Correct Multilevel Discrete-Continual Finite Element Method of Structural Analysis

Abstract

The distinctive paper is devoted to correct multilevel discrete-continual finite element method (DCFEM) of structural analysis based on precise analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients. Corresponding semianalytical (discrete-continual) formulations are contemporary mathematical models which currently becoming available for computer realization. Major peculiarities of DCFEM include universality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resulting systems and partial Jordan decompositions of matrices of coefficients, eliminating necessity of calculation of root vectors.

Contemporary Problems of Numerical Modelling of Unique Structures and Buildings

“…and semianalytical (discrete-continual) methods of structural analysis [1][2][3][4][5][6][7][8][9][10]23] are the most important aspects of ensuring safety of structures and buildings. Particularly the field of application of discretecontinual methods (discrete-continual finite element method, discrete-continual boundary element method, discrete-continual variationdifference method), which are now becoming available for computer realization, comprises structures with regular (in particular, constant or piecewise constant) physical and geometrical parameters in some dimension (so-called "basic" direction (dimension)).…”

Semianalytical analysis of shear walls with the use of discrete-continual finite element method. Part 1: Mathematical foundations

“…Resultant multipoint boundary problem for the first-order system of ordinary differential equations with piecewise-constant coefficients within DCFEM [14] has the form:°°® …”

“…The distinctive paper is devoted to two-dimensional (plane stress condition) semianalytical analysis of shear wall with the use of discrete-continual finite element method (DCFEM) [14,15,16]. It allows obtaining the exact analytical solution in one direction and decreasing the size of the problem to conventional one-dimensional finite element analysis.…”

About Solution of Multipoint Boundary Problems of Three-Dimensional Structural Analysis With the Use of Combined Application of Finite Element Method and Discrete-Continual Finite Element Method. Part 1: Formulation and Basic Principles of Approximation

“…Золотова [1] и развитого в ис-следованиях П.А. Акимова [2][3][4][5][6][7][8][9][10][11], М.Л. Моз-галевой [12][13][14][15][16][17][18][19][20][21][22], Моджтаба Аслами [3][4][5][6][16][17][18][19]23], О.А.…”