Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Local Deep Beam Analysis

2013 ◽  
Vol 405-408 ◽  
pp. 3165-3168 ◽  
Author(s):  
Pavel A. Akimov ◽  
Marina L. Mozgaleva
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Local Analysis ◽  
Geometrical Parameters ◽  
Deep Beam ◽  
Piecewise Constant ◽  
Beam Analysis ◽  
Constant Coefficients ◽  
Operational Formulation ◽  
Element Method

High-accuracy solution of the problem of deep beam analysis is normally required in some pre-known domains (regions with the risk of significant stresses that could potentially lead to the destruction of structure, regions which are subject to specific operational requirements). The distinctive paper is devoted to correct wavelet-based multilevel discrete-continual finite element method for local analysis of deep beams with regular (in particular, constant or piecewise constant) physical and geometrical parameters (properties) in one direction. Initial discrete-continual operational formulation of the considering problem and corresponding operational formulation with the use of wavelet basis are presented. Due to special algorithms of averaging within multigrid approach, reduction of the problem is provided. Resultant multipoint boundary problem of structural mechanics for system of ordinary differential equations with piecewise-constant coefficients is given.

Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Local Plate Analysis

2013 ◽  
Vol 351-352 ◽  
pp. 13-16 ◽  
Author(s):  
Pavel A. Akimov ◽  
Marina L. Mozgaleva
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Accuracy ◽  
Local Analysis ◽  
Geometrical Parameters ◽  
Piecewise Constant ◽  
Constant Coefficients ◽  
Plate Analysis ◽  
Operational Formulation ◽  
Element Method

High-accuracy solution of the problem of plate analysis is normally required in some pre-known domains (regions with the risk of significant stresses that could potentially lead to the destruction of structure, regions which are subject to specific operational requirements). The distinctive paper is devoted to correct wavelet-based multilevel discrete-continual finite element method for local analysis of plates with regular (in particular, constant or piecewise constant) physical and geometrical parameters (properties) in one direction. Initial discrete-continual operational formulation of the considering problem and corresponding operational formulation with the use of wavelet basis are presented. Due to special algorithms of averaging within multigrid approach, reduction of the problem is provided. Resultant multipoint boundary problem of structural mechanics for system of ordinary differential equations with piecewise-constant coefficients is given.

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.

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 WAVELET-BASED DISCRETE-CONTINUAL FINITE ELEMENT PLATE ANALYSIS WITH THE USE OF DAUBECHIES SCALING FUNCTIONS

2019 ◽  
Vol 15 (3) ◽  
pp. 96-108
Author(s):  
Marina Mozgaleva ◽  
Pavel Akimov ◽  
Taymuraz Kaytukov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thin Plate ◽  
Scaling Functions ◽  
Geometrical Parameters ◽  
Computer Implementation ◽  
Basic Direction ◽  
Piecewise Constant ◽  
Plate Analysis ◽  
Operational Formulation

The distinctive paper is detoded to special version of wavelet-based discrete-continual finite element method of plate analysis. Daubechies scaling functions are used within this version. Its field of application comprises plates with constant (generally piecewise constant) physical and geometrical parameters along one direction (so-called “basic” direction). Modified continual operational formulation of the problem with the use of the method of extended domain (proposed by A.B. Zolotov) is presented. Corresponding discrete-continual formulation is given as well. Brief information about computer implementation of the method with the use of MATLAB software is provided. Besides numerical sample of analysis of thin plate is considered.

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.

Local High-Accuracy Plate Analysis Using Wavelet-Based Multilevel Discrete-Continual Finite Element Method

2016 ◽  
Vol 685 ◽  
pp. 962-966 ◽  
Author(s):  
Pavel A. Akimov ◽  
Marina L. Mozgaleva ◽  
Mojtaba Aslami ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Problem ◽  
High Accuracy ◽  
Geometrical Parameters ◽  
Wavelet Basis ◽  
Basic Direction ◽  
Piecewise Constant ◽  
Plate Analysis ◽  
Element Method

The distinctive paper is devoted to application of wavelet-based discrete-continual finite element method (WDCFEM), to analysis of plates with piecewise constant physical and geometrical parameters in so-called “basic” direction. Initial continual and discrete-continual formulations of the problem are presented. Due to special algorithms of averaging using wavelet basis within multigrid approach, reduction of the problem is provided. Resultant multipoint boundary problem for system of ordinary differential equations is given.

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.

About Verification of Wavelet-Based Discrete-Continual Finite Element Method for Three-Dimensional Problems of Structural Analysis Part 2: Structures with Piecewise Constant Physical and Geometrical Parameters along Basic Direction

2014 ◽  
Vol 709 ◽  
pp. 109-112 ◽  
Author(s):  
Marina L. Mozgaleva ◽  
Pavel A. Akimov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Three Dimensional ◽  
Rate Of Change ◽  
Dimensional Structure ◽  
Geometrical Parameters ◽  
Basic Direction ◽  
Piecewise Constant ◽  
Element Method

This paper is devoted to verification of so-called wavelet-based discrete-continual finite element method (wDCFEM), proposed by authors, for three-dimensional problems of local structural analysis. Formulation of the problem for three-dimensional structure with piecewise constant physical and geometrical parameters along so-called its basic direction, solutions obtained by wDCFEM and discrete-continual finite element method (DCFEM) and their comparison are presented. It was confirmed that wDCFEM is rather 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.

scholarly journals Combined Semianalytical and Numerical Static Plate Analysis. Part 2: Resultant Multipoint Boundary Problem

2018 ◽  
Vol 196 ◽  
pp. 01011
Author(s):  
Oleg Negrozov ◽  
Pavel Akimov ◽  
Marina Mozgaleva
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Problem ◽  
Thin Plates ◽  
Geometrical Parameters ◽  
Element Mesh ◽  
Multipoint Boundary ◽  
Basic Dimension ◽  
Plate Analysis ◽  
Element Method

The distinctive paper is devoted to solution of multipoint boundary problem of plate analysis (Kirchhoff model) based on combined application of finite element method (FEM) and discrete-continual finite element method (DCFEM). As is known the Kirchhoff-Love theory of plates is a two-dimensional mathematical model that is normally used to determine the stresses and deformations in thin plates subjected to forces and moments. The given domain, occupied by considering structure, is embordered by extended one. The field of application of DCFEM comprises fragments of structure (subdomains) with regular (constant or piecewise constant) physical and geometrical parameters in some dimension (“basic” dimension). DCFEM presupposes finite element mesh approximation for non-basic dimension of extended domain while in the basic dimension problem remains continual. FEM is used for approximation of all other subdomains (it is convenient to solve plate bending problems in terms of displacements). Coupled multilevel approximation model for extended domain and resultant multipoint boundary problem are constructed. Brief information about software systems and verification samples are presented as well.

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