基于半隐式积分方案统一强度理论ANSYS二次开发

发布时间：2018-06-20 23:14

  本文选题：半隐式向后欧拉法 + Steffensen迭代法　； 参考：《岩土力学》2017年10期

【摘要】：目前,岩土工程中常用的塑性屈服准则多为局部不可导的分段函数,在隐式有限元求解中均采用显式向前欧拉法更新应力和Newton-Raphson迭代法求解方程。但显式向前欧拉法容易导致应力偏离屈服面和计算不收敛,而Newton-Raphson迭代法需频繁求导,对于分段函数而言这些方法均不利于求解。为此,提出了采用半隐式向后欧拉法和免导数的Steffensen迭代法联合更新应力与一致切线模量的方案。根据上述方案,利用ANSYS提供的User Mat模块编写了基于统一强度理论与拉破坏复合屈服准则的理想塑性模型。用自定义的本构模型模拟深埋圆形巷道弹塑性开挖过程,数值模拟结果与理论解很好地吻合,验证了模型代码和所提出方案的正确性和可行性。采用半隐式向后欧拉法与Steffensen迭代法相结合的手段,可简化应力与一致切线模量的求解,该方法避免了应力偏离屈服面和求解流动函数偏导,算法简便,易于推广应用。
[Abstract]:At present, most of the plastic yield criteria used in geotechnical engineering are piecewise functions which are not derivable locally. The explicit forward Euler method and Newton-Raphson iterative method are used to solve the equations in implicit finite element solution. However, explicit forward Euler method can easily lead to stress deviation from yield surface and non-convergence of calculation, while Newton-Raphson iterative method requires frequent derivation, which is unfavorable for piecewise functions. For this reason, a scheme is proposed to combine the semi-implicit backward Euler method and the derivative free Steffensen iteration method to update the stress and uniform tangent modulus. According to the above scheme, an ideal plastic model based on the unified strength theory and tensile failure composite yield criterion is developed by using the user Mat module provided by ANSYS. The elastic-plastic excavation process of deep buried circular roadway is simulated by using the self-defined constitutive model. The numerical simulation results are in good agreement with the theoretical solution, which verifies the correctness and feasibility of the model code and the proposed scheme. By using semi-implicit backward Euler method and Steffensen iterative method, the solution of stress and uniform tangent modulus can be simplified. The method avoids stress deviation from yield surface and solves partial derivative of flow function. The algorithm is simple and easy to be applied.
【作者单位】： 中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室;中国科学院大学;北京科技大学土木与环境工程学院;
【基金】：国家科技支撑计划课题(No.2012BAB08B02)~~
【分类号】：O241.82
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本文编号：2046059