横观各向同性层合板理论编程实现与验证

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...

Programming and Verification of Transverse Isotropic Laminate Plate Theory

Due to its special geometry, plate (shell) elements are usually used for structural analysis, which is more efficient than solid elements. In this paper, finite elements analysis based on MATLAB programming of a plate structure made of particleboard materials and static load test are carried out. First, the transversely isotropic material constitutive equation is applied to plate-form members, then the constitutive relationship and mechanical properties of three-layer composite laminate (represented by particleboard) is obtained. Subsequently, the construction method of DKT DKQ DST DSQ plate elements based on Kirchhoff thin plate and Mindlin-Reissner thick plate theories is introduced in detail, and the convergence performance between finite elements numerical solution and accurate theoretical solution of each plate element is 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 is explained. Finally, the influence of different plate elements on the numerical results of the finite elements model is analyzed by comparing with the measured value of the static load test of plate structure.