Differential quadrature method based on basis function satisfying multiple boundary conditions and its application
A modified differential quadrature method(MDQM)based on the basis functions satisfying multi-ple boundary conditions is proposed.The basis function of deflection is constructed to satisfy all the boundary conditions of beam by integration of multiple times,and then the weighting coefficient matrix in the differential quadrature method can be calculated using the basis function.Thus,the proposed method solves the prob-lem that it is difficult to use multiple boundary conditions at the same point when calculating the weighting co-efficient matrix by polynomial test function.In order to study the application of this method in various beam analyses,the deflection function corresponding to two kinds of beams under various boundary conditions is constructed at first.According to the vibration theory and stability theory of Euler-Bernoulli beam,the prob-lems of calculating the fundamental frequency and critical load of the beam are transformed into problems of solving the matrix eigenvalue based on the DQM,and the results are compared with the exact solution.In ad-dition,based on the plane bending theory of the elastic-plastic beam,the proposed method is applied to calcu-late the elastic-plastic displacement of beam under various boundary conditions,and the results are compared with those in literature.The results show that the proposed method has high computational efficiency and accu-racy for the stability analysis,fundamental frequency analysis and elastoplastic analysis of beams.
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