复合材料正交加筋板在横向载荷下挠度计算的半解析法

本文采用一种新的半解析法，即独特利用Heaviside函数建立与加筋板等效的变刚度模型来开展复合材料双向正交加筋板在横向载荷下的弯曲挠度分析．此模型可以准确地描述筋条在板面上的分布，以及由于筋条的存在而导致的板面刚度不均匀分布．使用Galerkin加权残值法求解该模型的控制方程，得到不同边界条件和载荷情况下的级数解．对于双向正交加筋板，将此半解析法的结果与传统均匀化方法和使用商业有限元软件ABAQUS建立的有限元模型所得到的弯曲挠度结果比较，验证了此方法的准确性和优越性．不同于传统均匀化方法，本双向正交加筋板的弯曲挠度半解析法可精确、有效地获取加筋间的局部弯曲挠度，可以促进复合材料结构的设计分析与优化的研究进展．

A Semi-Analytical Method for Deflection Analysis of Orthogonally-Stiffened Laminated Composite Plates under Transverse Loading

A new semi-analytical method using Heaviside function to establish an equivalent plate model with variable stiffness is developed to analyze the bending deflection of orthogonally-stiffened laminated composite plates under transverse load. The equivalent plate model can accurately describe the distribution of stiffeners along both directions of the plate and the uneven distribution of plate stiffness caused by the existence of stiffeners. The Galerkin method is used to solve the governing equations, and the series solutions under different boundary conditions and loads are obtained. For the plates with both longitudinal and transverse stiffeners, the results of the present semi-analytical method are compared with those obtained by the traditional stiffener homogenization (smeared) method and the finite element method using the commercial finite element software ABAQUS, verifying the accuracy and effectiveness of the present semi-analytical method. Different from the traditional smeared method, the present semi-analytical solution of the orthogonally-stiffened plates is capable of capturing the local deflection between the stiffeners, and thus can boost the design analysis and optimization of orthogonally-stiffened laminated composite plates.