【摘要】 本文以Mindlin-Reissner理论为基础推导出一种包括剪切变形的三角形板弯曲单元体,它以“自由公式”的形式通过“单体检验”,保证收敛于精确解。以一种特殊的方式计及剪切变形,利用板的平衡方程,几何关系和本构关系得到剪应变与板厚的平方成正比,随着板厚的减小Kirchhoff假设自动满足。因此,这种单元体通用于中厚板和薄板,不会出现“剪切闭锁”现象,也不存在多余零应变模式。用于各种不同形状中厚板、薄板分析中都得到很好的数值结果。这种单元体具有公式简单、精度高、收敛快等优点。更多还原

【Abstract】 In this paper a triangular plate bending element based on the Mindlin Reissner theory is described. The element passes IE(individual element) test by way of the so-called "free formulation" . Convergence to the correct solutions is guaranteed. A special way with the local equilibrium equations, the constitutive and geometrical relations is used to account for shear deformations which are proportional to square of plate thickness. In the limit of thin plates the Kirchhoff assumption is satisfied automatically. There is no "shear locking" difficulty. No spurious zero energy modes exist with the element. Very good numerical results of both deflections and stresses have been obtained by applying the element to analysing plates with various geometries and thickness. Some of the results are presented. The element has the advantages such as simple formulation, high accuracy, rapid convergence and so on.更多还原