Piotr Tauzowski, Ph.D., Eng.

Department of Information and Computational Science (ZIiNO)
Division of Computational Materials Science (PMKIM)
position: specialist
telephone: (+48) 22 826 12 81 ext.: 420
room: 414
e-mail: ptauzow

Doctoral thesis
2005-06-03Obiektowo-zorientowane środowisko obliczeniowe dla zagadnień mechaniki konstrukcji z zastosowaniem do analizy, optymalizacji kształtu i oceny niezawodności układów termolepkosprężystych ze zniszczeniem 
supervisor -- Prof. Michał Kleiber, Ph.D., Dr. Habil., Eng., IPPT PAN
730 
Recent publications
1.Tauzowski P., Błachowski B., Lógó J., Functor-oriented topology optimization of elasto-plastic structures, Advances in Engineering Software, ISSN: 0965-9978, DOI: 10.1016/j.advengsoft.2019.102690, Vol.135, pp.102690-1-11, 2019
Abstract:

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.

Keywords:

Topology optimization, Function object, Functor programming, Optimal design, Elasto-plastic structures, Finite element programming

Affiliations:
Tauzowski P.-IPPT PAN
Błachowski B.-IPPT PAN
Lógó J.-University of Technology and Economics (HU)
2.Tauzowski P., Lógó J., Pintér E., Parametric Study on the Element Size Effect for Optimal Topologies, Periodica Polytechnica Civil Engineering, ISSN: 0553-6626, DOI: 10.3311/PPci.11551, Vol.62, No.1, pp.267-276, 2018
3.Błachowski B., Tauzowski P., Lógó J., Modal Approximation Based Optimal Design of Dynamically Loaded Plastic Structures, Periodica Polytechnica Civil Engineering, ISSN: 0553-6626, DOI: 10.3311/PPci.11016, Vol.61, No.4, pp.987-992, 2017
Abstract:

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.

Keywords:

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

Affiliations:
Błachowski B.-IPPT PAN
Tauzowski P.-IPPT PAN
Lógó J.-University of Technology and Economics (HU)
4.Lasota R., Stocki R., Tauzowski P., Szolc T., Polynomial chaos expansion method in estimating probability distribution of rotor-shaft dynamic responses, BULLETIN OF THE POLISH ACADEMY OF SCIENCES: TECHNICAL SCIENCES, ISSN: 0239-7528, DOI: 10.1515/bpasts-2015-0047, Vol.63, No.2, pp.413-422, 2015
Abstract:

The main purpose of the study is an assessment of computational efficiency of selected numerical methods for estimation of vibrational response statistics of a large multi-bearing turbo-generator rotor-shaft system. The effective estimation of the probability distribution of structural responses is essential for robust design optimization and reliability analysis of such systems. The analyzed scatter of responses is caused by random residual unbalances as well as random stiffness and damping parameters of the journal bearings. A proper representation of these uncertain parameters leads to multidimensional stochastic models. Three estimation techniques are compared: Monte Carlo sampling, Latin hypercube sampling and the sparse polynomial chaos expansion method. Based on the estimated values of the first four statistical moments the probability density function of the maximal vibration amplitude is evaluated by the maximal entropy principle method. The method is inherently suited for an accurate representation of the probability density functions with an exponential behavior, which appears to be characteristic for the investigated rotor-shaft responses. Performing multiple numerical tests for a range of sample sizes it was found that the sparse polynomial chaos method provides the best balance between the accuracy and computational effectiveness in estimating the unknown probability distribution of the maximal vibration amplitude.

Keywords:

stochastic moment estimation, sparse polynomial chaos expansion, maximum entropy principle, rotor, uncertainties, hybrid mechanical model, random unbalance distribution

Affiliations:
Lasota R.-IPPT PAN
Stocki R.-other affiliation
Tauzowski P.-IPPT PAN
Szolc T.-IPPT PAN
5.Kowalczyk P., Rojek J., Stocki R., Bednarek T., Tauzowski P., Lasota R., Lumelskyy D., Wawrzyk K., NUMPRESS − integrated computer system for analysis and optimization of industrial sheet metal forming processes, HUTNIK - WIADOMOŚCI HUTNICZE, ISSN: 1230-3534, Vol.81, No.1, pp.56-63, 2014
Abstract:

The NUMPRESS System has been developed in IPPT PAN as a result of a project financially supported by European Regional Development Fund (within the Innovative Economy Programme) and is dedicated to small and middle enterprises dealing with sheet metal forming. The program consists of (i) an analytical module for analysis of forming processes with the finite element method, (ii) an optimization module controlling execution of the analytical module and performing optimization with respect to selected process parameters, in both deterministic and robust formulation, (iii) a reliability analysis module controlling execution of the analytical module to assess how random distribution of design parameters affects forming results, and (iv) a graphical user interface enabling communication between modules and easy definition of design parameters and optimization criteria. The analytical module consists of two independent programs up to the user's choice: NUMPRESS-Flow, a faster and less accurate program for implicit quasi-static analysis of rigid-viscoplastic shells (based on the flow approach) and NUMPRESS-Explicit, a program for explicit dynamical analysis of elastic-plastic and elastic-viscoplastic shells. Both programs are interfaced to a well-known commercial graphical pre- and postprocessor GiD. Fundamentals of formulations employed in the system and numerical examples are presented in the paper.

Keywords:

sheet metal forming, finite element method, deterministic and robust design optimization, reliability analysis

Affiliations:
Kowalczyk P.-IPPT PAN
Rojek J.-IPPT PAN
Stocki R.-IPPT PAN
Bednarek T.-IPPT PAN
Tauzowski P.-IPPT PAN
Lasota R.-IPPT PAN
Lumelskyy D.-IPPT PAN
Wawrzyk K.-IPPT PAN
6.Stocki R., Szolc T., Tauzowski P., Knabel J., Robust design optimization of the vibrating rotor shaft system subjected to selected dynamic constraints, MECHANICAL SYSTEMS AND SIGNAL PROCESSING, ISSN: 0888-3270, DOI: 10.1016/j.ymssp.2011.07.023, Vol.29, pp.34-44, 2012
Abstract:

The commonly observed nowadays tendency to weight minimization of rotor-shafts of the rotating machinery leads to a decrease of shaft bending rigidity making a risk of dangerous stress concentrations and rubbing effects more probable. Thus, a determination of the optimal balance between reducing the rotor-shaft weight and assuring its admissible bending flexibility is a major goal of this study. The random nature of residual unbalances of the rotor-shaft as well as randomness of journal-bearing stiffness have been taken into account in the framework of robust design optimization. Such a formulation of the optimization problem leads to the optimal design that combines an acceptable structural weight with the robustness with respect to uncertainties of residual unbalances – the main source of bending vibrations causing the rubbing effects. The applied robust optimization technique is based on using Latin hypercubes in scatter analysis of the vibration response. The so-called optimal Latin hypercubes are used as experimental plans for building kriging approximations of the objective and constraint functions. The proposed method has been applied for the optimization of the typical single-span rotor-shaft of the 8-stage centrifugal compressor.

Keywords:

Rotor-shaft system, Robust design optimization, Lateral vibrations, Rubbing effects, Random unbalance distribution

Affiliations:
Stocki R.-IPPT PAN
Szolc T.-IPPT PAN
Tauzowski P.-IPPT PAN
Knabel J.-IPPT PAN
7.Stocki R., Lasota R., Tauzowski P., Szolc T., Scatter assessment of rotating system vibrations due to uncertain residual unbalances and bearing properties, COMPUTER ASSISTED METHODS IN ENGINEERING AND SCIENCE, ISSN: 2299-3649, Vol.19, pp.95-120, 2012
Abstract:

The main objective of the presented study is an evaluation of the effectiveness of various methods for estimating statistics of rotor-shaft vibration responses. The computational effectiveness as well as the accuracy of statistical moment estimation are essential for efficient robust design optimization of the rotor-shaft systems. The compared methods include sampling techniques, the perturbation approach, the dimension reduction method and the polynomial chaos expansion method. For comparison, two problems of the rotor-shaft vibration analysis are considered: a typical single-span rotor-shaft of the 8-stage centrifugal compressor driven by the electric motor and a large multi-bearing rotor-shaft system of the steam turbo-generator. The most important reason for the observed scatter of the rotor-shaft vibration responses is the inherently random nature of residual unbalances as well as stiffness and damping properties of the journal bearings. A proper representation of these uncertain parameters leads to multidimensional stochastic models. It was found that methods that provide a satisfactory balance between the estimation accuracy and computational effectiveness are sampling techniques. On the other hand, methods based on Taylor series expansion in most of the analysed cases fail to approximate the rotor-shaft response statistics.

Keywords:

Scatter analysis, rotor-shaft vibrations

Affiliations:
Stocki R.-IPPT PAN
Lasota R.-IPPT PAN
Tauzowski P.-IPPT PAN
Szolc T.-IPPT PAN
8.Lógó J., Movahedi Rad M., Knabel J., Tauzowski P., Reliability based design of frames with limited residual strain energy capacity, Periodica Polytechnica Civil Engineering, ISSN: 0553-6626, Vol.55, No.1, pp.13-20, 2011
Abstract:

The aim of this paper is to create new type of plastic limit design procedures where the influence of the limited load carrying capacity of the beam-to-column connections of elasto-plastic steel (or composite) frames under multi-parameter static loading and probabilistically given conditions are taken into consideration. In addition to the plastic limit design to control the plastic behaviour of the structure, bound on the complementary strain energy of the residual forces is also applied. If the design uncertainties (manufacturing, strength, geometrical) are taken into consideration at the computation of the complementary strain energy of the residual forces the reliability based extended plastic limit design problems can be formed. Two numerical procedures are elaborated. The formulations of the problems yield to nonlinear mathematical programming which are solved by the use of sequential quadratic algorithm.

Keywords:

reliability analysis, limit analysis, residual strain energy, Monte Carlo simulation, optimal design

Affiliations:
Lógó J.-University of Technology and Economics (HU)
Movahedi Rad M.-University of Technology and Economics (HU)
Knabel J.-IPPT PAN
Tauzowski P.-IPPT PAN
9.Szolc T., Tauzowski P., Stocki R., Knabel J., Damage identification in vibrating rotor-shaft systems by efficient sampling approach, MECHANICAL SYSTEMS AND SIGNAL PROCESSING, ISSN: 0888-3270, Vol.23, pp.1615-1633, 2009
Abstract:

In the paper a stochastic method for fault detection and identification in the shafts of rotating machines is proposed. This approach is based on the Monte Carlo simulations of rotor-shaft lateral–torsional–longitudinal vibrations mutually coupled by transverse cracks of various possible and randomly selected depths and locations on the shaft. For this purpose the structural hybrid model of a real faulty object is applied. This model is characterized by a high practical reliability and great computational efficiency, so important for many hundred thousand single numerical simulations necessary for a creation of the databases applied for inverse problem solution finally leading to crack identification. These databases are created with an arbitrary assumed probability densities of crack parameters which ensures appropriate spread of the dynamic responses of the considered faulty mechanical system. A sufficiently large database determined for the investigated object enable us to estimate almost immediately, i.e. within less than 1 s, the crack depth and axial position with identification errors not exceeding 9% and 5%, respectively. Thus, the proposed method seems to be a very convenient diagnostic tool for engineering applications in the industry.

Keywords:

Rotor-shaft system, Dynamic diagnostics, Crack identification, Monte Carlo simulation, Coupled vibration analysis

Affiliations:
Szolc T.-IPPT PAN
Tauzowski P.-IPPT PAN
Stocki R.-IPPT PAN
Knabel J.-IPPT PAN
10.Szolc T., Tauzowski P., Knabel J., Stocki R., Nonlinear and parametric coupled vibrations of the rotor-shaft system as fault identification symptom using stochastic methods, NONLINEAR DYNAMICS, ISSN: 0924-090X, Vol.57, pp.533-557, 2009
Abstract:

In the paper several stochastic methods for detection and identification of cracks in the shafts of rotating machines are proposed. All these methods are based on the Monte Carlo simulations of the rotor-shaft lateral-torsional-longitudinal vibrations mutually coupled by transverse cracks of randomly selected depths and locations on the shaft. For this purpose there is applied a structural hybrid model of a real cracked rotor-shaft. This model is characterized by a high practical reliability and great computational effi-ciency, so important for hundreds of thousands numerical simulations necessary to build databases used in solving the inverse problem, i.e. crack parameter identifications. In order to ensure a good identification accuracy, for creating the Monte Carlo samples of data points there are proposed special probability density functions for locations and depths of the crack. Such an approach helps in enhancing databases corresponding to the most probable faults of the rotor-shaft system of the considered rotor machine. In the presentedstudy six different database sizes are considered to compare identification efficiency and accuracy of considered methods. A sufficiently large database enables us to estimate almost immediately (usually in less than one second) the crack parameters with precision that is in most of the cases acceptable in practice. Then, as a next stage, one of the proposed fast improvement algorithms can be applied to refine identification results in a reasonable time. The proposed methods seem to provide very convenient diagnostic tools for industrial applications.

Keywords:

Crack rotor dynamics, Nonlinear and parametric vibrations, Hybrid modeling, Monte Carlo simulation, Crack identification methods

Affiliations:
Szolc T.-IPPT PAN
Tauzowski P.-IPPT PAN
Knabel J.-IPPT PAN
Stocki R.-IPPT PAN
11.Stocki R., Kolanek K., Knabel J., Tauzowski P., FE based structural reliability analysis using STAND environment, COMPUTER ASSISTED METHODS IN ENGINEERING AND SCIENCE, ISSN: 2299-3649, Vol.16, pp.35-58, 2009
Abstract:

An assessment of structural reliability requires multiple evaluations of the limit state function for various realizations of random parameters of the structural system. In the majority of industrial applications the limit state functions cannot be expressed explicitly in terms of the random parameters but they are specified using selected outcomes of the FE analysis. In consequence, in order to be useful in practice, a structural reliability analysis program should be closely integrated with a FE module or it should be interfaced with an advanced external FE program. When the FE source code is not available, which is usually the case, the only option is to establish a communication between the reliability analysis program and an external FE software through the batch mechanism of data modification, job submission and results extraction. The main subject of this article is to present the reliability analysis capabilities of STAND software, which is being developed in the Institute of Fundamental Tech no logical Research of Polish Academy of Sciences. A special emphasis is put on the issues related to it s interfacing with external general purpose FE codes. It is shown that when shape type random variables are used, leading to modifications of the FE mesh, or when the limit state function contains numerical noise, standard algorithms for localizing the design point often fail to converge and a special method based on some response surface approximation is needed. A proposition of such a strategy that employs an adaptive response surface approximation of the limit state function is presented in this article. Development of a reliability analysis program is a challenging project and calls for such a code organization, which would facilitate a simultaneous work of many programmers and allow for easy maintenance and modifications. The so-called object-oriented programming seems to provide a convenient framework to realize these objectives. The object-oriented approach is used in STAND development. The advantages of this programming paradigm and a short description of the STAND’s class hierarchy are presented in the text. The study is concluded with two numerical examples of interfacing STAND with state of the art commercial FE programs.

Keywords:

Reliability, optimization software

Affiliations:
Stocki R.-IPPT PAN
Kolanek K.-IPPT PAN
Knabel J.-IPPT PAN
Tauzowski P.-IPPT PAN
12.Movahedi Rad M., Lógó J., Knabel J., Tauzowski P., Reliability based limit design of frames with limited residual strain energy capacity, Proceedings in Applied Mathematics and Mechanics, ISSN: 1617-7061, DOI: 10.1002/pamm.200910323, Vol.9, pp.709-710, 2009
Abstract:

The aim of this paper is to take into consideration the influence of the limited load carrying capacity of the connections on the plastic limit state of elasto-plastic steel (or composite) framed structures under multi-parameter stochastic loading and probabilistically given conditions. In addition to the plastic limit design to control the plastic behaviour of the structure, bound on the complementary strain energy of the residual forces is also applied. This bound has significant effect for the load parameter. If the design uncertainties (manufacturing, strength, geometrical) are expressed by the calculation of the complementary strain energy of the residual forces a reliability based extended limit design problem is formed. The formulations of the problems yield to nonlinear mathematical programming which are solved by the use of sequential quadratic algorithm. The bi-level optimization procedure governed by the reliability index calculation.

Keywords:

limit analysis of frames, reliability analysis, optimization

Affiliations:
Movahedi Rad M.-University of Technology and Economics (HU)
Lógó J.-University of Technology and Economics (HU)
Knabel J.-IPPT PAN
Tauzowski P.-IPPT PAN
13.Stocki R., Tauzowski P., Knabel J., Reliability analysis of a crashed thin-walled s-rail accounting for random spot weld failures, INTERNATIONAL JOURNAL OF CRASHWORTHINESS, ISSN: 1358-8265, DOI: 10.1080/13588260802055213, Vol.13, No.6, pp.693-706, 2008
Abstract:

Possibly the most common application of spot welding is in the automobile manufacturing industry, where it is almost universally used to weld the sheet-metal car components. However, due to manufacturing inaccuracies and fatigue failures an important number of spot welds may be missing in an operational vehicle. It seems that to properly analyse the reliability of such structures, in particular crashworthiness reliability, the spot weld failures must be considered. Representing properties of each spot weld in a stochastic model by corresponding random variables is extremely inefficient. Therefore, in this article an approach is proposed for handling spot-weld defects in the reliability analysis by accounting for their averaged influence on a failure criterion. The approach consists of the appropriate treatment of a random noise component of the limit state function. The noise results from the strategy of deleting a certain number of randomly selected spot-weld elements from the finite element model each time the limit state function value is computed.

Dealing with noisy limit state functions in structural reliability analysis is a challenging task. The only method that seems to be insensitive to this phenomenon is Monte Carlo sampling, which for most of the applications of practical interest is prohibitively expensive. Having this in mind, a method based on the algorithm proposed by Zou et al. and published in the journal of Reliability Engineering and System Safety in 2002 is investigated in this article. The method combines the best features of the first-order reliability method, the response surface technique and the importance sampling method to achieve both accuracy and efficiency. A detailed study on the reliability of thin-walled s-rail subjected to crash is performed. Some suggestions concerning the modification of the original algorithm are proposed.

Keywords:

crashworthiness reliability, response surface approximation, adaptive importance sampling, spot weld failures

Affiliations:
Stocki R.-IPPT PAN
Tauzowski P.-IPPT PAN
Knabel J.-IPPT PAN
14.Tauzowski P., Kleiber M., Parameter and shape sensitivity of thermo-viscoelastic response, COMPUTERS AND STRUCTURES, ISSN: 0045-7949, DOI: 10.1016/j.compstruc.2005.09.026, Vol.84, pp.385-399, 2006
Abstract:

Gradient-based optimization methods are still most efficient methods for solving structural optimization problems. The sensitivity formulation has been one of the central issues in the gradient-based optimization algorithm. Thermo-viscoelastic constitutive and parameter sensitivity formulation are presented in this paper. The model considered is composed of two coupled subproblems: the transient heat transfer problem and a rheological, viscoelastic material model known in literature as the standard model. Design variables considered are with material and shape-defining parameters. The investigation includes a finite element formulation and implementation in an object-oriented finite element environment. Results of numerical analysis are presented.

Keywords:

Finite element method, Sensitivity analysis, Viscoelasticity

Affiliations:
Tauzowski P.-IPPT PAN
Kleiber M.-IPPT PAN

List of recent monographs
1.
104
Tauzowski P., Obiektowo-zorientowane środowisko obliczeniowe dla zagadnień mechaniki konstrukcji, Rozprawa doktorska, IPPT Reports on Fundamental Technological Research, 3, pp.1-136, 2005
List of chapters in recent monographs
1.
163
Szolc T., Tauzowski P., Stocki R., Knabel J., Knowledge acquisition for hybrid systems of risk assessment and critical machinery diagnosis, rozdział: Stochastic approach of crack parameters identification of rotor shaft machines be means of Monte Carlo sampling, Silesian University of Technology (Gliwice), Moczulski W., Ciupke K. (Eds.), pp.161-178, 2008
2.
164
Stocki R., Tauzowski P., Knabel J., Szolc T., Knowledge acquisition for hybrid systems of risk assessment and critical machinery diagnosis, rozdział: Identification methods of crack parameters of rotor shaft machines monitored on-line applied to analysis of steam turbogenerator, Silesian University of Technology (Gliwice), Moczulski W., Ciupke K. (Eds.), pp.179-192, 2008

Conference papers
1.Błachowski B., Tauzowski P., Świercz A., Jankowski Ł., Topology optimization approach for dense sensor network distribution over large bridge structures, SMART 2019, 9th ECCOMAS Thematic Conference on Smart Structures and Materials, 2019-07-08/07-11, Paris (FR), pp.284-290, 2019
Abstract:

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.

Keywords:

Optimal sensor placement, Structural parameter identification, Topology optimization

Affiliations:
Błachowski B.-IPPT PAN
Tauzowski P.-IPPT PAN
Świercz A.-IPPT PAN
Jankowski Ł.-IPPT PAN
2.Logo J., Tauzowski P., Błachowski B., Reliability based elasto-plastic topology optimization, WCSMO-13, 13th World Congress of Structural and Multidisciplinary Optimization, 2019-05-20/05-24, Beijing (CN), No.A210492, pp.1-6, 2019
Abstract:

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.

Keywords:

Structural topology optimization, Elastoplastic analysis, Reliability based optimization

Affiliations:
Logo J.-other affiliation
Tauzowski P.-IPPT PAN
Błachowski B.-IPPT PAN
3.Blachowski B., Tauzowski P., Lógó J., Elasto-Plastic Topology Optimization Under Stochastic Loading Conditions, EngOpt, 6th International Conference on Engineering Optimization, 2018-09-17/09-19, Lizbona (PT), DOI: 10.1007/978-3-319-97773-7_7, pp.70-79, 2018
Abstract:

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.

Keywords:

Topology optimization, Stochastic load, Elastoplastic FE analysis

Affiliations:
Blachowski B.-IPPT PAN
Tauzowski P.-IPPT PAN
Lógó J.-University of Technology and Economics (HU)
4.Błachowski B., Tauzowski P., Logo J., Stress intensity driven topology optimization for morphogenesis of 3d elastoplastic structures, LSCE 2018, XXIV LIGHTWEIGHT STRUCTURES in CIVIL ENGINEERING - International Seminar Organized by Polish Chapters of International Association for Shell and Spatial Structures (IASS), 2018-12-07/12-07, Łódź (PL), pp.22-26, 2018
Abstract:

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.

Keywords:

topology optimization, computational morphogenesis, elastoplastic FE analysis

Affiliations:
Błachowski B.-IPPT PAN
Tauzowski P.-IPPT PAN
Logo J.-other affiliation
5.Stocki R., Szolc T., Tauzowski P., Knabel J., Robust design optimization of the vibrating rotor shaft system subjected to rubbing constraints, IFToMM, 8th International Conference on Rotor Dynamics, 2010-09-12/09-15, Seoul (KR), pp.1022-1029, 2010
Abstract:

The commonly observed nowadays tendency to weight minimization of rotor-shafts of the rotating machinery leads to a decrease of shaft bending rigidity making a risk of dangerous stress concentrations and rubbing effects more probable. Thus, a determination of the optimal balance between reducing the rotor-shaft weight and assuring its admissible bending flexibility is a major goal of this study. The random nature of residual unbalances of the rotor-shaft as well as randomness of journal bearing stiffness have been taken into account in the framework of robust design optimization. Such a formulation of the optimization problem leads to the optimal design that combines an acceptable structural weight with the robustness with respect to uncertainties of residual unbalances, the main source of bending vibrations causing the rubbing effects. The applied robust optimization technique is based on using Latin hypercubes in scatter analysis of the vibration response. The so-called optimal Latin hypercubes are used as experimental plans for building kriging approximations of the objective and constraint functions. The proposed method has been applied for the optimization of the typical single-span rotor-shaft of the 8-stage centrifugal compressor.

Keywords:

Rotor-shaft system, robust design optimization, lateral vibrations, rubbing effects, random unbalance distribution

Affiliations:
Stocki R.-IPPT PAN
Szolc T.-IPPT PAN
Tauzowski P.-IPPT PAN
Knabel J.-IPPT PAN

Conference abstracts
1.Logo J., Tauzowski P., Blachowski B., Topology optimization of elastoplastic structures under reliability constraints: A first order approach, CIVIL-COMP-OPTI 2019, Fifth International Conference on Soft Computing & Optimisation in Civil, Structural and Environmental Engineering, 2019-09-16/09-19, Riva del Garda (IT), pp.1-3, 2019
Abstract:

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.

Keywords:

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

Affiliations:
Logo J.-other affiliation
Tauzowski P.-IPPT PAN
Blachowski B.-IPPT PAN
2.Błachowski B., Tauzowski P., Świercz A., Jankowski Ł., Sensor placement for structural damage identification by means of topology optimization, PCM-CMM, 4th Polish Congress of Mechanics, 23rd International Conference on Computer Methods in Mechanics, 2019-09-08/09-12, Kraków (PL), pp.1, 2019
Abstract:

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.

Keywords:

Sensor Placement, Damage Identification, Topology Optimization

Affiliations:
Błachowski B.-IPPT PAN
Tauzowski P.-IPPT PAN
Świercz A.-IPPT PAN
Jankowski Ł.-IPPT PAN
3.Ostrowski M., Świercz A., Błachowski B., Tauzowski P., Jankowski Ł., Optimization of Sensor Placement Using Continuous Approaches, WEO2019, Workshop on Engineering Optimization 2019, 2019-11-04/11-04, Warszawa (PL), pp.22-23, 2019
Abstract:

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.

Affiliations:
Ostrowski M.-IPPT PAN
Świercz A.-IPPT PAN
Błachowski B.-IPPT PAN
Tauzowski P.-IPPT PAN
Jankowski Ł.-IPPT PAN
4.Blachowski B., Tauzowski P., Logo J., Topology optimization of elastoplastic structures: Stress intensity driven formulation and functor-oriented implementation, CST2018, 13th International Conference on Computational Structures Technology, 2018-09-04/09-06, Barcelona (ES), No.0090, pp.1-3, 2018
Abstract:

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.

Keywords:

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

Affiliations:
Blachowski B.-IPPT PAN
Tauzowski P.-IPPT PAN
Logo J.-University of Technology and Economics (HU)
5.Tauzowski P., Blachowski B., Lógó J., Functor-Oriented Finite Element Programming with Application to Structural Topology Optimization, SolMech 2018, 41st SOLID MECHANICS CONFERENCE, 2018-08-27/08-31, Warszawa (PL), No.P076, pp.490-491, 2018
Abstract:

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.

Keywords:

functor-oriented programming, topology optimization, elastoplastic FE analysis

Affiliations:
Tauzowski P.-IPPT PAN
Blachowski B.-IPPT PAN
Lógó J.-University of Technology and Economics (HU)
6.Tauzowski P., Błachowski B., Logo J., Stress constrained structural topology optimization with functor-oriented finite element implementation, Workshop on Semidefinite Programming: Theory and Applications, 2018-10-19/10-19, Edinburgh (GB), pp.1, 2018
Abstract:

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.

Keywords:

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

Affiliations:
Tauzowski P.-IPPT PAN
Błachowski B.-IPPT PAN
Logo J.-other affiliation
7.Dłużewski P., Wierzbicki R., Tauzowski P., Kret S., Kaleta A., Sadowski J., 3D strain field and STEM contrast modeling of core shell nanowirers containing magnetic nanoprecipitations, EUROMAT 2017 , European Congress and Exhibition on Advanced Materials and Processes, 2017-09-17/09-22, Thessaloniki (GR), pp.1, 2017
8.Dłużewski P., Maździarz M., Tauzowski P., Constitutive and FE modeling of Residual Stresses and Kirkendall Effect in Semiconductor Structures, 4th International Conference on Material Modeling, 2015-05-27/05-29, Berkeley (US), pp.79-80, 2015
Abstract:

The interdiffusion of chemical components coupled with vacancy movement can cause void formation and/or spinodal decomposition in crystal growth. In the case of SiC growth on Si, the higher mobility of Si atoms compared to C results in the migration of SiC/Si interface and formation of voids in the substrate in some thermodynamic conditions. In the case of In -rich InGaN layers deposited on GaN a precipitation of metallic indium bordering with voids is observed. In the current approach we consider interdiffusion, lattice distortion and chemical maps extracted from HRTEM images of SiC/Si and InGaN/GaN. Dislocations and void surface are treated as local regions of nucleation and annihilation of the vacancies transporting the mass in FE mesh. In result, the interface and FE mesh are convected with the crystal lattice drift. In the constitutive modeling applied [1] the lattice strain and the atom fraction of chemical component are used as two independent thermodynamic variables. Due to climbing of misfit dislocations the plastic distortion tensor field is taken into account in the form of additional nodal variables. This tensor field is spanned on corner nodes of Lagrangian finite elements (FE) which gives the possibility for reconstruction of the atomistic model of dislocation network interpenetrating the considered FE mesh [2,3]. The chemo-mechanical coupling is based on the use of Vegard's law formulated in terms of Biot strain. Due to the logarithmic strain applied in hyperelastic modeling, some transformation rule is considered for Vegard's law. This rule allowed us to eliminate artificial residual stresses yielding from incompatibe fields of the atom fraction and plastic distortions spanned on nodes by means of shape functions [2]. In the case of single finite elements, the mentioned approach allowed us to reduce spurious stresses in integration points from the level 100 MPa to 10^ -5 MPa, while at the same time holding the stress components yielding from Vegard's law at the level of 1 GPa (relaxed by plastic distortions).

Keywords:

Constitutive modelling, Finite Element Method

Affiliations:
Dłużewski P.-IPPT PAN
Maździarz M.-IPPT PAN
Tauzowski P.-IPPT PAN
9.Dłużewski P., Tauzowski P., The FE modelling of residual stresses and void formation observed during the growth of semiconductor layers, PCM-CMM 2015, 3rd Polish Congress of Mechanics and 21st Computer Methods in Mechanics, 2015-09-08/09-11, Gdańsk (PL), pp.553-554, 2015
Abstract:

In the current approach we consider interdiffusion, lattice distortions and chemical maps corresponding the growth of SiC/Si and In- GaN/GaN layers. Dislocations and free surfaces are treated as local regions for nucleation and annihilation of the vacancies transporting the mass between finite elements (FEs). In result, the interface and FE mesh are convected with the crystal lattice drift. In the constitutive modelling applied [1] the lattice distortion and the Si and vacancy molar fractions are used as independent nodal variables. Due to the climbing down of misfit dislocations the plastic distortion tensor field is taken into account in the form of additional nodal variables. This tensor field is spanned on corner nodes of the second order Lagrangian finite elements [2]. The chemo-mechanical coupling is based on the use of Vegard’s law formulated alternatively in terms of Biot or Hencky strains. Due to the logarithmic strain applied in hyperelastic modelling, some transformation rule is considered for Vegard’s law. This rule allowed us to eliminate artificial residual stresses yielding from incompatibility of the fields of atom fraction and plastic distortions spanned by means of the same shape functions on the corner nodes.

Keywords:

residual stresses, Kirkendall effect, diffusion, mass transport, semiconductor layers, crystal growth

Affiliations:
Dłużewski P.-IPPT PAN
Tauzowski P.-IPPT PAN
10.Kowalczyk P., Rojek J., Stocki R., Bednarek T., Tauzowski P., Lasota R., Lumelskyy D., Wawrzyk K., NUMPRESS – integrated computer system for analysis and optimization of industrial sheet metal forming processes: examples of use, AutoMetForm/SFU 2014, New Materials for Vehicle Components, 2014-11-03/11-05, Freiburg (DE), pp.284-286, 2014
Abstract:

This paper presents NUMPRESS System that has been developed in IPPT PAN as a result of a project financially supported by European Regional Development Fund (within the Innovative Economy Programme) and is dedicated to small and middle enterprises dealing with sheet metal forming. It seems undoubted that efficient design of an industrial sheet forming process requires reliable computer simulations and a tool for numerical optimization of the process parameters. It has to be also admitted that. among small and medium enterprises (SME) in this industrial branch, there are many who do not use any such numerical tools in their practice.
Computer simulation of sheet metal forming processes is a very specific branch of computational mechanics. Finite element systems dedicated strictly to this kind of processes are needed and actually present on the market. Commercial systems (like Autoform, PAM-Stamp, Stampack, etc.) are, due to their prices, usually beyond financial ability of SME.

Design of the drawing process and tools, i.e. choice of proper values of several design parameters, require efficient optimization strategy. In this process, random character of at least some of the parameters has to be taken into account. In view of this fact, the traditional, deterministic approach to optimization is insufficient and elements of robust design optimization techniques and reliability analysis have to be included in the formulation of the optimization problem. It has to be admitted that, even if some of the mentioned commercial simulation systems offer numerical optimization modules, not all of them reach beyond the deterministic concept of the optimization process.

Keywords:

sheet metal forming, finite element method, deterministic and robust design optimization, reliability analysis

Affiliations:
Kowalczyk P.-IPPT PAN
Rojek J.-IPPT PAN
Stocki R.-IPPT PAN
Bednarek T.-IPPT PAN
Tauzowski P.-IPPT PAN
Lasota R.-IPPT PAN
Lumelskyy D.-IPPT PAN
Wawrzyk K.-IPPT PAN
11.Kowalczyk P., Rojek J., Stocki R., Bednarek T., Tauzowski P., Lasota R., Lumelskyy D., Wawrzyk K., NUMPRESS – integrated computer system for analysis and optimization of industrial sheet metal forming processes: numerical investigation of square cup drawing, SolMech 2014, 39th Solid Mechanics Conference, 2014-09-01/09-05, Zakopane (PL), pp.237-238, 2014
Abstract:

This paper presents basic features of the NUMPRESS system and some examples ofuse. The system has been developed at IPPT PAN as a result of a project financially supported by European Regional Development Fund and is dedicated to small and middle enterprises (SME) dealing with sheet metal forming. The program consists of (i) an analytical finite element method module (ii) an optimization module, (iii) a reliability analysis module, and (iv) a graphical user interface enabling communication between modules. The analytical module consists of two independent programs up to the user’s choice: NUMPRESS-Flow, a faster and less accurate program for implicit quasi-static analysis of rigid-viscoplastic shells (based on the flow approach) and NUMPRESS-Explicit, a program for explicit dynamical analysis of elastic-plastic shells. Both programs are interfaced to a well-known commercial graphical pre-and postprocessor GiD.

Keywords:

sheet metal forming, finite element method, deterministic and robust design optimization, reliability analysis

Affiliations:
Kowalczyk P.-IPPT PAN
Rojek J.-IPPT PAN
Stocki R.-IPPT PAN
Bednarek T.-IPPT PAN
Tauzowski P.-IPPT PAN
Lasota R.-IPPT PAN
Lumelskyy D.-IPPT PAN
Wawrzyk K.-IPPT PAN
12.Dłużewski P., Maździarz M., Tauzowski P., Third-order elastic coefficients and logarithmic strain in finite element modelling of anisotropic elasticity, SolMech 2014, 39th Solid Mechanics Conference, 2014-09-01/09-05, Zakopane (PL), pp.35-36, 2014
Abstract:

Contrary to higher order elastic constants for momentum stresses the second (classical) and third-order elastic coefficients (TOEC) for symmetric elasticity are measured and tabulated successfully with good accuracy for tens of years. In the classical experimental measurements of TOEC, the correct recalculation of instantaneous stiffness changes onto TOEC has an important role. A similar problem arises in the constitutive and finite element (FE) modelling. Namely, because of a very strong dependency of TOEC on the strain measure choice, the constitutive and FE modelling of elastic materials is considered here in terms of different finite strain measures. To this aim, the known analytical formulae for calculation of two first derivatives of the isotropic tensor function of tensor variable are verified by means of the finite difference method. In result, the revised formulae are used for calculation of the tangent stiffness matrix. This paper closes with some remarks on the use of TOEC in finite element modelling.

Keywords:

nonlinear elasticity, third-order elastic coefficients, logarithmic strain

Affiliations:
Dłużewski P.-IPPT PAN
Maździarz M.-IPPT PAN
Tauzowski P.-IPPT PAN
13.Rojek J., Stocki R., Lasota R., Tauzowski P., Efficient reliability analysis of sheet metal forming processes accounting for forming limit curve uncertainty, CMM 2013, 20th International Conference on Computer Methods in Mechanics, 2013-08-27/08-31, Poznań (PL), No.MS05, pp.35-36, 2013
Abstract:

The failure probability estimation of FEM simulated sheet metal forming process is a computationally challenging task. The application of efficient gradient-based reliability techniques is very much limited due to the numerical noise introduced by the explicit dynamic algorithm used to perform the sheet stamping analysis and by the nonlinearity of the failure function. To cope with this difficulty, in the current study a two stage metamodel-based adaptive importance sampling method is employed. In order to assess the reliability of sheet metal forming operations the stochastic character of such parameters as friction, blankholding force, blank thickness, strain hardening parameters of the constitutive law as well as parameters defining the forming limit curve (FLC) are considered. Using the numerical example of a square cup deep drawing, the benchmark problem of the Numisheet’93 conference, it is investigated how the assumptions concerning the probabilistic distribution of the FLC location parameter affect the probability of sheet metal fracture.

Keywords:

Reliability, Metal forming

Affiliations:
Rojek J.-IPPT PAN
Stocki R.-IPPT PAN
Lasota R.-IPPT PAN
Tauzowski P.-IPPT PAN
14.Dłużewski P., Cholewiński J., Maździarz M., Tauzowski P., Nalepka K.T., Atomistic/continuum reconstruction of misfit dislocations and stacking faults in Cu/sapphire interfacial region, CMM 2011, 19th International Conference on Computer Methods in Mechanics, 2011-05-09/05-12, Warszawa (PL), pp.257-1-2, 2011
Abstract:

A method for reconstruction of atomistic models of dislocations and stacking faults in the interfacial region of heterostructures is presented. Its mathematical foundations come back to the algebra of the finite deformation fields related to introducing of discrete dislocations into an initially coherent interface. From the practical point of view the method concerns generation of interfacial regions with misfit/treading partial dislocations and stacking faults being formed in the interfacial region between crystal structures of different crystallographic type.

Keywords:

atomistic models, dislocations, stacking faults, lattice distortion

Affiliations:
Dłużewski P.-IPPT PAN
Cholewiński J.-IPPT PAN
Maździarz M.-IPPT PAN
Tauzowski P.-IPPT PAN
Nalepka K.T.-IPPT PAN
15.Stocki R., Lasota R., Tauzowski P., Szolc T., Scatter assessment of rotor-shaft vibration responses due to uncertain residual unbalances and bearing properties, CMM 2011, 19th International Conference on Computer Methods in Mechanics, 2011-05-09/05-12, Warszawa (PL), pp.056-1-2, 2011
Abstract:

The main objective of the presented study is an evaluation of the effectiveness of various methods for estimating statistics of rotor-shaft vibration responses. The computational effectiveness as well as the accuracy of statistical moment estimation are essential for efficient robust design optimization of the rotor-shaft systems. The most important sources of the observed response scatter are inherently random rotor-shaft residual unbalances as well as stiffness and damping properties of the journal bearings. A relevant representation of these parameters leads to multidimensional stochastic models. The compared stochastic moment estimation methods include sampling techniques, the dimension reduction method and the polynomial chaos expansion method. Two problems of the rotor-shaft vibration analysis are considered: a typical single-span rotor-shaft of the 8-stage centrifugal compressor driven by the electric motor and a large multi-bearing rotor-shaft system of the steam turbogenerator. It is shown that methods that provide a satisfactory balance between the estimation accuracy and computational effectiveness are sampling techniques. Methods employing polynomial chaos expansion perform well in the case of reduced stochastic models. On the other hand, low accuracy of the methods based on Taylor series expansion very often renders these techniques unsuitable for the robust design optimization of vibrating rotor shafts.

Keywords:

ibrations, robustness, numerical analysis, stochastic phenomena

Affiliations:
Stocki R.-IPPT PAN
Lasota R.-IPPT PAN
Tauzowski P.-IPPT PAN
Szolc T.-IPPT PAN