Limit Analysis of Functionally Graded Pressure Vessels

功能梯度材料壓力容器之極限分析

呂學育(Shyue-Yuh Leu) ； 洪得瑋(De-Wei Hung) ； 徐豪健(Hao-Chien Hsu)

《中華技術學院學報》 40期 (2009/06) Pp. 465-477

https://doi.org/10.7095/JCIT.200906.0465

摘要

本文旨在考慮功能梯度材料之厚壁圓柱壓力容器，利用極限分析理論求解塑性極限內壓。文中採用von Mises降伏準則，並且考量功能梯度材料之降伏強度為沿徑向作變化。首先依據極限分析理論的下限及上限之問題陳述，進行塑性極限內壓之解析推導，而分別得到塑性極限內壓之下限解及上限解，並由所得之下限解及上限解的相等性，從而得到功能梯度材料之厚壁圓柱壓力容器的塑性極限內壓的封閉型式正解。特別地，文中亦利用一綜合平滑化及持續逼近的計算法，進行有限元素極限分析，以提供塑性極限內壓之上限數值結果。藉由封閉型式正解與上限數值結果的良好吻合性，可驗證本文所推導之解析結果的正確性。

關鍵字

極限分析 ； 塑性極限內壓 ； 有限元素極限分析 ； 厚壁圓柱容器 ； 功能梯度材料 ； von Mises降伏準則

並列摘要

The paper is aimed to perform limit analysis of thick-walled cylindrical pressure vessels made of functionally graded materials under internal pressure. The von Mises yield criterion was adopted in the derivations and the yield strength was considered to vary radially. By conducting analytically both static and kinematic limit analysis, the equality relation between the greatest lower bound and the least upper bound was confirmed explicitly. Accordingly, exact closed-form solutions of plastic limit pressure were developed for thick-walled cylindrical vessels made of functionally graded materials. Particularly, numerical effort of finite-element limit analysis using a combined smoothing and successive approximation (CSSA) algorithm was also made for rigorous validations. Finally, good agreement between analytical solutions and numerical results validates the derivations presented in the paper.

並列關鍵字

Limit analysis ； Plastic limit pressure ； Finite-element limit analysis ； Thick-walled cylindrical vessel ； Functionally graded materials ； Von Mises yield criterion