特大增量步算法分析变截面梁问题  

THE ANALYSIS OF THE VARYING CROSS-SECTION BEAM PROBLEM USING LARGE INCREMENT METHOD

作　　者：贾红学[1] 龙丹冰[1] 刘西拉[2] 

机构地区：[1]上海交通大学工程力学系,上海200240 [2]上海交通大学土木工程系,上海200240

出　　处：《工业建筑》2013年第S1期189-191,280,共4页Industrial Construction

基　　金：国家自然科学基金项目(10872128)

摘　　要：针对工程结构中广泛应用的变截面梁,利用基于广义逆矩阵理论的特大增量步算法对变截面梁进行求解。该算法是一种新的迭代算法。在给定变截面梁截面参数后,利用能量原理推导出梁单元的柔度矩阵。通过迭代计算,结果将很快收敛到精确解。给出了两端固支变截面梁算例。计算表明,如果把变截面梁划分成分段等截面的梁单元进行计算,这就要求单元数必须足够多才能保证结果趋于精确解。然而,该算法相比位移法仅需要很少的单元就能得到满意的结果,计算效率和精度得到明显的提高。The large increment method(LIM) based on the generalized inverse matrix theory was employed to analyze the varying cross-sectional beam used wildly in engineering structures.LIM is a new iterative method.The flexibility matrix of the beam is derived by applying the energy principle and the parameters of the varying cross-sectional beam.The results were fast approach to the exact solutions by the iterative method.The numerical examples of two-end-fixed beam with varying cross-section were presented.The calculation results showed that more elements were required to approach the exact solution if the segment uniform elements were employed to the two varying cross-sectional beam.However,LIM reached the exact solution using significantly less number of elements as compared with the displacement-based finite element method,and the computation efficiency and the accuracy were improved significantly.

关 键 词：变截面梁 广义逆矩阵 特大增量步算法 柔度矩阵 

分 类 号：TU323.3[建筑科学—结构工程]