scholarly journals About Verification of Discrete-continual Finite Element Method of Structural Analysis. Part 1: Two-dimensional Problems

2014 ◽  
Vol 91 ◽  
pp. 2-7 ◽  
Author(s):  
Pavel A. Akimov ◽  
Marina L. Mozgaleva ◽  
Mojtaba Aslami ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Two Dimensional ◽  
Element Method

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.

scholarly journals Wavelet-based Discrete-continual Finite Element Method of Local Structural Analysis for Two-dimensional Problems

2014 ◽  
Vol 91 ◽  
pp. 8-13 ◽  
Author(s):  
Pavel A. Akimov ◽  
Marina L. Mozgaleva ◽  
Mojtaba Aslami ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Two Dimensional ◽  
Element Method

About Verification of Discrete-Continual Finite Element Method for Two-Dimensional Problems of Structural Analysis Part 2: Deep Beam with Piecewise Constant Physical and Geometrical Parameters along Basic Direction

2014 ◽  
Vol 1025-1026 ◽  
pp. 95-103 ◽  
Author(s):  
Pavel A. Akimov ◽  
Marina L. Mozgaleva ◽  
Mojtaba Aslami ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Rate Of Change ◽  
Geometrical Parameters ◽  
Deep Beam ◽  
Two Dimensional ◽  
Basic Direction ◽  
Piecewise Constant ◽  
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.

About Verification of Discrete-Continual Finite Element Method for Two-Dimensional Problems of Structural Analysis Part 1: Deep Beam with Constant Physical and Geometrical Parameters along Basic Direction

2014 ◽  
Vol 1025-1026 ◽  
pp. 89-94 ◽  
Author(s):  
Pavel A. Akimov ◽  
Marina L. Mozgaleva ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Rate Of Change ◽  
Geometrical Parameters ◽  
Deep Beam ◽  
Two Dimensional ◽  
Basic Direction ◽  
Standard Finite Element Method ◽  
Element Method

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.

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