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针对岩土工程中的复杂力学问题,在弹塑性力学理论框架和非线性有限元理论基础上,采用非关联等向硬化Drucker-Prager模型的完全隐式积分算法—返回映射算法(Return MappingAlgorithm)编制了有限元求解程序。该算法可以避免预测应力漂移屈服面的现象,对准静态变形条件下的本构方程可以获得准确解,在迭代中使用Newton-Raphson法获得近似平方的收敛速率,具有较高的精确性和稳定性。对岩土工程中的地基问题进行求解,计算得出位移、应力等结果,模拟了塑性区随载荷步增加的演化过程,对地基极限承载力进行了解析解和数值解的对比。结果表明了算法的优越性、程序的正确性和实用性。
Aiming at the problem of complex mechanics in geotechnical engineering, based on the theory of elasto-plastic mechanics and the nonlinear finite element theory, a complete implicit integration algorithm of the uncorrelated isotropic hardening Drucker-Prager model - Return Mapping Algorithm Finite element solver. The algorithm can avoid the phenomenon of stress drift yield surface, and get the accurate solution to the constitutive equation under static deformation. In the iteration, the Newton-Raphson method is used to obtain the approximate squared convergence rate with high accuracy and stability Sex. The solution to the problem of foundation in geotechnical engineering is given. The displacement and stress are calculated. The evolution of plastic zone with load step is simulated. The analytical solution and numerical solution are compared with the ultimate bearing capacity of foundation. The results show the superiority of the algorithm, the correctness and practicability of the program.