具有分布材料特性的梁反应分析方法  

A METHOD TO ANALYZE THE BEAM WITH DISTRIBUTED MATERIAL PROPERTIES

作　　者：李爽[1] 翟长海[1] 谢礼立[1,2] 

机构地区：[1]哈尔滨工业大学土木工程学院,黑龙江哈尔滨150090 [2]中国地震局工程力学研究所,黑龙江哈尔滨150080

出　　处：《工程力学》2009年第6期70-74,共5页Engineering Mechanics

基　　金：国家自然科学基金项目(90815014,90715021);地震行业科研专项基金项目(200808021)

摘　　要：同一梁单元内材料具有不同性质时,传统梁单元的单元位移插值函数不能合理地描述梁内部的位移变化,导致计算精度较低。给出了一种计算同一单元内具有分布材料特性的梁反应的有限元方法,有效解决了传统梁单元的局限性。同时,给出了同一单元内具有分布材料特性的梁单元的一致等效节点荷载和一致质量矩阵的建立方法。与传统梁单元相比,使用该方法进行静力分析和特征值分析均可获得较高的计算精度,并且使用一个单元即可给出精确的单元内力和位移分布。此研究为分析同一单元内具有分布材料特性的梁的静力与动力反应问题提供了简单的方法和有价值的理论基础。Since the element interpolation functions displacement filed in a beam with variable material of a traditional beam element cannot rationally describe the properties, inaccuracies will arise. A method to compute responses of a beam with distributed material properties is presented, which effectively avoids the limitation of traditional beam elements. The consistent equivalent nodal load and consistent mass matrix are derived for the presented beam element. Compared with the traditional beam element, higher accuracy of the presented element in the static analysis and eigenproblems is observed and the accurate internal element force and displacement fields can be modeled by only one element. This study provides a simple method and a useful theoretical basis for static and dynamic analyses of the beam with distributed material properties.

关 键 词：杆系结构 梁单元 单元平衡 分布材料特性 静力和动力分析 

分 类 号：TU323.3[建筑科学—结构工程]