About Verification of Discrete-Continual Finite Element Method for Two-Dimensional Problems of Structural Analysis Part 2: Deep Beam with Piecewise Constant Physical and Geometrical Parameters along Basic Direction

Abstract

This paper continues series of papers devoted to verification of discrete-continual finite element method (DCFEM) for two-dimensional problems of structural analysis. Formulation of the problem for deep beam with piecewise constant physical and geometrical parameters along so-called its basic direction, solutions obtained by DCFEM and finite element method (FEM) /with the use of ANSYS Mechanical/, their comparison are presented. It was confirmed that DCFEM is more effective in the most critical, vital, potentially dangerous areas of structure in terms of fracture (areas of the so-called edge effects), where some components of solution are rapidly changing functions and their rate of change in many cases can’t be adequately taken into account by the standard FEM.

Combined application of finite element method and discrete-continual finite element method

“…Combined (mixed) application of finite element method (FEM) [1,2] and DCFEM [3][4][5][6]7,8] can be effectively used for the analysis of general and complex structures. Some potentially dangerous areas of structure can be taken into account within DCFEM, and no special attention shall paid to compatibility method or time required to solve the corresponding mathematical problem, as the rest part of the structure which presents no interest in terms of fracture is considered by standard FEM.…”

“…The right subdomain is approximated by finite elements (within FEM [1,2,[11][12][13][14][15][16][17][18]) and the left subdomain is approximated by discrete-continual finite elements (within DCFEM [3][4][5][6]7,8]). Elasticity modulus of material of structure is equal to 3000 E kN/cm 2 .…”

“…Akimov and A.B. Zolotov [3][4][5][6]. But, as shown above, DCFEM is useful only for limited variety of constructions.…”

“…But, as shown above, DCFEM is useful only for limited variety of constructions. Combined (mixed) application of finite element method (FEM) [1,2] and DCFEM [3][4][5][6]7,8] is apparently preferable using the most powerful advantages of these methods and avoiding their disadvantages. The paper is devoted to such approach of semianalytical structural analysis.…”

Semianalytical analysis of shear walls with the use of discrete-continual finite element method. Part 2: Numerical examples, future development

“…Numerous examples have been considered for illustrating the efficiency of discretecontinual finite element method (DCFEM) [1][2][3][4][5][6][7][8] and two of them are presented below. Corresponding software has been developed with the use of Intel Parallel Studio XE [9] (FORTRAN programming language [10]).…”