Vladimir N. Sidorov

Correct Method of Analytical Solution of Multipoint Boundary Problems of Structural Analysis for Systems of Ordinary Differential Equations with Piecewise Constant Coefficients

This paper is devoted to correct method of analytical solution of multipoint boundary problems of structural analysis for systems of ordinary differential equations with piecewise constant coefficients. Its major peculiarities include universality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resultant systems and partial Jordan decomposition of matrix of coefficients, eliminating necessity of calculation of root vectors.

Solving Unsteady Boundary Value Problems Using Discrete-Analytic Method for Non-Iterative Simulation of Temperature Processes in Time

Method for solving a boundary value problem of inhomogeneous unsteady-state heat conduction transfer is considered. This physical process can be described by a boundary value problem for a partial differential equation of the 2nd order. Discrete-analytical method, which turns out the mathematical formulation of the initial problem to be normal system of differential equations, was used. There is the non-iterative solution of such system, which is the set of analytic functions. The theory of matrix functions, particularly the properties of matrix exponential, was applied to get the solution. This approach allows us to model the unsteady-state heat conduction processes with unstationary boundary conditions of different types, defined as time-dependent functions. Such modeling describes the real physical processes in structural materials more accurately.

Application of discrete-continual finite element method for global and local analysis of multilevel systems

This paper is devoted to discrete-continual finite element method (DCFEM) of analysis of structures with regular (constant or piecewise constant) physical and geometrical parameters in some coordinate direction (so-called “basic” direction). Effective qualitative multilevel analysis of local and global stress-strain state of such structures is normally required in various technical problems. It is commonly known that defects and failures are mostly local in nature. However total load-bearing capacity of the structure, associated with the condition of limit equilibrium, is determined by its global behavior. Therefore multilevel approach within DCFEM is peculiarly relevant and apparently preferable in all aspects for qualitative and quantitative analysis of calculation data. Wavelet analysis (wavelet-based DCFEM) provides effective and popular tool for such researches.