新型厚薄通用的压电层合板三角形CDST-S6E单元  

New Piezoelectric Laminated Plate Element CDST-S6E for Both Thin and Thick Plate

作　　者：田娇[1,2] 蔡永昌[1,2] 戴子枢[1,2] 田龙岗[1,2] 

机构地区：[1]同济大学土木工程学院地下建筑与工程系,上海200092 [2]同济大学岩土及地下工程教育部重点实验室,上海200092

出　　处：《力学季刊》2013年第3期393-402,共10页Chinese Quarterly of Mechanics

摘　　要：基于压电复合材料层合板一阶剪切变形理论及叠层理论,构造了一种新型三角形三节点压电层合板单元,简记为CDST-S6E单元。该单元采用压电耦合的运动方程求解位移场及电势场,层合板主体结构用一阶剪切变形理论模拟,其剪应变场及单元转角场由结点包含有两个剪切自由度的DST-S6单元理论确定。电势作为附加自由度,应用叠层理论对压电层合板的电势场沿厚度方向进行线性插值。该CDST-S6E单元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,可较好避免厚薄板单元的剪切闭锁问题且具有简洁的表达形式。数值算例表明,CDST-S6E单元具有较高的精度,可以较为精确地预测压电层合板的变形及电势场,是一种厚薄通用的优质压电层合板单元。Based on the first-order shear deformation laminated plate theory（FSDT） and layerwise theory （LT）, a new three node triangular piezoelectric laminated plate element, labeled here as CDST-S6E, was proposed. The equations of motion were formulated using a coupled piezoelectric formulation solving for the mechanical displacement and electric potential fields. The composite host structure was modelled u- sing the first-order shear deformation laminate theory, the transverse shear strains and rotations of the element were the same with DST-S6 （Discrete Shear Triangular element with 6 extra Shear degrees of freedom）. Linear through-the-thickness electric potential distribution was assumed,while deals with a layerwise-type modelling of the electric potential considered as an additional degree of freedom. The pro- posed CDST-S6E can eliminate the shear locking, without any numerical expediencies such as the reduced integration, the use of assumed strains/stresses, or the need for the stabilization of the attendant zero en- ergy mode. Besides, the expression of the CDST-S6 is simple in formulation. Numerical example indicates that CDST-S6E, which has a higher precision then the other elements, can accurately predict both the mechanical displacement and electric potential fields of the piezoelectric composites. So this good element, which is suitable for both thin and thick laminated plates, can be used to solve the mechanic-piezoelectric coupling problem in the engineering.

关 键 词：压电复合材料 层合板 一阶剪切变形理论 叠层理论 剪切自由度 

分 类 号：TB33[一般工业技术—材料科学与工程] TU33[建筑科学—结构工程]