Analysis of thin plates by the weak form quadrature element method

作者：Zhong HongZhi^*; Yue ZhiGuang

来源：Science China Physics,Mechanics & Astronomy, 2012, 55(5): 861-871.

DOI：10.1007/s11433-012-4684-y

• C-1 continuity
• mesh distortion
• thin plate
• weak form quadrature element

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 C-1 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.

• 出版日期2012-5
• 单位清华大学