《有限元及程程序设计方案》课程设计方案说明书.doc

河北工程大学 《有限元及程序设计》课程设计说明书 课程设计题目：平面钢架有限元程序功能修改设计 副标题：1增加非节点荷载为集中力偶、纵向均布力以及线性分布力时固端反力的计算功能 2 结果以文件形式输出 指导教师： 班 级： 姓 名： 学 号： 摘 要 有限元法是现代工程数值分析中应用广泛的一种方法，本文根据线性有限元理论对受有五种不同荷载的三杆钢架进行静力分析，将结构离散为三个单元四个节点。分别建立每个单元的单元刚度矩阵和节点荷载列阵，根据刚度集成法建立了结构的总刚度矩阵和节点荷载列阵，得出结构的平衡方程，并用对角线元素置一法引入边界条件，用高斯消元法求解平衡方程。最后编写C程序求解此问题，并通过与手算的比较验证了程序的准确性，通过增加一个杆件说明程序的通用性 键词：有限元法 杆平面刚架 刚度矩阵 对角线元素置一法 C语言 Abstract Finite Element Method (FEM) makes an extensive use in the numerical analysis of modern construction. In this paper, we study Static state of the Plane frame which is loaded by five different kinds of loads based on linear finite element theory loads; the structure is divided into three units and four nodes. The stiffness matrix array node load of each unit is set up, According to Stiffness integration method we establish the total stiffness matrix and load node array of the structure which is aimed drawing the balance equation of the structure, and then introduce the boundary conditions by buy-one-diagonal elements .we can use Gaussian elimination method for solving equilibrium equations. Finally, we program procedures for the preparation of C to solve this problem, and through comparison with the hand count to verify the accuracy of the procedure, by adding a bar to descript generic property of the procedure Key words: Finite Element Method (FEM) Planar rigid frame Buy-one-diagonal elements Stiffness matrices C language 目 录 设计题目说明-------------------------------------------------4 用有限元法进行手算----------------------------------------4 1.1化分单元，选取坐标系----------------------------------------------4 1.2求局部坐标系下各单元的单元刚度矩阵--------------------------------5 1.3求整体坐标系下各单元的单元刚度矩阵--------------------------------5 1.4求整体刚度矩阵----------------------------------------------------6 1.5求非节点荷载引起的等效节点荷载及节点荷载列阵----------------------6 1.6列整刚方程，求节点位移--------------------------------------------9 1.7求单元内力----- --------------------------------------------------10 1.7.1转换位移列阵- -----------