Papers by Vladimir Sladek
Composite Structures, 2017
Computer methods in materials science, 2018
MATEC Web of Conferences, 2020
The path-independent J-integral is derived for fracture mechanics analysis of decagonal quasicrys... more The path-independent J-integral is derived for fracture mechanics analysis of decagonal quasicrystals (QCs). The gradient theory of quasicrystals is developed here to consider large strain gradients at the crack tip vicinity. The constitutive equations contain phonon and phason stresses, and the higher-order stress tensor. The higher-order elastic material parameters are proportional to the internal length material parameter and the conventional elastic coefficients. The FEM equations are derived to solve general boundary value problems for the strain gradient theory of the QCs.
Nanomaterials, 2021
The Timoshenko beam model is applied to the analysis of the flexoelectric effect for a cantilever... more The Timoshenko beam model is applied to the analysis of the flexoelectric effect for a cantilever beam under large deformations. The geometric nonlinearity with von Kármán strains is considered. The nonlinear system of ordinary differential equations (ODE) for beam deflection and rotation are derived. Moreover, this nonlinear system is linearized for each load increment, where it is solved iteratively. For the vanishing flexoelectric coefficient, the governing equations lead to the classical Timoshenko beam model. Furthermore, the influence of the flexoelectricity coefficient and the microstructural length-scale parameter on the beam deflection and the induced electric intensity is investigated.
International Applied Mechanics, 2004
The paper addresses the three-dimensional problem on steady-state vibrations of an elastic body c... more The paper addresses the three-dimensional problem on steady-state vibrations of an elastic body consisting of two perfectly joined dissimilar half-spaces with an elliptic mode I crack located in one of the half-spaces normally to the interface. The problem is reduced to a boundary integral equation for the crack opening function. The integration domain of the equation is bounded by the crack domain, and the interaction between the crack and the interface is described by a regular kernel. The equation is solved using the mapping method. Numerical results are obtained for the case where the surfaces of the elliptic crack are subjected to harmonic loading with constant amplitude. The dependences of the stress intensity factors on the wave number are presented for various relationships among the mechanical constants that ensure the absence of near-surface waves.
Nanomaterials, 2021
The non-classical linear governing equations of strain gradient piezoelectricity with micro-inert... more The non-classical linear governing equations of strain gradient piezoelectricity with micro-inertia effect are used to investigate Love wave propagation in a layered piezoelectric structure. The influence of flexoelectricity and micro-inertia effect on the phase wave velocity in a thin homogeneous flexoelectric layer deposited on a piezoelectric substrate is investigated. The dispersion relation for Love waves is obtained. The phase velocity is numerically calculated and graphically illustrated for the electric open-circuit and short-circuit conditions and for distinct material properties of the layer and substrate. The influence of direct flexoelectricity, micro-inertia effect, as well as the layer thickness on Love wave propagation is studied individually. It is found that flexoelectricity increases the Love-wave phase velocity, while the micro-inertia effect reduces its value. These effects become more significant for Love waves with shorter wavelengths and small guiding layer th...
Crystals, 2016
A meshless approximation and local integral equation (LIE) formulation are proposed for elastodyn... more A meshless approximation and local integral equation (LIE) formulation are proposed for elastodynamic analysis of a hollow cylinder made of quasicrystal materials with decagonal quasicrystal properties. The cylinder is assumed to be under shock loading. Therefore, the general transient elastodynamic problem is considered for coupled phonon and phason displacements and stresses. The equations of motion in the theory of compatible elastodynamics of wave type for phonons and wave-telegraph type for phasons are employed and can be easily modified to the elasto-hydro dynamic equations for quasicrystals (QCs). The angular dependence of the tensor of phonon-phason coupling coefficients handicaps utilization of polar coordinates, when the governing equations would be given by partial differential equations with variable coefficients. Despite the symmetry of the geometrical shape, the local weak formulation and meshless approximation are developed in the Cartesian coordinate system. The response of the cylinder in terms of both phonon and phason stress fields is obtained and studied in detail.
Engineering Fracture Mechanics, 2015
Path-independent integrals are successfully utilized for accurate evaluation of fracture paramete... more Path-independent integrals are successfully utilized for accurate evaluation of fracture parameters in crystalic materials, where atomic arrangement is periodic. In quasicrystals (QC) the atomic arrangement is quasiperiodic in one-, two-or three-directions. The 2-d elastic problem for quasicrystal is described by coupled governing equations for phonon and phason displacements. Conservation laws for quasicrystals are utilized to derive path-independent integrals for cracks. The relation between the energy release and stress intensity factor for a crack under the mode I is given for decagonal QCs. The path-independent integral formulation is valid also for cracks in QCs with continuously varying material properties.
International Journal of Computational Methods and Experimental Measurements, 2017
In this paper, we present briefly the derivation of the equations of motion and boundary conditio... more In this paper, we present briefly the derivation of the equations of motion and boundary conditions for elastic plates with functionally graded Young's modulus and mass density of the plate subjected to transversal transient dynamic loads. The unified formulation is derived for three plate bending theories, such as the Kirchhoff-Love theory (KLT) for bending of thin elastic plates and the shear deformation plate theories (the first order-FSDPT, and the third order-TSDPT). It is shown that the transversal gradation of Young's modulus gives rise to coupling between the bending and inplane deformation modes in plates subject to transversal loading even in static problems. In dynamic problems, there are also the inertial coupling terms. The influence of the gradation of material coefficients on bending and in-plane deformation modes with including coupling is studied in numerical experiments with consideration of Heaviside impact loading as well as Heaviside pulse loading. To decrease the order of the derivatives in the coupled PDE with variable coefficients, the decomposition technique is employed. The element-free strong formulation with using meshless approximations for spatial variation of field variables is developed and the discretized ordinary differential equations with respect to time variable are solved by using time stepping techniques. The attention is paid to the stability of numerical solutions. Several numerical results are presented for illustration of the coupling effects in bending of elastic FGM (Functionally Graded Material) plates. The role of the thickness and shear deformations is studied via numerical simulations by comparison of the plate response in three plate bending theories.
Boundary Elements and Other Mesh Reduction Methods XXIX, 2007
This paper is a comparative study for various numerical implementations of local integral equatio... more This paper is a comparative study for various numerical implementations of local integral equations developed for stress analysis in plane elasticity of solids with functionally graded material coefficients. Besides two meshless implementations by the point interpolation method and the moving least squares approximation, the element based approximation is also utilized. The numerical stability, accuracy, convergence of accuracy and cost efficiency (assessed by CPU-times) are investigated in numerous test examples with exact benchmark solutions.
International Journal for Numerical Methods in Engineering, 2003
A strongly non-local boundary element method (BEM) for structures with strain-softening damage tr... more A strongly non-local boundary element method (BEM) for structures with strain-softening damage treated by an integral-type operator is developed. A plasticity model with yield limit degradation is implemented in a boundary element program using the initial-stress boundary element method with iterations in each load increment. Regularized integral representations and boundary integral equations are used to avoid the di culties associated with numerical computation of singular integrals. A numerical example is solved to verify the physical correctness and e ciency of the proposed formulation. The example consists of a softening strip perforated by a circular hole, subjected to tension. The strainsoftening damage is described by a plasticity model with a negative hardening parameter. The local formulation is shown to exhibit spurious sensitivity to cell mesh reÿnements, localization of softening damage into a band of single-cell width, and excessive dependence of energy dissipation on the cell size. By contrast, the results for the non-local theory are shown to be free of these physically incorrect features. Compared to the classical non-local ÿnite element approach, an additional advantage is that the internal cells need to be introduced only within the small zone (or band) in which the strain-softening damage tends to localize within the structure. Copyright ? 2003 John Wiley & Sons, Ltd.
Engineering Analysis with Boundary Elements, 2013
The von Karman plate theory of large deformations is applied to express the strains, which are th... more The von Karman plate theory of large deformations is applied to express the strains, which are then used in the constitutive equations for magnetoelectroelastic solids. The in-plane electric and magnetic fields can be ignored for plates. A quadratic variation of electric and magnetic potentials along the thickness direction of the plate is assumed. The number of unknown terms in the quadratic approximation is reduced, satisfying the Maxwell equations. Bending moments and shear forces are considered by the Reissner-Mindlin theory, and the original three-dimensional (3D) thick plate problem is reduced to a two-dimensional (2D) one. A meshless local Petrov-Galerkin (MLPG) method is applied to solve the governing equations derived based on the Reissner-Mindlin theory. Nodal points are randomly distributed over the mean surface of the considered plate. Each node is the centre of a circle surrounding it. The weak form on small subdomains with a Heaviside step function as the test function is applied to derive the local integral equations. After performing the spatial MLS approximation, a system of algebraic equations for certain nodal unknowns is obtained. Both stationary and timeharmonic loads are then analyzed numerically.
Engineering Analysis with Boundary Elements, 2006
Computational Mechanics, 2003
The nonlinear integro-differential Berger equation is used for description of large deflections o... more The nonlinear integro-differential Berger equation is used for description of large deflections of thin plates. An iterative solution of Berger equation by the local boundary integral equation method with meshless approximation of physical quantities is proposed. In each iterative step the Berger equation can be considered as a partial differential equation of the fourth order. The governing equation is decomposed into two coupled partial differential equations of the second order. One of them is Poisson's equation whereas the other one is Helmholtz's equation. The local boundary integral equation method is applied to both these equations. Numerical results for a square plate with simply supported and/or clamped edges as well as a circular clamped plate are presented to prove the efficiency of the proposed formulation.
Computational Mechanics, 2005
An efficient numerical method is proposed for 2-d potential problems in anisotropic media with co... more An efficient numerical method is proposed for 2-d potential problems in anisotropic media with continuously variable material coefficients. The method is based on the local integral relationships (integral form of balance equation and/or integral equations utilizing fundamental solutions) and consistent approximation of field variable using standard domain-type elements. The accuracy and convergence of the proposed method is tested by several examples and compared with benchmark analytical solutions. Keywords Potential problems AE Integral equation method AE Integral balance equation AE Fundamental solution AE Finite elements AE Anisotropic and non-homogeneous media
A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in t... more A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-D) magneto-electric-elastic solids with continuously varying material properties. Stationary and transient dynamic problems are considered in this paper. The local weak formulation is employed on circular subdomains where surrounding nodes randomly spread over the analyzed domain. The test functions are taken as unit step functions in derivation of the local integral equations (LIEs). The moving least-squares (MLS) method is adopted for the approximation of the physical quantities in the LIEs. Introduction Modern smart structures made of piezoelectric and piezomagnetic materials offer certain potential performance advantages over conventional ones due to their capability of converting the energy from one type to other (among magnetic, electric, and mechanical) [1]. Former activities were focused on modeling of magneto-electric-elastic fields to determine the field varia...
Boundary Elements and Other Mesh Reduction Methods XXXIII, 2011
The paper deals with the numerical solution of initial-boundary value problems for diffusion equa... more The paper deals with the numerical solution of initial-boundary value problems for diffusion equation with variable coefficients by using a local weak formulation and a meshless approximation of spatial variations of the field variable. The time variation is treated either by the Laplace transform technique or by the linear Lagrange interpolation in the time stepping approach. Advanced formulation for local integral equations is employed. A comparative study of numerical results obtained by the Laplace transform and the time stepping approach is given in a test example for which the exact solution is available and utilized as a benchmark solution.
The paper deals with an accurate numerical integration of the weakly singular and nearly singular... more The paper deals with an accurate numerical integration of the weakly singular and nearly singular integrals occuring in the BEM formulations. Optimal transformations of the integration variables are proposed in order to make the integrands to be distributed uniformly as much as possible over the whole integration area. Then, the integration can be performed with a sufficient accuracy by using standard integration quadratures without increasing the computational effort.
It is presented an integral formulation for computatin of T-stresses in a finite cracked body und... more It is presented an integral formulation for computatin of T-stresses in a finite cracked body under static, dynamic and thermal loads. The reciprocity theorems for all three cases are utilized to find the integral formula. The auxiliary fields are properly selected to elliminate singular terms which contain stress intensity factors. A pure contour integral formula for the T-stress is obtained only in elastostatics. In elastodynamics and thermoelasticity the integral formula has a contour-domain character. For solution of a boundary value problem of a cracked body and for evaluation of variables needed in the integral T-formula the boundary element method is used. To illustrate computational capabilities numerical examples for a stationary crack in a rectangular plate under the impact tension and the cracked tube under a stationary thermal gradient are presented.
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Papers by Vladimir Sladek