含剪切自由度的厚薄通用三角形层合板单元

A New Laminated Plate Element CDST S6 for Thin or Thick Plates

摘要:

基于1阶剪切变形理论（FSDT），构造了一种新型的消除剪切闭锁的三角形层合板单元，简记为CDST S6单元.该单元剪应变场及单元转角场由结点包含有2个剪切自由度的DST S6单元理论确定，不需要借助减缩积分，假设应力或应变等辅助数学手段，也不会产生对稳定性带来影响的附加零能模式，较好地解决了厚薄板单元的剪切闭锁难题，且其公式推导过程和最终的表达式比目前能考虑剪切变形的绝大多数层合板单元更为简单，可方便地进行有限元数值求解分析.数值算例表明，CDST S6单元有较高的精度和收敛性，是一种厚薄通用的优质层合板单元.

Abstract:

Based on the first order shear deformation laminated plate theory (FSDT), a new three node triangular laminated plate element, labelled here as composite discrete shear triangular element with 6 extra shear degrees of freedom(CDST S6), is proposed. The transverse shear strains and rotations of the element are the same with DST S6. The proposed CDST S6 can eliminate the shear locking without any numerical expediencies such as the reduced integration, the use of the assumed strains/stresses, or the need for the stabilization of the attendant zero energy mode. The expression of the CDST S6 is simple in formulation and easy to be implemented by using finite element method. Numerical examples indicate that the element has high accuracy and high convergence rates for solving thin or thick laminated plates.