scholarly journals Solution of Multipoint Boundary Problem of Two-Dimensional Theory of Elasticity Based on Combined Application of Finite Element Method and Discrete-Continual Finite Element Method

2017 ◽  
Vol 6 ◽  
pp. 182-189 ◽  
Author(s):  
Pavel A. Akimov ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Problem ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Multipoint Boundary ◽  
Combined Application ◽  
Element Method

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

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 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.

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.

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 2: SPECIAL ASPECTS OF FINITE ELEMENT APPROXIMATION

2017 ◽  
Vol 13 (4) ◽  
pp. 14-36
Author(s):  
Pavel A. Akimov ◽  
Alexander M. Belostotsky ◽  
Taymuraz B. Kaytukov ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Problem ◽  
Finite Element Approximation ◽  
Element Model ◽  
Discrete Models ◽  
Element Approximation ◽  
Multipoint Boundary ◽  
Joint Application ◽  
Element Method

As is well known, the formulation of a multipoint boundary problem involves three main components: a description of the domain occupied by the structure and the corresponding subdomains; description of the conditions inside the domain and inside the corresponding subdomains, the description of the conditions on the boundary of the domain, conditions on the boundaries between subdomains. This paper is a continuation of another work published earlier, in which the formulation and general principles of the approximation of the multipoint boundary problem of a static analysis of deep beam on the basis of the joint application of the finite element method and the discrete-continual finite element method were considered. It should be noted that the approximation within the fragments of a domain that have regular physical-geometric parameters along one of the directions is expedient to be carried out on the basis of the discrete-continual finite element method (DCFEM), and for the approximation of all other fragments it is necessary to use the standard finite element method (FEM). In the present publication, the formulas for the computing of displacements partial derivatives of displacements, strains and stresses within the finite element model (both within the finite element and the corresponding nodal values (with the use of averaging)) are presented. Boundary conditions between subdomains (respectively, discrete models and discrete-continual models and typical conditions such as “hinged support”, “free edge”, “perfect contact” (twelve basic (basic) variants are available)) are under consideration as well. Governing formulas for computing of elements of the corresponding matrices of coefficients and vectors of the right-hand sides are given for each variant. All formulas are fully adapted for algorithmic implementation.

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