scholarly journals Semianalytical Structural Analysis Based on Combined Application of Finite Element Method and Discrete-continual Finite Element Method Part 1: Two-Dimensional Theory of Elasticity

2016 ◽  
Vol 153 ◽  
pp. 8-15 ◽  
Author(s):  
Pavel A. Akimov ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Combined Application ◽  
Element Method

scholarly journals LOCALIZATION OF SOLUTION OF THE PROBLEM OF TWO-DIMENSIONAL THEORY OF ELASTICITY WITH THE USE OF B-SPLINE DISCRETE-CONTINUAL FINITE ELEMENT METHOD

2021 ◽  
Vol 17 (2) ◽  
pp. 83-104
Author(s):  
Marina Mozgaleva ◽  
Pavel Akimov ◽  
Taymuraz Kaytukov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Theory Of Elasticity ◽  
Basis Functions ◽  
Numerical Implementation ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
B Spline ◽  
Element Method

Localization of solution of the problem of two-dimensional theory of elasticity with the use of B-spline discrete-continual finite element method (specific version of wavelet-based discrete-continual finite element method) is under consideration in the distinctive paper. The original operational continual and discrete-continual formulations of the problem are given, some actual aspects of construction of normalized basis functions of a B-spline are considered, the corresponding local constructions for an arbitrary discrete-continual finite element are described, some information about the numerical implementation and an example of analysis are presented.

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.

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