基于牛顿-拉夫逊的拉压不同模量问题的数值求解

针对拉压模量不同引起的材料本构非线性，首先，通过引入改进的Heaviside函数将本构方程连续光滑化；然后，基于特征值与特征向量的求导策略，推导有限元求解模型中切线刚度矩阵的列式；最终，提出基于牛顿-拉夫逊迭代格式的拉压不同模量问题的数值求解算法。数值算例验证了本文算法比传统算法具有更稳定的收敛性和更高的求解精度，特别适合于工程分析中大规模计算问题的求解。

A numerical algorithm for the problem of different modulus in tension and compression based on the newton-raphson scheme

For strong nonlinear constitutive relationship due to the different moduli in tension and compression,the Heaviside function is introduced into constitutive equation to make it continuous and smoothing.Then,based on the derivatives of eigenvalues and eigenvectors,the formula of tangent stiffness matrix in the finite element model is derived.Finally,a numerical algorithm is presented for the problem of bi-modulus materials based on the Newton-Raphson scheme.Numerical examples are given to demonstrate the more stable convergence and the higher accuracy of the method in this paper than those of the traditional method.The proposed method is particularity suitable for large-scale computations in engineering.