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Using Fourier Series Method Analyze the Bucking of Rectangular Moderately-thick Plates with Multi-Edges

Author: YingYing
Tutor: WangKeLin；LiuXinDong
School: Xi'an University of Architecture and Technology
Course: Engineering Mechanics
Keywords: Fourier series Re trigonometric series Rectangular plate Orthotropic Flexion
CLC: O343
Type: Master's thesis
Year: 2009
Downloads: 81
Quote: 0
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Abstract


In this paper, based on the transverse shear deformation theory of anisotropic rectangular plate ( АмьарцумянСА.ТеорияАнизотропныхПластин ) , derivation and references orthotropic rectangular plate buckling control differential equations and a variety of internal force expression , the use of Fu Fourier series method and re- trigonometric series discussed by a computer program and the detailed process of the exact solution . In this paper, using the method of Fourier series , the introduction of the re - trigonometric series to solve the problem . The use of Fourier series expansion of the anti- symmetry , any deflection angle, torque and buckling load into the heavy form of trigonometric series . Will control the decomposition of differential equations and boundary conditions , in accordance with the principle of superposition Finally, according to the boundary conditions and superimposed combination , simplification , the expression a simple and uniform , so the differential equation simplifies into algebraic equations , and ultimately get this problem into solving the matrix the generalized eigenvalue problem and find the critical force , the calculation is greatly simplified . Finally, the paper several analysis using MATLAB programming examples , drawn by the program board deformation maps under different parameters , easy visual comparison and verification . The main purpose of this paper is to solve the anisotropic rectangular plate buckling problems in a variety of boundary conditions . The research work of this paper enriches the theory of plate . The results of this study can be widely applied to the plate for the design and construction of model engineering examples , solve practical problems to solve , have a good guide .

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