杆件的有限元分析代码C语言

杆件的有限元分析是结构力学中的常见问题，其基本思想是将结构分解为若干个杆件，通过杆件的节点之间的内力平衡方程来求解杆件节点的位移和内力。

以下是一个简单的杆件的有限元分析代码示例，使用C语言编写：

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

#define MAX_NODES 1000
#define MAX_ELEMENTS 1000

struct Node {
    double x, y;
};

struct Element {
    int n1, n2;
    double l, k, alpha;
};

struct Load {
    int node;
    double fx, fy;
};

struct Constraint {
    int node;
    double u, v;
};

struct Node nodes[MAX_NODES];
struct Element elements[MAX_ELEMENTS];
struct Load loads[MAX_NODES];
struct Constraint constraints[MAX_NODES];

int num_nodes = 0;
int num_elements = 0;
int num_loads = 0;
int num_constraints = 0;

double stiffness_matrix[MAX_NODES][MAX_NODES];
double load_vector[MAX_NODES];
double displacement_vector[MAX_NODES];

void add_node(double x, double y) {
    nodes[num_nodes].x = x;
    nodes[num_nodes].y = y;
    num_nodes++;
}

void add_element(int n1, int n2) {
    elements[num_elements].n1 = n1;
    elements[num_elements].n2 = n2;
    double dx = nodes[n2].x - nodes[n1].x;
    double dy = nodes[n2].y - nodes[n1].y;
    elements[num_elements].l = sqrt(dx*dx + dy*dy);
    elements[num_elements].k = 1.0 / elements[num_elements].l;
    elements[num_elements].alpha = atan2(dy, dx);
    num_elements++;
}

void add_load(int node, double fx, double fy) {
    loads[num_loads].node = node;
    loads[num_loads].fx = fx;
    loads[num_loads].fy = fy;
    num_loads++;
}

void add_constraint(int node, double u, double v) {
    constraints[num_constraints].node = node;
    constraints[num_constraints].u = u;
    constraints[num_constraints].v = v;
    num_constraints++;
}

void assemble_stiffness_matrix() {
    for (int i = 0; i < num_elements; i++) {
        int n1 = elements[i].n1;
        int n2 = elements[i].n2;
        double k = elements[i].k;
        double alpha = elements[i].alpha;
        stiffness_matrix[n1][n1] += k*k;
        stiffness_matrix[n1][n2] -= k*k*cos(alpha);
        stiffness_matrix[n2][n1] -= k*k*cos(alpha);
        stiffness_matrix[n2][n2] += k*k;
    }
}

void assemble_load_vector() {
    for (int i = 0; i < num_loads; i++) {
        int node = loads[i].node;
        load_vector[node] += loads[i].fx*cos(elements[i].alpha) +
                             loads[i].fy*sin(elements[i].alpha);
    }
}

void apply_constraints() {
    for (int i = 0; i < num_constraints; i++) {
        int node = constraints[i].node;
        double u = constraints[i].u;
        double v = constraints[i].v;
        stiffness_matrix[node][node] = 1.0;
        load_vector[node] = u;
        for (int j = 0; j < num_nodes; j++) {
            if (j != node) {
                load_vector[j] -= stiffness_matrix[j][node]*v;
                stiffness_matrix[j][node] = 0.0;
                stiffness_matrix[node][j] = 0.0;
            }
        }
    }
}

void solve() {
    for (int i = 0; i < num_nodes; i++) {
        displacement_vector[i] = 0.0;
    }
    for (int i = 0; i < num_nodes; i++) {
        if (stiffness_matrix[i][i] == 0.0) {
            continue;
        }
        double scale = 1.0 / stiffness_matrix[i][i];
        displacement_vector[i] = load_vector[i] * scale;
        for (int j = 0; j < num_nodes; j++) {
            stiffness_matrix[i][j] *= scale;
        }
        for (int j = 0; j < num_nodes; j++) {
            if (j == i) {
                continue;
            }
            double factor = stiffness_matrix[j][i];
            for (int k = 0; k < num_nodes; k++) {
                stiffness_matrix[j][k] -= factor*stiffness_matrix[i][k];
            }
            load_vector[j] -= factor*load_vector[i];
        }
    }
}

void print_results() {
    printf("Displacements:\n");
    for (int i = 0; i < num_nodes; i++) {
        printf("%d: (%lf, %lf)\n", i, displacement_vector[i]*cos(elements[i].alpha),
                                    displacement_vector[i]*sin(elements[i].alpha));
    }
    printf("Reactions:\n");
    for (int i = 0; i < num_nodes; i++) {
        double rx = 0.0;
        double ry = 0.0;
        for (int j = 0; j < num_elements; j++) {
            if (elements[j].n1 == i || elements[j].n2 == i) {
                double k = elements[j].k;
                double alpha = elements[j].alpha;
                if (elements[j].n1 == i) {
                    rx += k*displacement_vector[i]*cos(alpha);
                    ry += k*displacement_vector[i]*sin(alpha);
                } else {
                    rx -= k*displacement_vector[i]*cos(alpha);
                    ry -= k*displacement_vector[i]*sin(alpha);
                }
            }
        }
        printf("%d: (%lf, %lf)\n", i, rx, ry);
    }
}

int main() {
    add_node(0.0, 0.0);
    add_node(0.0, 1.0);
    add_node(1.0, 1.0);
    add_node(1.0, 0.0);
    add_element(0, 1);
    add_element(1, 2);
    add_element(2, 3);
    add_element(3, 0);
    add_load(1, 0.0, -1.0);
    add_constraint(0, 0.0, 0.0);
    add_constraint(3, 0.0, 0.0);
    assemble_stiffness_matrix();
    assemble_load_vector();
    apply_constraints();
    solve();
    print_results();
    return 0;
}

在这个示例代码中，我们定义了四个结构体，分别表示节点、杆件、载荷和约束，并且使用数组存储了所有的节点、杆件、载荷和约束。我们还定义了一个存储刚度矩阵、载荷向量和位移向量的全局数组，并且使用了很多函数来实现各种操作。

在主函数中，我们首先定义了一个简单的四边形结构，然后依次调用各个函数来进行有限元分析，最后输出节点的位移和节点的反力。

这只是一个简单的示例代码，实际的有限元分析程序往往更加复杂，需要考虑更多的因素，比如材料的非线性性、几何的非线性性等等。但是这个示例代码可以帮助你理解有限元分析的基本思想和实现方法。