Semianalytical solution of multipoint boundary problems of structural analysis with the use of combined application of finite element method and discrete-continual finite element method

2017 ◽  
Author(s):  
Pavel Akimov ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Boundary Problems ◽  
Multipoint Boundary ◽  
Combined Application ◽  
Element Method

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.

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.

scholarly journals 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

2018 ◽  
Vol 14 (2) ◽  
pp. 14-29
Author(s):  
Pavel A. Akimov ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Dimensional Structure ◽  
Basic Principles ◽  
Multipoint Boundary ◽  
Combined Application ◽  
Element Method

The distinctive paper is devoted to formulation and basic principles of approximation of multipoint boundary problem of static analysis of three-dimensional structure with the use of combined application of finite element method and discrete-continual finite element method. Basic notation system, design model, general formulation of the problem (based on three-dimensional theory of elasticity), 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 discrete-continual approx­imation models for subdomains is under consideration as well

Modified Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Local Structural Analysis - Part 1: Continual and Discrete-Continual Formulations of the Problems

2014 ◽  
Vol 670-671 ◽  
pp. 720-723 ◽  
Author(s):  
Pavel A. Akimov ◽  
Marina L. Mozgaleva ◽  
Mojtaba Aslami ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Three Dimensional ◽  
Accurate Solution ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Boundary Problems ◽  
Piecewise Constant ◽  
Element Method

The distinctive paper is devoted to wavelet-based discrete-continual finite element method (WDCFEM) of structural analysis. Two-dimensional and three-dimensional problems of analysis of structures with piecewise constant physical and geometrical parameters along so-called “basic” direction are under consideration. High-accuracy solution of the corresponding problems at all points of the model is not required normally, it is necessary to find only the most accurate solution in some pre-known local domains. Wavelet analysis is a powerful and effective tool for corresponding researches. Initial continual and discrete-continual formulations of multipoint boundary problems of two-dimensional and three-dimensional structural analysis are presented.

Modified Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Local Structural Analysis - Part 2: Reduced Formulations of the Problems in Haar Basis

2014 ◽  
Vol 670-671 ◽  
pp. 724-727 ◽  
Author(s):  
Pavel A. Akimov ◽  
Marina L. Mozgaleva ◽  
Mojtaba Aslami ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Three Dimensional ◽  
Haar Wavelet ◽  
Wavelet Basis ◽  
Two Dimensional ◽  
Governing Equations ◽  
Boundary Problems ◽  
Element Method

The distinctive paper is devoted to wavelet-based discrete-continual finite element method (WDCFEM) of structural analysis. Discrete-continual formulations of multipoint boundary problems of two-dimensional and three-dimensional structural analysis are transformed to corresponding localized formulations by using the discrete Haar wavelet basis and finally, with the use of averaging and reduction algorithms, the localized and reduced governing equations are obtained. Special algorithms of localization with respect to each degree of freedom are presented.

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