of attention during the last three decades. The reason for that is the fact that large number of existing civil infrastructures reached their service life and growing number of structures is equipped with Structural Health Monitoring (SHM) systems. A successful structural damage identification is determined by three inseparably coupled factors: sensor placement, damage location and its extend, and finally location and time-frequency characteristics of the applied excitation. The purpose of this study is to address the first of the mentioned aspects, namely optimal sensor placement. A vast literature has been devoted to optimal sensor placement methods among which Effective Independence (EI) method proposed by Kammer and Tinker is one of the most successfully applied in practice. However, EI method is dedicated rather to test-analysis correlation and therefore more specific methods for damage identification are still needed. Additionally, in the case of large civil structures, which are intended to be equipped with large amount of sensors of different type, other sensor placement methods can be more efficient. Recently, a promising idea of utilizing a topology optimization approach for the purpose of sensor placement has been proposed by Bruggi and Mariani. The goal of this study is to extend their method, which has been verified on a plate structure, to the case of a FE model of a real arch bridge structure consisting a few thousands degrees of freedom. The main purpose of this work is to find the optimal arrangement of sensors on the structure to detect defects most accurately. The objective function for the problem formulated in this way is the total, weighted difference between the deformation of a damaged and undamaged state. This problem is very similar to the topological optimization, where we search for the optimal material distribution minimizing the mass of the structure while meeting the conditions related to some mechanical properties such as the maximum displacement of the structure, stress intensity or load capacity. This similarity led us to apply topological optimization to the problem of optimal placement of damage sensors. Several numerical examples prove the applicability of topological optimization for optimal sensor placement problem.

Sensor Placement, Damage Identification, Topology Optimization

W ostatnim czasie wiele prac naukowych poświęcono problemom półaktywnego sterowania drganiami układów mechanicznych. Większość tych prac jednak dotyczy zagadnienia tłumienia drgań, natomiast znacznie mniej z nich obejmuje strategie sterowania na potrzeby odzyskiwania energii z drgających układów. Celem niniejszej pracy jest opracowanie strategii półaktywnego sterowania drganiami, mającej za zadanie przenosić energię drgań wzbudzanych losowo do jednej wybranej postaci drgań własnych. Sterowanie takie realizowane jest przy pomocy dynamicznie rozłączanych węzłów konstrukcyjnych. Węzły w zależności od sygnału sterowania mogą być blokowane w celu przenoszenia momentu zginającego pomiędzy łączonym członami konstrukcji lub odblokowywane, aby pracować jak połączenie przegubowe. Prowadzone badania podstawowe mają wiele potencjalnych zastosowań. Wraz ze zmianą postaci drgań, istnieje możliwość zmiany amplitudy w miejscach, w których zainstalowany jest tłumik lub urządzenie odzyskujące energię (ang. energy-harvester). Możliwe jest również szybkie przeniesienie energii mechanicznej do postaci drgań, która nie zakłóca funkcjonalności konstrukcji lub nie powoduje jej uszkodzenia bądź zmęczenia. W porównaniu do sterowania aktywnego stosowanie sterowania półaktywnego pozwala obniżyć koszty układu, dodatkowo nie powodując destabilizacji konstrukcji [1]. Sterowanie takie może z powodzeniem znaleźć zastosowanie w konstrukcjach o wielu stopniach swobody [2]. Strategia półaktywnego sterowania z użyciem blokowalnych węzłów pierwotnie została opracowana w celu przeniesienia energii drgań do wyższych postaci własnych w celu skutecznej ich redukcji przez tłumienie materiałowe [3]. W niniejszej pracy zaprezentowany zostanie model matematyczny transferu energii oraz oparte na nim prawo sterowania. Dodatkowo przedstawiony zostanie przykład numeryczny pokazujący, że transfer energii mechanicznej jest możliwy nawet wtedy, gdy mierzone są tylko pierwsze – podstawowe – postacie drgań własnych. Prowadzone badania zostały wsparte przez Narodowe Centrum Nauki w ramach projektu Re-Conf (DEC-2017/25/B/ST8/01800).

sterowanie półaktywne, analiza modalna, blokowane węzły

The present study provides a comprehensive framework for sensor layout optimization aiming at accurate estimation of the modal coordinates coming from the structural response. The proposed procedure consists of two steps briefly described below. The first step is a selection of vibrational modes taking part in the motion of structures during their normal operation – in this case subjected to traveling load. Among these structures there are various types of bridges especially railway bridges. In the case of present study structural responses are obtained from rigorous finite element (FE) model of the bridge. The FE model is calibrated with measured response of real bridge located in Huta Zawadzka. The calibration process is based on the displacement signals of the bridge under the traveling load. In the second step modes of interest are selected and a set of candidate sensor locations is proposed. It is a subset of all degrees of freedom (DOFs) of the FE model from which several locations are chosen as best possible locations for the displacement sensors. The above sensor placement problem is a combinatorial task. Many methods for solving such problems have been developed previously, but in the case of large scale structures they require tremendous computational effort. To reduce this effort the so-called convex relaxation is incorporated into optimization process. The technique consists in reformulation of combinatorial problem into continuous convex one. Then, the convex relaxation is achieved by introducing the so-called sensor density function, which assigns a certain metric for individual candidate sensor location. Next, the value of this function is optimized in such a way that it maximize determinant of the Fisher Information Matrix. It has been shown that above algorithm is very effective and is distributing a number of sensors in several iterations only. Finally, it is worth noting that presented method can be used to distribute sensors for structural health monitoring. Moreover, it can be also applied in modal control strategies in vibration suppression.

This study is devoted to a practical method for topology optimization of elastoplastic structures subjected to stress constraints. Instead of the classical compliance minimization problem the aim of this work is to find a minimum weight structure, which is able to carry given load and the corresponding stresses do not exceed an allowable limit. The general form of the problem is based on the classical limit design formulations of plasticity. The proposed method finds optimal structure in an iterative way using only stress intensity distribution and doesn't require computing of any gradients or sensitivities. Our method starts with determining representative stresses in every quadrilateral finite element. At first an elastoplastic analysis is performed to obtain stress values in four Gaussian points, then by the use of von Misses criterion and these stress values the resultant stress is calculated. Next, having obtained stress intensity distribution within the structure we apply penalization to avoid stress concentration issues. Finally, the material is removed proportionally to the stress intensities of individual finite elements. The above mentioned procedure is repeated until limit load capacity is achieved for a given loading vector. The checkerboard problem is solved by means of design filter. Two benchmark problems have been selected as illustrative examples. They are: cantilever and simply supported beam. For these examples parametric studies on different length to height ratios and support patterns are conducted. Additionally, the results of topology optimization for different values of filter radius and penalty parameter are presented.
Finally, efficient computer implementation based on functor-oriented programming is discussed. It is demonstrated how Functor and Template-based programming can be utilized to create versatile Finite Element environment. Within this environment computation of all element matrices and loading vectors can be called in the same way, this in turn allows for implementation of effective aggregation procedure.

topology optimization, minimum-weight design, functor-oriented programming, stress constraints

The subject of this study is an efficient approach to the development of a finite element framework, which is intended to be used for solving a variety of problems in computational solid mechanics. One of such problems, recently becoming an active field of research, is topology optimization of structures made of elastic-plastic materials. For finding the optimal topology of real, practical and complex structures the knowledge of a number of numerical algorithms is required, to mention a few: modification of finite element meshes, aggregation of tangent stiffness matrices, or direct and iterative solvers. The classical computer implementation of the original Classical Optimality Criteria method (COC) of the topology optimization problem given by Bendsoe and Sigmund is relatively simple and contains 99 lines of code in the MATLAB language. However, it assumes that there exists only a single loading case, single displacement (compliance) constraint, the material is linearly elastic and the optimal topology can be found using the so-called Solid Isotropic Material with Penalization (SIMP) algorithm, which is based on the original COC method. In reality, engineers face a slightly different problem. They need to find the topology of a minimum weight structure subjected to multiple loading cases, made of an elasto-plastic material, and with a limit on stresses. The above mentioned SIMP approach may not lead to an optimal solution.

functor-oriented programming, topology optimization, elastoplastic FE analysis

The vibration attenuation problem has been solved using many different methods, some of which involve the use of advanced control algorithms. The topic of harvesting the energy of structural vibrations is less explored. For that reason, this contribution studies the problem of conversion of mechanical energy of vibrations. The paper presents a method of semi-active control, which is applied to dynamically transfer the vibration energy into a selected vibration mode. The target mode is selected in such a way that the amount of energy that can be recovered during the vibration process is maximized. In other words, switching between two modes is not intended to dissipate the energy of vibrations, but rather to maximize the energy-harvesting potential of the overall system. The concept will be illustrated using an example of a simple frame structure, in which semi-actively controlled lockable joints modify the modal properties of the structure.

semi-active control, lockable joints, energy-harvesting

Classical programming of finite elements contains usual class, which duty is not only to approximate some physical field of interest (displacements, accelerations or temperature), but also definition of matrices necessary for particular analysis. It often leads to sophisticated class hierarchy of finite elements. In our approach matrices necessary for FE analysis are in separate classes. Hierarchy of these classes can be developed almost separately from declaration of the finite element class. Also finite elements hierarchy is much smaller, because each class represents one kind of matrix computed in FE analysis. In our opinion the functor is best suited object for this kind of approach. The functor represents one subroutine and it can also be invoked as function. The study presents application of functor oriented programming to finite element analysis.

stress constrained topology optimization, finite element programming, functor-oriented implemenetation

The purpose of this study is the mechanism of the spatial movement of a human during walking. The human is considered to be a rigid body with six degrees of freedom, and its mobility is reduced by two constraints. One of the constraints is related to an assumption of constant length of the leg, foot of which is moving along given straight line. The second constraint corresponds to an assumption that human's centre of mass can move only in vertical plane. The dynamic model of the mechanism is built under above assumptions connected to the human gait kinematics. Then, kinetic energy function is derived. In the next step of the study the muscle force in the stance leg, together with its potential, is discussed. It is assumed that this force is piecewise-linear, which can be reasonably approximated by a cubic polynomial. For that purpose a smoothing procedure is proposed and finally with the aid of the Lagrange function dynamic equations for the 3D human gait are formulated. The last part of the paper is devoted to the numerical solution of obtained nonlinear equations, arising from the Lagrange procedure.

human walking, gait analysis, lagrangian dynamics

A substructuring method for the prediction of the dynamic response of footbridges subjected to loadings induced by a pedestrian is presented. The dynamic system is composed of two independent subsystems. The first one is the model of the suspension footbridge, and the second one is the model of a pedestrian. The former is obtained using the standard finite element method, while the latter is created by applying a two-step identification approach. The first step is an inverse kinematics based on an experimental human motion analysis. The second one relies on Proper Orthogonal Decomposition extracting a number of most important modes, describing the motion of the pedestrian. The presented methodology will be demonstrated by a numerical example of the pedestrian-footbridge interaction.

dynamic substructuring, human-structure interaction, suspension footbridges

A relatively simple method of finding discrete minimum structural weight is proposed. It is based on a tree graph, representing discrete values of the structural volume. In the proposed method, the number of analyses is limited to the order of two. The paper is illustrated with an example containing up to 42 to the power 38 combinations.

structural optimization, problem oriented optimization, discrete optimization, combinatorial optimization, graphs, structural static and dynamic analyses, time domain, frequency domain

The paper is illustrated with numerical examples of two bar and 25 bar tower structures. Results of different assumptions, applied to the structural elements connections are discussed.

Transmission towers, monitoring of structures

In this study, the idea of removing redundant material is enhanced by combining the continuous and discrete solutions. At the end of the paper, several numerical examples, with numbers of combinations up to 308 are presented and their effectiveness is validated.

discrete optimization, removing redundant material

The objective of this paper is a numerical simulation of vibration control of a mast supported by tendons. This problem requires knowledge from many different disciplines such as multibody dynamics, control theory and numerical methods.

vibration control, wind disturbances