複合板の線形マルチスケール解析のための数値平板試験

• 発表時期：2015年1月
• 著者：寺田 賢二郎, 平山 紀夫, 山本 晃司, 松原 成志朗
• 学会/論文誌名：日本計算工学会論文集 Vol. 2015

内容

A new method of multi-scale analyses for composite plates with in-plane periodic heterogeneity is proposed. While a thick plate model with transverse shear deformation is employed at macro-scale, the micro-scale governing equations are formulated as three-dimensional solids. The homogenization process to evaluate the macroscopic plate stiffnesses is called “numerical plate testing” (NPT) in this study, which is in fact a series of microscopic analysis on a unit cell. The specific functional forms of microscopic displacements are assumed so that the relationship between the macroscopic generalized resultant stresses and strains/curvatures to be consistent with the microscopic equilibrated state. In order to perform NPT by using general-purpose FEM software, we introduce the control nodes to faciliate the multiple-point constraints equivalent to the inplane periodicity conditions of heterogeneity-induced fluctuated displacement fields. In numerical examples, unit cells of homogeneous and laminated composite plates are used to demonstrate that the proposed method of NPT reproduces the plate stiffness in classical plate and laminate theories. We also perform a series of NMT (or homogenization analysis), macroscopic and localization analyses for an in-plane heterogeneous composite plate to validate the proposed method.