In this paper, we investigate how the form of the conventional elastodynamic equations changes under curvilinear transformations. The equations get mapped to a more general form in which the density is anisotropic and additional terms appear which couple the stress not only with the strain but also with the velocity, and the momentum gets coupled not only with the velocity but also with the str...

Elastodynamic models are used for real-time simulation of deformable objects in virtual reality applications. To obtain a realistic simulation, the physical parameters of the model must be defined appropriately. Furthermore, the usability of elastodynamic models in virtual reality applications depends on the used simulation algorithm to a great part, since interactions with the simulated object...

This paper is concerned with the fast multipole boundary element method (FMBEM) in two dimensional frequency domain elastodynamics. The fast multipole method (FMM) is derived by the Galerkin vector in the elastodynamic field. The elastodynamic field is expressed as the sum of the longitudinal and transverse wave fields, and the Galerkin vector FMM is simply derived from the scalar wave FMM. Mul...

The reciprocity theorem is a fundamental theorem of the Theory of Elasticity (Betti 1872, Rayleigh 1873). The theorem connects the body forces, the surface tractions and the displacements of two elastodynamic states in a domain of an elastic body, by a volume integral and a surface integral. In this talk it is shown that the reciprocity theorem of elastodynamics can be used to solve actual prob...

[1] We introduce a new model which both generates a selforganizing complex segmented fault system which then accommodates finite strain, and generates sequences of elastodynamic events on that complex fault system. This opens up a new realm of study of populations of cascading elastodynamic ruptures on complex fault systems. We examine the distribution of sizes of events in the model, and its d...

We present several time integration algorithms of second-order accuracy that are numerically simple and effective for nonlinear elastodynamic problems. These algorithms are based on a general four-step scheme that has a resemblance to the backward differentiation formulas. We also present an extension to the composite strategy of the Bathe method. Appropriate values for the algorithmic paramete...

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...

A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in a homogeneous anisotropic medium. The Heaviside step function is used as the test functions in the local weak form. It is leading to derive local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace transfor technique is applied and the ...