An exact element method for bending of nonhomogeneous thin plates

1992 ◽  
Vol 13 (8) ◽  
pp. 683-690 ◽  
Author(s):  
Ji Zhen-yi ◽  
Yeh Kai-yuan
Keyword(s):  
Thin Plates ◽  
Exact Element Method ◽  
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.

Postbuckling Analysis of Plates Under Combined Loads by a Mixed Finite Element and Boundary Element Method

1993 ◽  
Vol 115 (3) ◽  
pp. 262-267 ◽  
Author(s):  
J. Q. Ye
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Mixed Boundary ◽  
Mixed Finite Element ◽  
Plane Deformation ◽  
Thin Plates ◽  
Combined Loads ◽  
Element Method

The postbuckling behavior of thin plates under combined loads is studied in this paper by using a mixed boundary element and finite element method. The transverse and the in-plane deformation of the plates are analyzed by the boundary element method and the finite element method, respectively. Spline functions were used as the interpolation functions and shape functions in the solution of both methods. A quadratic rectangular spline element is adopted in the finite element procedure. Numerical results are given for typical problems to show the effectiveness of the proposed approach. The possibilities to extend the method developed in this paper to more complicated postbuckling problems are discussed in the concluding section.

scholarly journals Energy Flow Boundary Element Method for Vibration Analysis of One and Two Dimension Structures

2008 ◽  
Vol 15 (1) ◽  
pp. 33-50 ◽  
Author(s):  
Ho-Won Lee ◽  
Suk-Yoon Hong ◽  
Do-Hyun Park ◽  
Hyun-Wung Kwon
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
High Frequency ◽  
Energy Flow ◽  
Vibration Analysis ◽  
Thin Plates ◽  
Two Dimensional ◽  
Flow Boundary ◽  
Energy Equations ◽  
Element Method

In this paper, Energy Flow Boundary Element Method (EFBEM) was developed to predict the vibration behavior of one- and two-dimensional structures in the medium-to-high frequency ranges. Free Space Green functions used in the method were obtained from EFA energy equations. Direct and indirect EFBEMs were formulated for both one- and two-dimensional cases, and numerically applied to predict the energy density and intensity distributions of simple Euler-Bernoulli beams, single rectangular thin plates, and L-shaped thin plates vibrating in the medium-to-high frequency ranges. The results from these methods were compared with the EFA solutions to verify the EFBEM.

scholarly journals Transverse Vibration of the Thin Plates: Frequency-Domain Spectral Element Modeling and Analysis

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Ilwook Park ◽  
Usik Lee ◽  
Donghyun Park
Keyword(s):  
Frequency Domain ◽  
Computational Efficiency ◽  
Element Model ◽  
Spectral Element ◽  
Thin Plates ◽  
Plate Element ◽  
Kantorovich Method ◽  
Arbitrary Boundary ◽  
Finite Plate ◽  
Element Method

It has been well known that exact closed-form solutions are not available for non-Levy-type plates. Thus, more accurate and efficient computational methods have been required for the plates subjected to arbitrary boundary conditions. This paper presents a frequency-domain spectral element model for the rectangular finite plate element. The spectral element model is developed by using two methods in combination: (1) the boundary splitting and (2) the super spectral element method in which the Kantorovich method-based finite strip element method and the frequency-domain waveguide method are utilized. The present spectral element model has nodes on four edges of the finite plate element, but no nodes inside. This can reduce the total number of degrees of freedom a lot to improve the computational efficiency significantly, when compared with the standard finite element method (FEM). The high solution accuracy and computational efficiency of the present spectral element model are evaluated by the comparison with exact solutions and the solutions by the standard FEM.

Finite Element Method for Analysis of Flexural Vibration Propagating in Ternary Phononic Crystal Thin Plates

2012 ◽  
Vol 256-259 ◽  
pp. 596-599
Author(s):  
Zong Jian Yao ◽  
Gui Lan Yu ◽  
Yue Sheng Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Point Defect ◽  
Phononic Crystal ◽  
Flexural Vibration ◽  
Expansion Method ◽  
Square Lattice ◽  
Thin Plates ◽  
Response Curves ◽  
Element Method

Propagation of flexural vibration in a ternary phononic crystal thin plate with a point defect are explored using finite element method. The thin concrete plate is composed of steel cylinders hemmed around by rubber with a square lattice. Absolute band gaps, point defect bands and transmission response curves with low frequency are investigated. Comparing the results of finite element method with that of improved plane wave expansion method, precise identifications are obtained to identify the point defect states. The results show that the finite element method is suitable for the exploring of flexural vibration propagating in ternary phononic crystal thin plates.

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