A polygonal finite element method for plate analysis

2017 ◽  
Vol 188 ◽  
pp. 45-62 ◽  
Author(s):  
H. Nguyen-Xuan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Plate Analysis ◽  
Element Method ◽  
Polygonal Finite Element

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 LOCALIZATION OF SOLUTION OF THE PROBLEM OF ISOTROPIC PLATE ANALYSIS WITH THE USE OF B-SPLINE DISCRETE-CONTINUAL FINITE ELEMENT METHOD

2021 ◽  
Vol 17 (1) ◽  
pp. 55-74
Author(s):  
Marina Mozgaleva ◽  
Pavel Akimov ◽  
Taymuraz Kaytukov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Isotropic Plate ◽  
Basis Functions ◽  
Numerical Implementation ◽  
B Spline ◽  
Plate Analysis ◽  
Element Method

Localization of solution of the problem of isotropic plate analysis with the use of B-spline discrete-continual finiteelement method (specificversion of wavelet-based discrete-continual finiteelement 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 finiteelement are described, some information about the numerical implementation and an example of analysis are presented.

Hyperelastic analysis based on a polygonal finite element method

2017 ◽  
Vol 25 (11) ◽  
pp. 930-942 ◽  
Author(s):  
Amirtham Rajagopal ◽  
Markus Kraus ◽  
Paul Steinmann
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Element Method ◽  
Polygonal Finite Element

scholarly journals Combined Semianalytical and Numerical Static Plate Analysis. Part 1: Formulation of the Problem and Approximation Models

2018 ◽  
Vol 196 ◽  
pp. 01010
Author(s):  
Oleg Negrozov ◽  
Pavel Akimov ◽  
Marina Mozgaleva
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thin Plates ◽  
Geometrical Parameters ◽  
Element Mesh ◽  
Combined Application ◽  
Basic Dimension ◽  
Plate Analysis ◽  
Element Method ◽  
Approximation Models

The distinctive paper is devoted to solution of multipoint (particularly, two-point) 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). Discrete (within FEM) and discrete-continual (within DCFEM) approximation models for subdomains are under consideration.

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