具裂縫Mindlin方形板之有限元應力分析

Abstract

利用有限元素法較易於模擬複雜幾何之特性。本研究以二階形狀函數之有限元素法配合角函數，並求解具裂縫之Mindlin方形厚板靜力問題。角函數僅疊加於奇異點處之區域，用於描述裂縫尖端附近之應力奇異行為。本論文以收斂性分析，驗證所發展分析方法及電腦程式之正確性；並進一步探討具不同支承邊界條件、靜載、寬厚比及不同裂縫配置之方形厚板，對奇異點附近內力分佈之影響。依據結果顯示，在奇異點處加入角函數確實能有效率地提升奇異點附近內力解之準確性。

It is well known that finite element approaches can describe the complex geometry of the problem under consideration very well. The work supplements corner functions to the traditional finite element solutions and solves the static problems for cracked square Mindlin plates. Corner functions are used only in the region near the crack tip to describe properly the stress singularity behaviors at the neighborhood of the crack tip. Convergence study is carefully performed to ensure the correctness of the proposed approach and the developed computer code. Then, the approach is applied to investigate the distribrtions of the stress resultants near the crack tips of cracked square plates with various boundary conditions, thickness to side length ratios, loading conditions and crack configurations. The obtained results show that the corner functions indeed enhance the accuracy of the solutions for stress resultants near the crack tip.