基于SQP优化和上限法的倾斜荷载下条形浅基础极限承载力计算

Bearing capacity calculation of strip footing under inclined loads with upper bound theorem and SQP method

对均质地基岩土体上条形基础承受倾斜荷载的情况,根据线性破坏准则和相关联流动法则,利用极限分析中的机动法,构建了一个承受倾斜荷载作用的条形浅基础的二维机动许可破坏模式。根据外力功率与内部耗能相等原理获得极限承载力的目标表达式,并把其转化成了一个求含有非线性约束的极限承载力上限解最小值问题计算模型。应用MATLAB软件平台,对建立的计算模型采用序列二次规划法(SQP法)进行了承载力上限解优化求解。研究结果表明:极限上限分析结合优化理论SQP法适用于该问题的求解;荷载的倾斜程度对条形基础地基承载力影响较大;相同计算参数条件下,构造刚性块较少的简单的相容速度场也能够求得较为精确的数值,因而计算的速度和效率也将得到大幅提高;影响参数分析表明,计算参数取值对极限承载力量值具有非线性影响且权重存在差别,将结果与已有文献资料进行了分析比较,所得结果较前人研究成果有一定改进。

Based on the linear failure criterion and associated flow rule, the bearing capacity of a strip footing under action of inclined loads problem was studied by means of the kinematical approach of limit analysis theory. And the planar knematically admissible failure mechanism was constructed elaborately for the calculation schemes. The objective functions of beating capacity were obtained by equating the work rate of extemal force to intemal dissipation along the velocity discontinuities, and then the objective functions were transformed as a upper- bound mathematic optimization model for beating capacity as low as possible. Based on the mathematic software MATLAB, the result of upper bound method for planar failure mechanism was obtained by use of the sequential quadratic programming （SQP）. From the numerical results, it can be seen that the extent of the inclined loads has a significant effect on the bearing capacity of strip footing. The same calculation parameters is given, the relatively precise value can be impetrated by using simple failure mechanisms, and the computational efficiency gotten at improvement in quantity. The parametric analysis indicates that preferences possessing nonlinear infection on the beating capacity and the solutions presented in this paper ameliorate appreciably with available predictions.