c++编写三维单元刚度矩阵

三维单元刚度矩阵是用于有限元分析中的一个重要计算工具，其表示了一个三维单元的刚度特性。下面是一个用C语言编写的三维单元刚度矩阵的示例代码：

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

// 定义三维单元刚度矩阵的函数
void element_stiffness(double k, double E, double v, double **stiffness_matrix)
{
    double lambda = E*v/((1+v)*(1-2*v));
    double mu = E/(2*(1+v));
    
    // 计算刚度矩阵
    stiffness_matrix[0][0] = lambda+2*mu;
    stiffness_matrix[0][1] = lambda;
    stiffness_matrix[0][2] = lambda;
    stiffness_matrix[0][3] = 0;
    stiffness_matrix[0][4] = 0;
    stiffness_matrix[0][5] = 0;

    stiffness_matrix[1][0] = lambda;
    stiffness_matrix[1][1] = lambda+2*mu;
    stiffness_matrix[1][2] = lambda;
    stiffness_matrix[1][3] = 0;
    stiffness_matrix[1][4] = 0;
    stiffness_matrix[1][5] = 0;

    stiffness_matrix[2][0] = lambda;
    stiffness_matrix[2][1] = lambda;
    stiffness_matrix[2][2] = lambda+2*mu;
    stiffness_matrix[2][3] = 0;
    stiffness_matrix[2][4] = 0;
    stiffness_matrix[2][5] = 0;

    stiffness_matrix[3][0] = 0;
    stiffness_matrix[3][1] = 0;
    stiffness_matrix[3][2] = 0;
    stiffness_matrix[3][3] = mu;
    stiffness_matrix[3][4] = 0;
    stiffness_matrix[3][5] = 0;

    stiffness_matrix[4][0] = 0;
    stiffness_matrix[4][1] = 0;
    stiffness_matrix[4][2] = 0;
    stiffness_matrix[4][3] = 0;
    stiffness_matrix[4][4] = mu;
    stiffness_matrix[4][5] = 0;

    stiffness_matrix[5][0] = 0;
    stiffness_matrix[5][1] = 0;
    stiffness_matrix[5][2] = 0;
    stiffness_matrix[5][3] = 0;
    stiffness_matrix[5][4] = 0;
    stiffness_matrix[5][5] = mu;
    
    // 计算刚度矩阵系数
    double coef = k/(6*(1-v*v));
    for (int i=0; i<6; i++)
    {
        for (int j=0; j<6; j++)
        {
            stiffness_matrix[i][j] *= coef;
        }
    }
}

int main()
{
    // 定义材料参数和单元参数
    double k = 1.0;
    double E = 210000.0;
    double v = 0.3;
    double **stiffness_matrix;

    // 动态分配刚度矩阵数组
    stiffness_matrix = (double **)malloc(6 * sizeof(double *));
    for (int i=0; i<6; i++)
    {
        stiffness_matrix[i] = (double *)malloc(6 * sizeof(double));
    }

    // 计算刚度矩阵
    element_stiffness(k, E, v, stiffness_matrix);

    // 输出刚度矩阵
    printf("Element stiffness matrix:\n");
    for (int i=0; i<6; i++)
    {
        for (int j=0; j<6; j++)
        {
            printf("%10.3f ", stiffness_matrix[i][j]);
        }
        printf("\n");
    }

    // 释放刚度矩阵数组
    for (int i=0; i<6; i++)
    {
        free(stiffness_matrix[i]);
    }
    free(stiffness_matrix);

    return 0;
}

在上述代码中，我们通过定义函数`element_stiffness`来计算三维单元刚度矩阵。其中，输入参数包括材料参数和单元参数，输出参数为一个6x6的刚度矩阵数组。在主函数中，我们动态分配了刚度矩阵数组的内存空间，并调用`element_stiffness`函数来计算刚度矩阵，最后输出结果并释放内存空间。