New Numerical Methods for Structural Mechanics Problems in Unbounded Domains

Abstract

The article is devoted to the problem of numerical simulation of unbounded domains in structural mechanics. Nowadays there are many numerical methods to analyze structural mechanics problems in infinite domains. A brief analytical review of existing numerical methods is presented. Among them are finite difference method, boundary element method (BEM), finite element method (FEM) and scaled boundary finite element method (SBFEM). No one suggests general approach for all kinds of problem statements. Vast majority of industrial software realize FEM. Considering this fact it is more reasonable to modify FEM for mechanical problems in unbounded domains. New variational differential method and new FEM modification, based on the approach of quasi-uniform grids modelling in finite difference method, are proposed. New numerical methods enable to solve problems in semi-infinite and infinite domains without introduction of artificial boundaries and setting special non-reflecting conditions. The article shows basic steps of new numerical algorithms for problems in one-dimensional semi-infinite computational domain.