Stochastic Response Analysis of FRP using the Second-Order Perturbation-Based Homogenization Method

Abstract

本論文は,微視的不確実性を考慮した繊維強化複合材料の均質化問題のための摂動ベース均質化法を用いた確率的応答解析について議論する。一次摂動ベース均質化法を用いた期待値と分散のような確率的特性の推定結果は,ある場合には大きな誤差を含むので,二次以上の摂動法の適用性と有効性を調べるべきである。本論文では,まず,二次摂動ベース均質化法を定式化した。直交異方性材料の等価弾性定数の確率的特性を推定するための二次摂動ベース手法も導入した。次に,二次摂動ベース確率的均質化法を,ミクロ組織の材料特性の不確実性により生じる均質化弾性特性の確率的解析に適用した。数値例として,微視的な材料不確実性に起因する一方向繊維強化プラスチックの均質化弾性特性の確率的特性を,1次および2次摂動法であるMonte‐Calroシミュレーションを用いて推定した。また,均質等方性材料の詳細な確率解析を行った。数値結果から,二次摂動法の有効性と問題点を示した。This paper discusses a stochastic response analysis using the perturbation-based homogenization method for a homogenization problem of a fiber-reinforced composite material considering microscopic uncertainty. Since an estimated result of the stochastic characteristics such as the expectation and variance using the first order perturbation-based homogenization method includes a large error in some cases, applicability and effectiveness of the second or higher order perturbation method should be investigated. In this paper, at first, the second-order perturbation-based homogenization method is formulated. A second order perturbation-based procedure for estimating the stochastic characteristics of equivalent elastic constants of an orthotropic material is also introduced. Next, the second-order perturbation-based stochastic homogenization method is applied to the stochastic analysis of a homogenized elastic property caused by uncertainty in material property of a microstructure. As a numerical example, the stochastic characteristics of the homogenized elastic properties of a unidirectional fiber reinforced plastic caused by the microscopic material uncertainty are estimated using the Monte-Calro simulation, the first and second order perturbation method. Also, a detailed stochastic analysis for a homogeneous isotropic material is performed. From the numerical results, effectiveness and a problem of the second-order perturbation method are illustrated.