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Hamiltonian system in anisotropic plate bending problems in the application

Author: SuBin
Tutor: ZhongWanZuo；YaoWeiAn
School: Dalian University of Technology
Course: Computational Mechanics
Keywords: Anisotropy Plate bending Hamiltonian system Separation of variables Eigenfunction expansion
CLC: O343.8
Type: Master's thesis
Year: 2000
Downloads: 227
Quote: 2
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Abstract


In the plane elasticity and plate bending similarity exists between the basic equation of the same biharmonic equation, plane elastic strain , stress function - stress relationships , stress - strain relation corresponding to plate bending moment , deflection - curvature relationship moment - curvature relationship . Modeled on the plane elasticity , acrid system can also be used to solve plate bending problems . From the variational principle to proceed, and HR from anisotropic plates available dual variational principle equations and Hamiltonian operator matrix , separation of variables become transverse Hamiltonian matrix eigen problem . Its eigenvectors between Conjugate orthogonal relationship , so either a full state vector always be eigensolutions to expand . For nonzero Eigensolution write the general solution of the form into two sides of the boundary conditions are non-zero eigenvalues ??on transcendental equation can be obtained non-zero eigenvalues ??, and then get a nonzero eigenvector . According Conjugate orthogonal expansion theorem can be written according to the nature of the domain satisfy equations and boundary conditions are two sides of an expression into both ends of the boundary conditions which can be obtained with constant coefficients in the solution of the original problem . This paper presents an analytical solution of several examples , the results showed several before taking the eigenvalues ??can achieve high accuracy. New Methods of separation of variables , eigenfunction expansion method gives the analytical solution of anisotropic rectangular plates , breaking the limitations of traditional methods , and has broad application prospects.

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CLC: > Mathematical sciences and chemical > Mechanics > Solid Mechanics > Elasticity > Anisotropic elasticity
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