完全隐式返回映射算法对岩土地基问题的求解

FULLY IMPLICIT RETURN MAPPING ALGORITHM FOR SOLVING THE PROBLEMS OF GEOTECHNICAL FOUNDATION

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。

To solve complicated mechanics problems in geotechnical engineering, the finite element program is compiled with fully implicit integration algorithm which is return mapping algorithm of non-associative isotropic hardening Drucker-Prager criterion based on the elastic-plastic mechanics theory frame and the nonlinear finite element theory. Return mapping algorithm can avoid the drift phenomenon of the trial stress, and can achieve the accurate solution of the constitutive equation on the condition of the quasi-static deformation, a quadratic convergence rate when using the Newton-Raphson iteration scheme, higher accuracy and stability. To solve the problems of foundations in geotechnical engineering, displacements and stresses are calculated, and the evolution process of plastic zones is simulated. The ultimate bearing capacity of the analytical solution is compared with that from the numerical solution. The results demonstrate the superiority of the algorithm, and the correctness and the practicality of the program.