ansys二次开发

通过C语言，实现龙格库塔法，用四阶龙格库塔法求解一阶微分方程组。(Through the C language, the realization of Runge-Kutta method with fourth-order Runge-Kutta method for solving first-order differential equations.)

几个使用的解线性方程组的程序，包括高斯消去法，高斯列主元法，高斯——赛德尔消去法。简明实用。(Gauss elimaination, Gauss_seidel ellimination)

最优化的bfgs算法，是采用matlab编程(BFGS optimization algorithm, using matlab programming)

复合材料破坏失效vumat子程序，使用hsshin准则判断失效，具有刚度缩减，(The VUMAT subroutine for failure of composite materials is judged by hsshin criterion, and stiffness is reduced.)

说明：  牛顿法又称牛顿-拉弗森方法（Newton-Raphson method），是一种在实数域和复数域上近似求解方程的方法。本程序收敛速度快，迭代步数可取大一些(Newton method, also known as Newton-Raphson method, is an approximate method for solving equations in real and complex fields. The program has fast convergence speed so the number of iteration steps can be larger.)

lyapunov指数求解，采用wolf法，计算速度极快(lyapunov Index solving, using wolf law, the calculation speed)

非负矩阵分解的最经典算法，1999发表在自然科学杂志上的那一篇文章的代码(classic Nonnegative matrix factorization)

说明：  线弹性umat钛合金,有cae文件，可以进行晶体塑性模拟(linear umat for titanium aloy)

Fourier bessel transform

市场最优配置，通过拉格朗日算子进行计算，并派出最优方案 (Market, the optimal configuration, through the Lagrangian operator is calculated, and to send the optimal program)