Partner: Prof. Ryszard Buczkowski, Ph.D., Dr. Habil., Eng.

West Pomeranian University of Technology Szczecin (PL)

Habilitation thesis
2000Statistical modelling of rough surfaces and finite element contact analysis 
Recent publications
1.Taczała M., Buczkowski R., Kleiber M., Nonlinear buckling and post-buckling response of stiffened FGM plates in thermal environments, COMPOSITES PART B-ENGINEERING, ISSN: 1359-8368, DOI: 10.1016/j.compositesb.2016.09.023, Vol.109, pp.238-247, 2017
Abstract:

We present a nonlinear finite element method to investigate the nonlinear stability of stiffened functionally graded materials (FGM) plates considered as a whole unit. The plates are subjected to mechanical and thermal loads. The material properties are assumed to be temperature dependent and varied gradually across the thickness according to a power law distribution. The nonlinear equations of FGM plates are based on the first-order shear order plate theory. The influence of material, geometrical properties of stiffeners and initial deflections on the buckling and post-buckling response of the stiffened plates are studied in detail. Including the latest information no work has been oriented towards post-buckling analysis of stiffened FGM plates considered as a whole unit.

Keywords:

FGM stiffened plate, nonlinear finite element analysis, post-buckling

Affiliations:
Taczała M.-West Pomeranian University of Technology Szczecin (PL)
Buczkowski R.-West Pomeranian University of Technology Szczecin (PL)
Kleiber M.-IPPT PAN
2.Taczała M., Buczkowski R., Kleiber M., Nonlinear free vibration of pre- and post-buckled FGM plates on two-parameter foundation in the thermal environment, COMPOSITE STRUCTURES, ISSN: 0263-8223, DOI: 10.1016/j.compstruct.2015.11.017, Vol.137, pp.85-92, 2016
Abstract:

The geometrically nonlinear free vibration of functionally graded thick plates resting on the elastic Pasternak foundation is investigated. The motion equations are derived applying the Hamilton principle. We consider the first order shear deformation plate theory (FSDT), in which the modified shear correction factor is required. A 16-noded Mindlin plate element of the Lagrange family which is free from shear locking due to small thickness of the plate used. The material properties are assumed to be temperature-dependent and expressed as a nonlinear function of temperature. Because the FGM plates are not homogeneous, the basic equations are calculated in the equivalent physical neutral surface which differs from the geometric mid-plane. In the pre-buckling range natural frequencies decrease ultimately reaching zero for critical stress in the bifurcation point.

Keywords:

FGM plates, Two-parameter elastic foundation, Nonlinear free vibration, Finite element method

Affiliations:
Taczała M.-West Pomeranian University of Technology Szczecin (PL)
Buczkowski R.-West Pomeranian University of Technology Szczecin (PL)
Kleiber M.-IPPT PAN
3.Buczkowski R., Kleiber M., A study of the surface roughness in elasto-plastic shrink fitted joint, TRIBOLOGY INTERNATIONAL, ISSN: 0301-679X, DOI: 10.1016/j.triboint.2016.02.021, Vol.98, pp.125-132, 2016
Abstract:

The aim of the present study is to provide a methodology for improving the design of a shrink-fitted assembly by focusing on two objectives: (i) taking into account the surface roughness of components, (ii) introducing a non-classical hardening friction law in which tangential micro-slip displacements are considered. The calculations have been made for elasto-plastic properties of component in axisymmetric conditions. Both the loading and unloading processes have been considered. After finite element simulations, it is observed that overall static behaviour of the assembly is influenced considerably by the surface finish of the mating components. The current numerical results of the shrink fitted assembly received from the coarse mesh could be treated as contact benchmark for further finite element analyses using as closely as possible identical input data.

Keywords:

Shrink-fit, Roughness, Finite elements, Elasto-plasticity

Affiliations:
Buczkowski R.-West Pomeranian University of Technology Szczecin (PL)
Kleiber M.-IPPT PAN
4.Taczała M., Buczkowski R., Kleiber M., Postbuckling analysis of functionally graded plates on an elastic foundation, COMPOSITE STRUCTURES, ISSN: 0263-8223, DOI: 10.1016/j.compstruct.2015.06.055, Vol.132, pp.842-847, 2015
Abstract:

First, we discuss characteristics of functionally graded materials and describe methods of their manufacturing. Then, we provide an overview of analytical and numerical methods for calculating plates, with characteristics of functionally graded materials, resting on elastic foundation. The presented numerical results have been obtained by the finite elements method, referring to post-bifurcation problems of thermally loaded plates. The first-order shear deformation theory (FSDT) has been employed. In numerical calculations we have used a new 16-node plate element, free of problems related to shear locking.

Keywords:

Thick plates, Functionally graded materials, Finite elements method

Affiliations:
Taczała M.-West Pomeranian University of Technology Szczecin (PL)
Buczkowski R.-West Pomeranian University of Technology Szczecin (PL)
Kleiber M.-IPPT PAN
5.Buczkowski R., Taczała M., Kleiber M., A 16-node locking-free Mindlin plate resting on two-parameter elastic foundation - static and eigenvalue analysis, COMPUTER ASSISTED METHODS IN ENGINEERING AND SCIENCE, ISSN: 2299-3649, Vol.22, pp.99-114, 2015
Abstract:

The Pasternak elastic foundation model is employed to study the statics and natural frequencies of thick plates in the framework of the finite element method. A new 16-node Mindlin plate element of the Lagrange family and a 32-node zero-thickness interface element representing the response of the foundation are used in the analysis. The plate element avoids ill-conditioned behaviour due to its small thickness. In the case of the eigenvalue analysis, the equation of motion is derived by applying the Hamilton principle involving the variation of the kinetic and potential energy of the plate and foundation. Regarding the plate, the firstorder shear deformation theory is used. By employing the Lobatto numerical integration in which the integration points coincide with the element nodes, we obtain the diagonal form of the mass matrix of the plate. In practice, diagonal mass matrices are often employed due to their very attractive timeintegration schemes in explicit dynamic methods in which the inversion of the effective stiffness matrix as a linear combination of the damping and mass matrices is required. The numerical results of our analysis are verified using thin element based on the classical Kirchhoff theory and 16-node thick plate elements.

Keywords:

Mindlin plate, two-parameter elastic foundation, Lobatto integration, bending and eigenvalue analysis

Affiliations:
Buczkowski R.-West Pomeranian University of Technology Szczecin (PL)
Taczała M.-West Pomeranian University of Technology Szczecin (PL)
Kleiber M.-IPPT PAN
6.Starzyński G., Buczkowski R., Ultrasonic Measurements of Contact Stiffness Between Rough Surfaces, Journal of Tribology, ISSN: 0742-4787, DOI: 10.1115/1.4027132, Vol.136, pp.034503-1-5, 2014
Abstract:

We have used an ultrasonic method to determine the normal and shear stiffness for three different surfaces. The degree of hysteresis for the loading/unloading and stiffness ratio is a function of roughness. Nonlinear contact stiffness characteristics are obtained. The ratio of tangential to normal stiffness KT/KN slowly increases in proportion to normal loading. The novelty of our setup is that at the same time we can measure the reflection coefficient, obtain results for three transducers simultaneously, and measure the approach as a function of load. The presented experimental results of normal contact stiffness measurements have been used for the verification of our theoretical model based on a fractal description of rough surfaces (Buczkowski et al., “Fractal Normal Contact Stiffness of Rough Surfaces,” Arch. Mech. (submitted for publication).

Keywords:

Surface roughness, Stress, Reflectance, Stiffness, Ultrasonic measurement, Waves

Affiliations:
Starzyński G.-IPPT PAN
Buczkowski R.-West Pomeranian University of Technology Szczecin (PL)
7.Buczkowski R., Kleiber M., Starzyński G., Normal contact stiffness of fractal rough surfaces, ARCHIVES OF MECHANICS, ISSN: 0373-2029, Vol.66, No.6, pp.411-428, 2014
Abstract:

We used the fractal theory based on a single variable Weierstrass–Mandelbrot function to obtain the normal contact stiffness if rough and smooth isotropic surfaces are pressed against each other. Because in the original fractal theory the distribution of contact area is assumed geometrically, we propose the method in which the actual deformation of asperities and a correction due to asperity coupling (interaction) will be taken into account. This correction is equivalent to an increase of the effective separation by a quantity proportional to the nominal pressure and it has a significant effect on contact stiffness at larger normal loads (low separations). The numerical results demonstrate a nonlinear evolution of the contact stiffness with the normal load in particular in the first stage of loading at low squeezing pressures. We have compared the results of the theoretical contact stiffness using the fractal method with the experimental ultrasonic measurements. Experimental results made on real surfaces agree remarkably well with the theoretical predictions.

Keywords:

fractal model, contact stiffness, ultrasonic measurements

Affiliations:
Buczkowski R.-West Pomeranian University of Technology Szczecin (PL)
Kleiber M.-IPPT PAN
Starzyński G.-IPPT PAN
8.Buczkowski R., Kleiber M., Statistical models of rough surfaces for finite element 3D contact analysis, ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING, ISSN: 1134-3060, Vol.16, pp.399-424, 2009
Abstract:

The present study is divided in two parts. In the first one the complete elasto-plastic microcontact model of anisotropic rough surfaces is given. Rough surfaces are modelled as a random process in which the height of the surface is considered to be a two-dimensional random variable. It is assumed that the surface is statistically homogeneous. The description of anisotropic random surfaces is concentrated on strongly rough surfaces; for such surfaces the summits are represented by highly eccentric elliptic paraboloids. The model is based on the volume conservation of asperities with the plasticity index modified to suit more general geometric contact shapes during plastic deformation process. This model is utilized to determine the total contact area, contact load and contact stiffness which are a combination of the elastic, elasto-plastic and plastic components. The elastic and elastoplastic stiffness coefficients decrease with increasing variance of the surface height about the mean plane. The standard deviation of slopes and standard deviation of curvatures have no observable effects on the normal contact stiffness. The part two deals with the solution of the fully three-dimensional contact/friction problem taking into account contact stiffnesses in the normal and tangential directions. An incremental non-associated hardening friction law model analogous to the classical theory of plasticity is used. Two numerical examples are selected to show applicability of the method proposed.

Affiliations:
Buczkowski R.-West Pomeranian University of Technology Szczecin (PL)
Kleiber M.-IPPT PAN
9.Buczkowski R., Kleiber M., Elasto-plastic statistical model of strongly anisotropic rough surfaces for finite element 3D-contact analysis, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 0045-7825, DOI: 10.1016/j.cma.2005.11.014, Vol.195, No.37-40, pp.5141-5161, 2006
Abstract:

The complete elasto-plastic microcontact model of anisotropic rough surfaces is proposed. The description of anisotropic random surfaces is restricted here to strongly rough surfaces; for such surfaces the summits are represented by highly eccentric elliptic paraboloids having their semi-major axes oriented in the direction of the grain. The present model is based on the volume conservation of asperities in which the plasticity index is modified to suit more general geometric contact shapes during plastic deformation process. This model is utilized to determine the total contact area, contact load and contact stiffness which are a mixture of both the elastic and plastic components. For low nominal pressures both the elastic and elasto-plastic contact stiffness is found to be almost linear in relation to the normal load. The elastic and elasto-plastic stiffness coefficients decrease with increasing variance of the surface height about the mean plane. The standard deviation of slopes and standard deviation of curvatures have no observable effects on the normal contact stiffness.

Keywords:

Rough surfaces, Statistical modelling, Contact stiffness, Finite element method

Affiliations:
Buczkowski R.-West Pomeranian University of Technology Szczecin (PL)
Kleiber M.-IPPT PAN
10.Buczkowski R., Statistical Modelling of Rough Surfaces and Finite Element Contact Analysis (Praca habilitacyjna), Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.3, pp.1-119, 1999

List of recent monographs
1.
516
Buczkowski R., Kleiber M., Mechanika kontaktu ciał o powierzchniach chropowatych, Wydawnictwo Naukowe PWN, pp.1-214, 2014
List of chapters in recent monographs
1.
570
Kleiber M., Taczała M., Buczkowski R., Advances in Computational Plasticity, rozdział: Elasto-Plastic Response of Thick Plates Built in Functionally Graded Material Using the Third Order Plate Theory, Springer International Publishing, pp.185-199, 2018
2.
411
Taczała M., Buczkowski R., Kleiber M., Współczesna Mechanika Konstrukcji w Projektowaniu Inżynierskim, rozdział: Stateczność płyt o cechach materiałów gradientowych na podłożu sprężystym, Polska Akademia nauk, Komitet Inżynierii Lądowej i Wodnej, pp.375-388, 2015