摘要
The recently proposed weak form quadrature element method （QEM） is applied to flexural and vibrational analysis of thin plates The integrals involved in the variational description of a thin plate are evaluated by an efficient numerical scheme and the par- tial derivatives at the integration sampling points are then approximated using differential quadrature analogs. Neither the grid pattern nor the number of nodes is fixed, being adjustable according to convergence need. The C~ continuity conditions char- acterizing the thin plate theory are discussed and the robustness of the weak form quadrature element for thin plates against shape distortion is examined. Examples are presented and comparisons with analytical solutions and the results of the finite element method are made to demonstrate the convergence and computational efficiency of the weak form quadrature element method. It is shown that the present formulation is applicable to thin plates with varying thickness as well as uniform plates.
The recently proposed weak form quadrature element method(QEM) is applied to flexural and vibrational analysis of thin plates.The integrals involved in the variational description of a thin plate are evaluated by an efficient numerical scheme and the partial derivatives at the integration sampling points are then approximated using differential quadrature analogs.Neither the grid pattern nor the number of nodes is fixed,being adjustable according to convergence need.The C1 continuity conditions characterizing the thin plate theory are discussed and the robustness of the weak form quadrature element for thin plates against shape distortion is examined.Examples are presented and comparisons with analytical solutions and the results of the finite element method are made to demonstrate the convergence and computational efficiency of the weak form quadrature element method.It is shown that the present formulation is applicable to thin plates with varying thickness as well as uniform plates.
基金
supported by the National Natural Science Foundation of China (Grant Nos.51178247 and 50778104)
the National High Technology Research and Development Program of China (Grant No.2009AA04Z401)
