横观各向同性层合板理论编程实现与验证  

Programming and Verification of Transverse Isotropic Laminate Plate Theory

作　　者：陈州 杜新喜[2] 张慎[1] 袁焕鑫[2] CHEN Zhou;DU Xin-xi;ZHANG Shen;YUAN Huan-xin(Central-south Architectural Design Institute Co.,Ltd.,Wuhan 430071,China;School of Civil Engineering,Wuhan University,Wuhan 430072,China)

机构地区：[1]中南建筑设计院股份有限公司,武汉430071 [2]武汉大学土木建筑工程学院,武汉430072

出　　处：《科学技术与工程》2022年第29期12716-12732,共17页Science Technology and Engineering

基　　金：住房和城乡建设部科学技术计划(2017-K5-014)。

摘　　要：板式构件因其自身特殊的几何形状,进行结构分析时,通常采用比实体单元效率更高的板(壳)单元。基于MATLAB编程,对刨花板材料构成的板式结构进行了有限元数值分析与静力荷载试验。首先,将横观各向同性材料本构方程应用于板式构件,得到了以刨花板为代表的三层结构复合材料层合板的力学性能本构关系。其次,介绍了基于Kirchhoff薄板及Mindlin-Reissner中厚板理论的离散Kirchhoff三角形(discrete Kirchhoff triangle, DKT)、离散Kirchhoff四边形(discrete Kirchhoff quadrilateral, DKQ)、离散剪切三角形(discrete shear triangle, DST)单元和离散剪切四边形(discrete shear quadrangle, DSQ)板有限单元的构造方法,并验证了各个板单元有限元数值解与理论精确解的收敛性能;通过将板构件在空间内组装,说明了材料参数及节点自由度在单元局部坐标系与空间整体坐标系间的转换方法。最后,通过对比板结构静力试验测量值与有限元模型数值解,分析了不同板单元对有限元计算结果的影响。结果表明,由于DST考虑了横向剪切作用,对复合材料层合板结构的力学性能模拟具有较好的计算精度。Due to its special geometry,plate(shell)elements are usually used for structural analysis,which is more efficient than solid elements.Finite elements analysis based on MATLAB programming of a plate structure made of particleboard materials and static load test were carried out.Firstly,the transversely isotropic material constitutive equation was applied to plate-form members,the constitutive relationship and mechanical properties of three-layer composite laminate(represented by particleboard)was obtained.Secondly,the construction methods of discrete Kirchhoff triangle(DKT),discrete Kirchhoff quadrilateral(DKQ),discrete shear triangle(DST),discrete shear quadrangle(DSQ)plate elements based on Kirchhoff thin plate and Mindlin-Reissner thick plate theories were introduced in detail,and the convergence performance between finite elements numerical solution and accurate theoretical solution of each plate element was verified.By assembling the plate members in space,law of change of reference for material parameters and nodal degrees of freedom between the element local and spatial global coordinate systems was explained.Finally,the influence of different plate elements on the numerical results of the finite elements model was analyzed by comparing with the measured value of the static load test of plate structure.The results show that the DST element has better calculation accuracy for the mechanical properties simulation of composite laminate structure due to the consideration of transverse shear effect.

关 键 词：板理论 横观各向同性 本构关系 层合板 刨花板 板有限元 Kirchhoff薄板 Mindlin-Reissner中厚板 

分 类 号：O342[理学—固体力学]