三维地基极限承载力的数值极限分析

根据塑性下限定理,借助有限元技术,建立了极限承载力三维情况下的锥形规划形式。采用原-对偶内点法求解非线性规划问题,基于相应的理论计算框架,构造满足条件的静态容许应力场。该方法克服了屈服函数的线性化或光滑近似;利用对偶性,在求解下限解的同时获得对偶命题(上限)的解。与矩形基础地基极限承载力解析结果比较,精度和准确性有了较大提高;对刚、柔性基础下的地基极限承载力的特性也作了探讨。数值极限分析为计算矩形地基的极限承载力提供了一种简便有效的方法。

3D analysis of ultimate bearing capacity by numerical limit analysis

Based on the lower bound theorem of classical plasticity,the 3D limit analysis of rigid-perfect plastic structures was performed as a discrete nonlinear mathematical(second-order cone) programming problem by means of finite element technique.A statically admissible stress field was constructed derived from the solution of the lower bound nonlinear programming problem,which was obtained by primal-dual interior point method.The theoretical calculation framework was also presented.Both the linearization and the approximation process for 3D yield function could be removed by adopting nonlinear programming.Based on the duality with the lower bound and the upper bound,the solutions of the primal and the dual problem could be solved at the same time.The characteristics of rigid and flexible foundations were also discussed.It was shown by comparison with analytical solutions that the numerical analysis strategy was vastly superior in terms of the correctness and effectiveness of the procedure.A simple and effective computing method for the ultimate bearing capacity of foundations was provided by the 3D limit analysis.