Correct Discrete-Continual Finite Element Method of Structural Analysis Based on Precise Analytical Solutions of Resulting Multipoint Boundary Problems for Systems of Ordinary Differential Equations

2012 ◽  
Vol 204-208 ◽  
pp. 4502-4505 ◽  
Author(s):  
Pavel A. Akimov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Analytical Solutions ◽  
Computational Stability ◽  
Boundary Problems ◽  
Multipoint Boundary ◽  
Element Method

The distinctive paper is devoted to correct 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 uni-versality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resulting systems and partial Jordan decompositions of matrices of coeffi-cients, eliminating necessity of calculation of root vectors.

Correct Multilevel Discrete-Continual Finite Element Method of Structural Analysis

2014 ◽  
Vol 1040 ◽  
pp. 664-669 ◽  
Author(s):  
Pavel A. Akimov ◽  
Alexandr M. Belostosky ◽  
Marina L. Mozgaleva ◽  
Mojtaba Aslami ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Analytical Solutions ◽  
Computational Stability ◽  
Boundary Problems ◽  
Piecewise Constant ◽  
Computer Realization ◽  
Constant Coefficients ◽  
Element Method

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.

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

2011 ◽  
Vol 250-253 ◽  
pp. 3652-3655 ◽  
Author(s):  
Pavel A. Akimov ◽  
Vladimir N. Sidorov
Keyword(s):  
Structural Analysis ◽  
Analytical Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Computational Stability ◽  
Boundary Problems ◽  
Piecewise Constant ◽  
Multipoint Boundary ◽  
Correct Method ◽  
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.

scholarly journals ABOUT SOLUTION OF MULTIPOINT BOUNDARY PROBLEMS OF TWO-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

2017 ◽  
Vol 13 (1) ◽  
pp. 23-33
Author(s):  
Pavel A Akimov ◽  
Vladimir N. Sidorov ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Deep Beam ◽  
Boundary Problems ◽  
Basic Principles ◽  
Multipoint Boundary ◽  
Combined Application ◽  
Discrete Finite Element ◽  
Element Method

The distinctive paper is devoted to formulation and basic principles of approximation of multipoint boundary problem of static analysis of deep beam with the use of combined application of finite element method and discrete-continual finite element method. Design model, general formulation of the problem, basic principles of domain approximation, rule of numbering of subdomains, rule of numbering of finite elements, rule of numbering of discrete-continual finite elements are considered. Construction of discrete (finite element) and discretecontinual approximation models for subdomains is under consideration as well.

Sign in / Sign up

Export Citation Format

Share Document