微分幾何学を用いた回位のモデリングと応力場の数値解析

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  • Modeling and numerical analysis of stress fields around a disclination on the basis of differential geometry

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<p>In this study, we conduct isogeometric analysis to obtain the internal stress field around wedge disclination. Our formulation is based on the continuous theory of disclinations developed by Yavari and Goriely. In this framework, distributed disclinations are identified as the curvature tensor in a Riemann manifold. Riemann metric in the manifold is determined by using Cartan structural equation in differential geometry. Elastic deformation is obtained so as to minimize the strain energy functional by numerically solving weak form of nonlinear stress equilibrium equation. The distribution of the second Piola-Kirchhoff stress tensor around the disclination, which is obtained by the numerical analysis, agreed qualitatively well with the previous study reported by Lazar.</p>

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