三維異向性材料旋轉體與楔形體之應力奇異性分析

Abstract

本研究為探討三維異向性材料旋轉體及楔型體於邊界與材料性質不連續處之應力奇異性。利用特徵函數展開法，並結合級數解之技巧以建立旋轉體及楔形體之彈性應力奇異性漸進解。該漸進解為直接求解以位移分量表示之三維力平衡方程式。利用比較文憲中等向性材料之結果確認本研究所推導解之正確性。本研究考慮組成旋轉體與楔形體之材料可為等向性材料(Isotropic material)、正交性材料(Orthotropic material)及三斜晶體（Triclinic material）。數值結果顯示單一異向性材料或雙材料(正交性/等向性，三斜晶體/等向性)之奇異性階數，明顯受幾何形狀、邊界條件與材料性質之影響。此些結果均見於文獻，可做為將來發展數值解之比對。

The work investigates the stress singularities induced by discontinuities of boundaries or material properties in anisotropic bodies of revolution and wedges. An eigenfunction expansion approach is combined with a power series solution technique to establish the asymptotic solutions around the singular points in bodies of revolution and wedges. The asymptotic solutions are developes by directly solving the 3D equations of equilibrium in terms of displacement components. The correctness of the proposed solutions are validated by comparing the present results with the published ones for isotropic bodies of revolution and wedges. Bodies of revolution and wedges under consideration are made of isotropic, orthotropic or triclinic materials. Numerical results reveal that the geometrically-induced stress singularities in bodies of revolution or wedges made of a single anisotropic material or two materials (orthotropic/isotropic, triclinic/isotropic) are significantly affected by geometry, boundary conditions and material properties. The present results can be used as a check on the solutions via numerical techniques such as finite element approaches.