岑松, 龙志飞. 对转角场和剪应变场进行合理插值的厚板元[J]. 工程力学, 1998, 15(3): 1-14.
引用本文: 岑松, 龙志飞. 对转角场和剪应变场进行合理插值的厚板元[J]. 工程力学, 1998, 15(3): 1-14.
Cen Song, Long Zhifei. A MINDLIN TRIANGULAR PLATE ELEMENT WITHIMPROVED INTERPOLATION FOR THE ROTATION ANDSHEAR STRAIN FIELDS[J]. Engineering Mechanics, 1998, 15(3): 1-14.
Citation: Cen Song, Long Zhifei. A MINDLIN TRIANGULAR PLATE ELEMENT WITHIMPROVED INTERPOLATION FOR THE ROTATION ANDSHEAR STRAIN FIELDS[J]. Engineering Mechanics, 1998, 15(3): 1-14.

对转角场和剪应变场进行合理插值的厚板元

A MINDLIN TRIANGULAR PLATE ELEMENT WITHIMPROVED INTERPOLATION FOR THE ROTATION ANDSHEAR STRAIN FIELDS

  • 摘要: 本文提出构造厚板三角形元的一种合理方法,先按Timoshenko厚梁理论导出单元各边的转角和剪应变公式,然后进行合理插值,导出单元的转角场、曲率场和剪应查场。当板的厚度变小时,厚梁理论自动退化为薄梁理论,各边剪应变以及单元剪应变插值函数自动退化为零,厚板单元自动退化为薄板单元,彻底消除了剪切闭锁现象。此单元对厚板和薄板都给出高精度的结果。

     

    Abstract: Abstract A rational approach to formulate Mindlin triangular element is proposed in this paper. Firstly, the variation functions of rotation and shear strain along each side of the element are determined based on the Timoshenko beam theory. Secondly, the rotation, curvature and shear strain fields in the domain of the element are determined with improved interpolation. The resulting element is free of shear locking in the case of thin plates. Numerical examples show that the element, called TMT, is a high-performance element for thick and thin plates.

     

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