写出节点类、材料类、荷载类、空间梁单元类的C++计算程序

以下是一个简单的C++计算程序，包含节点类、材料类、荷载类和空间梁单元类：

#include <iostream>
#include <vector>

using namespace std;

// 定义节点类
class Node {
public:
    double x, y, z; // 节点坐标
    Node(double x, double y, double z) {
        this->x = x;
        this->y = y;
        this->z = z;
    }
};

// 定义材料类
class Material {
public:
    double E, G, rho; // 弹性模量、剪切模量、密度
    Material(double E, double G, double rho) {
        this->E = E;
        this->G = G;
        this->rho = rho;
    }
};

// 定义荷载类
class Load {
public:
    double fx, fy, fz; // 节点受力
    Load(double fx, double fy, double fz) {
        this->fx = fx;
        this->fy = fy;
        this->fz = fz;
    }
};

// 定义空间梁单元类
class BeamElement {
public:
    int node1, node2; // 梁单元两端节点
    double length; // 梁单元长度
    Material* material; // 梁单元材料
    Load* load; // 梁单元荷载
    BeamElement(int node1, int node2, double length, Material* material, Load* load) {
        this->node1 = node1;
        this->node2 = node2;
        this->length = length;
        this->material = material;
        this->load = load;
    }
};

int main() {
    // 定义节点
    Node node1(0, 0, 0);
    Node node2(0, 1, 0);
    Node node3(1, 1, 0);
    Node node4(1, 0, 0);

    // 定义材料
    Material material(210e9, 81e9, 7800);

    // 定义荷载
    Load load(0, 0, -1000);

    // 定义梁单元
    vector<BeamElement> elements;
    elements.push_back(BeamElement(1, 2, 1, &material, &load));
    elements.push_back(BeamElement(2, 3, 1, &material, &load));
    elements.push_back(BeamElement(3, 4, 1, &material, &load));
    elements.push_back(BeamElement(4, 1, 1, &material, &load));

    // 计算各节点受力
    vector<Load> nodeLoads;
    for (int i = 0; i < 4; i++) {
        Load nodeLoad(0, 0, 0);
        for (int j = 0; j < elements.size(); j++) {
            BeamElement element = elements[j];
            if (element.node1 == i + 1 || element.node2 == i + 1) {
                double length = element.length;
                double E = element.material->E;
                double G = element.material->G;
                double rho = element.material->rho;
                double fx = element.load->fx;
                double fy = element.load->fy;
                double fz = element.load->fz;

                double l = sqrt((node1.x - node2.x) * (node1.x - node2.x) + (node1.y - node2.y) * (node1.y - node2.y) + (node1.z - node2.z) * (node1.z - node2.z));
                double cosTheta = (node2.x - node1.x) / l;
                double sinTheta = sqrt(1 - cosTheta * cosTheta);
                double cosPhi = (node2.z - node1.z) / l;
                double sinPhi = sqrt(1 - cosPhi * cosPhi);

                double k11 = E * material->A / l;
                double k12 = E * material->A / l * cosTheta;
                double k13 = -E * material->A / l * cosPhi;
                double k14 = -G * material->J / l;
                double k21 = E * material->A / l * cosTheta;
                double k22 = E * material->A / l * cosTheta * cosTheta + G * material->J / l * sinTheta * sinTheta;
                double k23 = -E * material->A / l * cosTheta * cosPhi;
                double k24 = G * material->J / l * sinTheta * sinPhi;
                double k31 = -E * material->A / l * cosPhi;
                double k32 = -E * material->A / l * cosTheta * cosPhi;
                double k33 = E * material->A / l * cosPhi * cosPhi + G * material->J / l * sinPhi * sinPhi;
                double k34 = -G * material->J / l * sinTheta * sinPhi;
                double k41 = -G * material->J / l;
                double k42 = G * material->J / l * sinTheta * sinPhi;
                double k43 = -G * material->J / l * sinTheta * sinPhi;
                double k44 = G * material->J / l * sinPhi * sinPhi + G * material->J / l * sinTheta * sinTheta;

                double k[4][4] = {{k11, k12, k13, k14},
                                  {k21, k22, k23, k24},
                                  {k31, k32, k33, k34},
                                  {k41, k42, k43, k44}};

                double u[4] = {0, 0, 0, 0};
                u[0] = node1.x;
                u[1] = node1.y;
                u[2] = node2.x;
                u[3] = node2.y;

                double f[4] = {0, 0, 0, 0};
                f[0] = fx * l / 2;
                f[1] = fy * l / 2;
                f[2] = fx * l / 2;
                f[3] = fy * l / 2;

                for (int m = 0; m < 4; m++) {
                    for (int n = 0; n < 4; n++) {
                        nodeLoad.fx += k[m][n] * u[n] + f[m];
                    }
                }
            }
        }
        nodeLoads.push_back(nodeLoad);
    }

    // 输出各节点受力
    for (int i = 0; i < nodeLoads.size(); i++) {
        cout << "Node " << i + 1 << " load: (" << nodeLoads[i].fx << ", " << nodeLoads[i].fy << ", " << nodeLoads[i].fz << ")" << endl;
    }

    return 0;
}

说明：

- 节点类包含三个坐标值；
- 材料类包含弹性模量、剪切模量和密度；
- 荷载类包含三个方向的受力值；
- 空间梁单元类包含两个节点、长度、材料和荷载；
- 主程序中定义四个节点、一个材料、一个荷载和四个梁单元；
- 主程序中计算每个节点的受力，并输出结果。