Solution of boundary problems of structural mechanics with the combined application use of Discrete-Continual Finite Element Method and Finite Element Method

Abstract

In most structural problems the object is usually to find the distribution of stress in elastic body produced by an external loading system. The theory of elasticity is a methodology that creates a linear relation between the imposing force (stress) and resulting deformation (strain), for the majority of materials, which behave fully or partially elastically. This paper is devoted to combined semianalytical and numerical static analysis of three-dimensional structures. The stress-strain or constitutive behavior is given for isotropic materials. Solution of multipoint (particularly, two-point) boundary problem of three-dimensional elasticity theory based on combined application of finite element method (FEM) and discrete-continual finite element method (DCFEM) is under consideration. The given domain, occupied by structure, is embordered by extended one within method of extended domain. The application field of DCFEM comprises fragments of structure (subdomains) with regular (constant or piecewise constant) physical and geometrical parameters in some dimension (“basic” dimension). DCFEM presupposes finite element mesh approximation for non-basic dimensions of extended domain while in the basic dimension problem remains continual (corresponding correct analytical solution is constructed). FEM is used for approximation of all other subdomains. Discrete (within FEM) and discrete-continual (within DCFEM) approximation models for subdomains and coupled multilevel approximation model for extended domain are constructed.