高度非线性弹塑性模型的改进显式算法数值实现

Improved Explicit Numerical Integration of a Highly Nonlinear ElastoPlastic Constitutive Model

摘要:

当采用传统的全显式算法对高度非线性的弹塑性本构模型进行数值实现过程中，存在计算效率低、误差积累、精度较低的缺点.为提高计算效率和改善计算精度，采用四阶的Dormand and Prince RungeKutta法代替传统的全显式算法中的向前Euler法，并结合切平面算法形成了改进显式算法.以考虑土体结构性的SANICLAY模型为例，对传统的全显式算法、改进显式算法和隐式算法在计算收敛性、效率和精度方面进行对比.将改进显式算法用于隧道开挖工程多单元计算中.结果表明，与隐式算法相比，传统的全显式算法的计算精度和计算效率均比较低，改进显式算法计算效率和计算精度均比传统的全显式算法高很多.

Abstract:

When implementing a highly nonlinear stressstrain model to solve boundaryvalued problems, one of the major challenges is how to reduce the accumulative error and to maintain the effectiveness of the numerical integration. In general, the conventional explicit algorithm tends to have a lower computational efficiency and a higher accumulative error. In order to deal with these challenges, this paper proposes an improvedexplicit algorithm combining with the cuttingplane method, in which the Dormand and Prince RungeKutta method is used instead of the forward Euler. Using the highly nonlinear SANICLAY model for structured clay as an example, the convergence, the computational efficiency, and the accuracy of three algorithms, namely the conventional explicit algorithm, the improvedexplicit algorithm, and the implicit algorithm, are compared via numerical simulations of single element tests. Finally, the improvedexplicit algorithm is applied to the multielement calculation of tunnel excavation. Compared with the implicit algorithm, the conventional explicit algorithm has a lower computational efficiency and a higher accumulative error. The improvedexplicit algorithm can greatly improve the computational efficiency and accuracy.