The distinctive paper is devoted to general principles of mesh approximation for boundary problems of structural analysis with the use of so-called method of extended domain, proposed by Prof. Alexander B. Zolotov. In particular we studied questions dealing with approximation of domain, approximation of functions and approximations of operators. Mesh functions are introduced as well as corresponding mesh operations and various types of implementation. The results are rather efficient algorithms in respect to number of operations, computing time and required memory.

The distinctive paper is 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 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 finite element method.

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.

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.

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