文档介绍：西安理工大学
硕士学位论文
桁架结构的有限元分析与优化设计研究
姓名:董旭刚
申请学位级别:硕士
专业:结构工程
指导教师:宋俐
20050301
摘要

桁架结构的有限元分析
与优化设计研究
学科名称结构工程
作者姓名董旭刚作者签名
导师姓名宋俐导师签名
导师职称教授答辩日期

摘要
桁架由于其结构简单拆装方便刚性好抗震能力强能够承受多方向的荷
载而广泛应用于各种工程领域合理地设计桁架使它在满足多种约束条件下每
根杆件都能最大限度地承受载荷就可以使结构合理的分配承载能力达到减轻结
构重量的目的
本文应用结构力学有限元优化等理论对桁架结构的优化设计进行了研究
作者在有限元理论的基础上推导了杆单元的单元刚度矩阵和总体刚度矩阵并根
据有限元分析流程用 FORTRAN 语言编制了三维桁架结构的有限元分析程序模
块多个算例表明用该程序模块进行桁架结构的受力变形分析结果是正确的
作者根据结构的满应力优化设计思想建立了桁架的优化设计数学模型用
FORTRAN 语言编制了相应的满应力优化程序模块优化设计主程序在保证设计满
足应力强度约束条件外还进一步考虑了结构的局部失稳结点的位移限制等因素
对设计的影响同时主程序也保证了有限元分析模块和满应力优化模块之间数据
正确通畅自动地传递文中用所编程序通过多个算例对单工况或多工况下
平面空间静定桁架超静定桁架进行了优化设计并分析讨论了设计结果及
约束对结果的影响文中所做的工作研究所采用的方法对实际工程结构设计会有
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西安理工大学硕士学位论文
一定的参考意义和应用价值
关键词桁架有限元分析满应力优化设计局部失稳结点位移约束

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Abstract

TITLE: RESEARCH ON FINITE ELEMENT ANALYSIS AND
OPTIMIZATION DESIGN OF TRUSS STRUCTURE

MAJOR SUBJECT: Structural Engineering
AUTHOR: DONG Xu-Gang Signature:
ADVISER: Li Signature:

Abstract

In this paper, optimizing design of truss was studied based on the theory of structural
mechanics, finite element and optimization. Stiffness matrix of an elementary bar and total
stiffness matrix were deduced and the program for 3D-truss analysis was developed using
puter language according to flow chart of finite element analysis. Based on the
theory of full stress design, the mathematic model of optimization design for truss was
founded and the program was developed by Fortran. Partial stability of structure and
restriction of nodes displacements were taken into account in the main program of
optimization design for truss except constraint of strength. Optimizing designs of plan,
space, statically determinate and statically indeterminate trusses in different instances of
loads were carried out by the program and the calculating results and process showed that
the program were correct, co