基于弹塑性有限元分析土工安定性计算方法及其应用

Shakedown analysis of soil structures based on elasto-plastic FEM

将弹塑性有限元法与安定性分析的 Melan静力型定理相结合发展了一种土工极限分析与安定性分析的数值计算方法 ,依此可以预测一般土工结构的极限荷载和安定荷载 .利用弹塑性分析求解弹塑性应力场与弹性应力场 ,构造安定性分析所需的残余应力场 ,摆脱了传统分析方法中的大型数学规划运算 ,解决了计算中的维数障碍问题 .残余应力场的构造与土工结构的弹塑性分析是同时进行的 ,而且无需对屈服面进行线性化处理 ;求解的精度依赖于弹塑性分析 .通过算例 ,验证分析方法与计算程序是可靠的 ,并利用此方法计算了条形地基的极限荷载与安定荷载 .

The computational method which combines elasto-plastic analysis with Melan's theorem is applied to evaluate limit loads and shakedown loads of soil structures. Elasto-plastic analyses are performed to obtain elasto-plastic stress field and elastic stress field. Then a residual stress field is constructed. This methodology avoids the operation of mathematical programming in traditional method of shakedown analysis, and therefore obstruction due to large scale mathematical programming is overcome. The method for constructing a residual stress field based on the elasto-plastic analysis of soil structures doesn't need linearization of the yield condition. The accuracy of numerical solution depends on elasto-plastic analysis. Two numerical examples show that the computed results are in good agreement with theoretical solutions available. Finally, limit loads and shakedown loads of strip footing are computed by this method.