杆件的有限元分析代码C语言
时间: 2023-06-13 12:06:36 浏览: 48
以下是一个简单的杆件有限元分析的代码示例,使用了C语言:
```
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define MAX_NODES 100
#define MAX_ELEMS 100
/* Define element structure */
typedef struct {
int node1;
int node2;
double length;
double area;
} Element;
/* Define node structure */
typedef struct {
double x;
double y;
} Node;
/* Define global arrays */
Node nodes[MAX_NODES];
Element elems[MAX_ELEMS];
double k[MAX_NODES][MAX_NODES];
double f[MAX_NODES];
/* Function to calculate stiffness matrix for an element */
void calc_elem_stiffness(int elem) {
double dx = nodes[elems[elem].node2].x - nodes[elems[elem].node1].x;
double dy = nodes[elems[elem].node2].y - nodes[elems[elem].node1].y;
double L = elems[elem].length = sqrt(dx*dx + dy*dy);
double A = elems[elem].area;
double E = 200e9; /* Young's modulus for steel */
double k_elem = (E*A/L);
double c = dx/L;
double s = dy/L;
double k11 = c*c;
double k12 = c*s;
double k21 = c*s;
double k22 = s*s;
k[elems[elem].node1][elems[elem].node1] += k11*k_elem;
k[elems[elem].node1][elems[elem].node2] += k12*k_elem;
k[elems[elem].node2][elems[elem].node1] += k21*k_elem;
k[elems[elem].node2][elems[elem].node2] += k22*k_elem;
}
/* Function to calculate global stiffness matrix */
void calc_global_stiffness(int n_nodes, int n_elems) {
int i, j, e;
for (e = 0; e < n_elems; e++) {
calc_elem_stiffness(e);
}
}
/* Function to calculate force vector */
void calc_force_vector(int n_nodes, int n_elems) {
int i, j, e;
for (i = 0; i < n_nodes; i++) {
f[i] = 0.0;
}
/* Apply nodal loads */
f[0] = -1000.0;
}
/* Function to solve system of equations */
void solve_system(int n_nodes) {
int i, j, k;
for (k = 0; k < n_nodes-1; k++) {
for (i = k+1; i < n_nodes; i++) {
double factor = k[i][k] / k[k][k];
for (j = k; j < n_nodes; j++) {
k[i][j] -= factor * k[k][j];
}
f[i] -= factor * f[k];
}
}
/* Back substitution */
for (i = n_nodes-1; i >= 0; i--) {
double sum = 0.0;
for (j = i+1; j < n_nodes; j++) {
sum += k[i][j] * f[j];
}
f[i] = (f[i] - sum) / k[i][i];
}
}
/* Main function */
int main(int argc, char **argv) {
int n_nodes = 3;
int n_elems = 2;
nodes[0].x = 0.0; nodes[0].y = 0.0;
nodes[1].x = 0.0; nodes[1].y = 1.0;
nodes[2].x = 1.0; nodes[2].y = 0.0;
elems[0].node1 = 0; elems[0].node2 = 1; elems[0].area = 0.01;
elems[1].node1 = 0; elems[1].node2 = 2; elems[1].area = 0.02;
calc_global_stiffness(n_nodes, n_elems);
calc_force_vector(n_nodes, n_elems);
solve_system(n_nodes);
printf("Displacements:\n");
for (int i = 0; i < n_nodes; i++) {
printf("Node %d: %f\n", i, f[i]);
}
return 0;
}
```
该示例实现了一个简单的三节点两杆件的有限元分析,使用了C语言实现。代码中使用了结构体来定义节点和单元,以及全局数组来存储刚度矩阵和力向量。程序包括计算单元刚度矩阵、计算全局刚度矩阵、计算力向量、以及解决线性方程组的函数。主函数中定义了一个简单的三节点两杆件的模型,并输出了计算得到的节点位移。