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中文摘要：
极限分析上限元法常用三角形常应变单元和线性化的莫尔–库仑屈服函数来形成较易求解的线性规划模型。针对四边形单元上限法不能充分利用线性规划算法的不足,通过对单元建立积分意义上的协调方程的弱形式,得到可以调整单元内部速度场的线性化的协调方程,从而可以克服插值速度场为非线性的缺点,有着更好的求解效率和收敛性。引入双曲线强度折减到四边形单元上限法,可以较快地得到边坡最终安全系数和临界滑动速度场,2个算例说明了该方法的正确性。
英文摘要：
Triangular meshes together with the linearized Mohr-Coulomb criterion are commonly used in the finite element upper bound solution to form a linear programming model. In addition to higher accuracy and solution efficiency,quadrilateral meshes can adjust the velocity field of the element and converge more rapidly to the realistic upper bound solution. To overcome the shortcoming that the linear programming algorithm cannot be implemented directly for quadrilateral meshes,a weak form of compatibility equations was established based on the integration over the whole elements and the linearization of the compatibility equations was obtained for linear programming. With the hyperbolic strength reduction,the final safety factor of slope and the critical field of slipping velocity were obtained quickly. The validity of the method was verified with two examples.
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