基于解析试函数的各向异性材料厚薄通用板单元  

THICK AND THIN PLATE ELEMENTS WITH ANISOTROPIC MATERIALS BASED ON ANALYTICAL TRIAL FUNCTIONS

作　　者：田歌[1] 傅向荣[1] 邓娇[1] 张鹏[1] 刘浩宇[1] 

机构地区：[1]中国农业大学水利与土木工程学院,北京100083

出　　处：《工程力学》2012年第11期65-70,79,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(10872108);国家重点基础研究发展计划项目(2010CB731503)

摘　　要：该文采用满足Kirchhoff假设的薄板理论,推导了各向异性材料系列解析试函数,并利用该系列解析试函数构造了一个四边形应力杂交板单元。首先,该文从薄板理论的基本方程出发,推导了各向异性材料薄板中面挠度w应满足的特征微分方程。然后,从该方程出发求得w的系列特征通解,由w特征通解可进一步求得广义位移、广义应变和广义应力的解析试函数。同时,根据广义应力利用平衡条件构造了相应的横向剪力解析试函数。最后,根据已有的广义应力和横向剪力解析试函数构造了一个四边形应力杂交板单元ATF-PH4。数值算例表明:上述方法构造出的单元模型有很好的精度、收敛性,且对网格畸变不敏感,同时能较好地解决板单元的厚薄通用性问题。In this paper, the Kirchhoff thin plate theory is applied to derive serial analytical trial functions of the plate with anisotropic materials. Then these functions are used to construct a quadrilateral hybrid stress plate element. Firstly, the deflection w of an anisotropic materials plate is derived from the differential equations of thin plate theory. Secondly, the analytical trial functions of generalized displacements/strains/stresses of thin plate theory are obtained from the general characteristics solution of w. Thirdly, the generalized shear stresses are derived from the generalized stresses according to the equations of equilibrium. Finally, a quadrilateral hybrid stress plate element ATF-PH4 is constructed with the analytical trial functions of generalized stresses and generalized shear stresses. The numerical examples show that the element thusly constructed has high precision, good convergence, and is not sensitive to the mesh distortion. And it fits to both thick and thin plate problems.

关 键 词：复合材料 解析试函数 薄板单元 网格畸变 特征通解 厚薄通用板 

分 类 号：O302[理学—力学]