Refined 9-Dof triangular Mindlin plate elements

摘要

Based on the Mindlin/Reissner plate theory, two refined triangular thin/thick plate elements, the conforming displacement element DKTM with one point quadrature for the part of shear strain and the element RDKTM with the re-constitution of the shear strain, are proposed. In the formulations the exact displacement function of the Timoshenko's beam is used to derive the element displacements of the refined elements. Numerical examples are presented to show that the present models indeed possess properties of high accuracy for thin and thick plates, is capable of passing the patch test required for Kirchhoff thin plate elements, and does not exhibits extra zero energy modes. The element RDKTM is free of locking for very thin plate analysis and its convergence can be ensured theoretically. However, the element DKTM is not free of shear locking when the thickness/span ratios less than 10~(-2).