Vladimir Sladek

Bio: Vladimir Sladek is an academic researcher from Slovak Academy of Sciences. The author has contributed to research in topics: Integral equation & Boundary value problem. The author has an hindex of 47, co-authored 346 publications receiving 7118 citations. Previous affiliations of Vladimir Sladek include Shinshu University & Institute of Chemistry, Slovak Academy of Sciences.

Stress analysis by boundary element methods

Abstract: 1. Solution of Partial Differential Equations by the Boundary Integral Equation Method (BIEM). Ordinary differential equations. Partial differential equations. 2. Elastostatics. Governing equations and fundamental solutions. The Somigliana identity. Boundary integral equations (BIE). Integral representation of stresses. Boundary integro-differential equations (BIDE). Stresses on the boundary. BIE and BIDE for an anisotropic medium. Axisymmetric problems. Semi-infinite problems. Numerical implementation. Numerical examples. 3. Elastodynamics. Equations of motion. Fundamental solutions. Integral representations of displacements and stresses. Boundary integral and integro-differential equations. Numerical solution. Alternative formulation of boundary element method. Numerical examples. 4. Thermoelasticity. Governing equations. Fundamental solutions. Integral representations of displacements and temperature. Integral representations of temperature gradients and stresses. Boundary integral and integro-differential equations. Numerical implementation. Alternative BEM formulation. Application to fracture mechanics. Numerical examples. 5. Micropolar Thermoelasticity. Equations of motion. Fundamental solutions in three dimensions. Fundamental solutions for plane problems. Fundamental solutions for antiplane problems. Integral representations. BIE and BIDE. Applications to fracture mechanics. 6. Elastoplasticity. Governing equations. Boundary integral formulations. Elastoplastic stress-strain relations. Incremental computations for elastoplasticity. 7. Viscoelasticity. Rheological models and the correspondence principle. Boundary integral formulation. Schapery's inversion algorithm. Application to fracture mechanics. 8. Thin Elastic Plates in Bending. Governing equations in classical plate theory. Integral formulation. Numerical solution. Large deflections. Berger equation. Plates on elastic foundations. 9. Stress Analysis by Hybrid Methods. Computation of stresses at internal points from stresses on boundary. Combination of BIE with holographic interferometry measurements. Hybrid method in fracture mechanics. Appendices. References. Subject Index.

The local boundary integral equation (LBIE) and it's meshless implementation for linear elasticity

Abstract: The meshless method based on the local boundary integral equation (LBIE) is a promising method for solving boundary value problems, using an local unsymmetric weak form and shape functions from the moving least squares approximation. In the present paper, the meshless method based on the LBIE for solving problems in linear elasticity is developed and numerically implemented. The present method is a truly meshless method, as it does not need a “finite element mesh”, either for purposes of interpolation of the solution variables, or for the integration of the energy. All integrals in the formulation can be easily evaluated over regularly shaped domains (in general, spheres in three-dimensional problems) and their boundaries. The essential boundary conditions in the present formulation can be easily imposed even when the non-interpolative moving least squares approximation is used. Several numerical examples are presented to illustrate the implementation and performance of the present method. The numerical examples show that high rates of convergence with mesh refinement for the displacement and energy norms are achievable. No post-processing procedure is required to compute the strain and stress, since the original solution from the present method, using the moving least squares approximation, is already smooth enough.

Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties

Abstract: This paper presents the local boundary integral formulation for an elastic body with nonhomogeneous material properties. All nodal points are surrounded by a simple surface centered at the collocation point. Only one nodal point is included in each the sub-domain. On the surface of the sub-domain, both displacements and traction vectors are unknown generally. If a modified fundamental solution, for governing equation, which vanishes on the local boundary is chosen, the traction value is eliminated from the local boundary integral equations for all interior points. For every sub-domain, the material constants correspond to those at the collocation point at the center of sub-domain. Meshless and polynomial element approximations of displacements on the local boundaries are considered in the numerical analysis.

Modeling and Analysis of Functionally Graded Materials and Structures

Abstract: This paper presents a review of the principal developments in functionally graded materials (FGMs) with an emphasis on the recent work published since 2000. Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper. They include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture. The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions. DOI: 10.1115/1.2777164

Electrodynamics Of Continuous Media

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Meshfree and particle methods and their applications

Abstract: Recent developments of meshfree and particle methods and their applications in applied mechanics are surveyed. Three major methodologies have been reviewed. First, smoothed particle hydrodynamics ~SPH! is discussed as a representative of a non-local kernel, strong form collocation approach. Second, mesh-free Galerkin methods, which have been an active research area in recent years, are reviewed. Third, some applications of molecular dynamics ~MD! in applied mechanics are discussed. The emphases of this survey are placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics. This review article includes 397 references. @DOI: 10.1115/1.1431547#

Methods of Numerical Integration

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