变厚度多层介质结构的一种三维数值半解析方法

A New 3 D Numerical Semi analytical Algorithm for Multiply Composite Structures with Varied Thickness

应用复合材料层合结构分层理论思维，建立起以样条函数、级数及插值相结合的新型三维数值半解析算法，以期解决复材层合变厚度结构的变形及内力分析，并作为该类型结构优化设计的高精度内核计算工具。本文方法克服了一般半解析方法对解析函数类型的过分依赖性；在原始数据准备、计算规模、数值精度、收敛特性及稳定性诸方面都较有限元方法有显著改善；特别对复材层合结构的变厚度区段，无需引入任何理论假设。

Based on stratified theoretical methodology of composite laminates, a new 3 D numerical semi analytical algorithm for multiply composite structures has been established, which constructs its displacement functions through the combination of spline function, functional series and numerical interpolation. This present algorithm overcomes dependence on the selection of analytical functions for different loading conditions in normal semi analytical methods, and no special assumptions are needed for varied thickness structural region of composite laminates. Compared with ordinary finite element method, this method has taken noticeable advantages and much better improvement on data preparation, numerical accuracy, convergence and stability, which are shown by some numerical examples.