薄壁杆件结构一维有限元精确刚度矩阵  

One-dimensional FEM exact stiffness matrix for thin-walled bar structures

作　　者：周华强[1] 聂孟喜[1] 

机构地区：[1]清华大学水利水电工程系,北京100084

出　　处：《清华大学学报（自然科学版）》2009年第9期1503-1506,共4页Journal of Tsinghua University(Science and Technology)

摘　　要：薄壁杆件结构广泛应用于公路桥梁、航空、造船、海洋工程等领域,但其结构分析计算较为复杂,为了得到更好的计算效果,研究了其静力分析的新方法。考虑弯扭耦合作用并重新推导了广义力和广义位移的关系,求解静力下的微分方程组时,把矩阵特征值解法与多项式特征解法结合在一起,得到了用于薄壁结构静力分析计算的有限元精确刚度矩阵。编写了有限元计算程序并引入算例验证,算例的结果表明:该方法的计算结果高效、准确,只用很少的有限元单元数目便可得到很精确的计算结果。Thin-walled bar structures are widely used in engineering projects such as highways, bridges, aviation, shipbuilding, marine engineering and other fields, but their structure mechanics analysis is complicated. In order to get better analysis results of this kind structure, a new method in the static condition is presented in this paper. The relationship between the generalized force and the generalized displacement used in exited methods is modified to consider the coupling of bending and torsion. The solution of the static differential equation integrates the matrix eigenvalue method and the characteristic polynomial method to get the exact stiffness matrix for the static analysis of thin wailed structures. A finite element method analysis using the matrix shows that this method is efficient and accurate for improved analysis of thin-walled structures. Accurate computational results could he obtained by using this method with much less number of finite elements.

关 键 词：薄壁结构 弯扭耦合 变分原理 多项式特征解 精确刚度矩阵 

分 类 号：O343[理学—固体力学]