弹性梁非线性热屈曲行为与辛本征解展开方法  

Non-linear thermal buckling of elastic beams and expanding method of symplectic eigensolutions

作　　者：褚洪杰[1] 徐新生[1] 林志华[2] 江南[1] 马建青[1] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024 [2]香港城市大学建筑系

出　　处：《大连理工大学学报》2011年第1期1-6,共6页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(11072054);工业装备结构分析国家重点实验室基金资助项目(S08202;GZ0809)

摘　　要：基于Hamilton体系,研究了弹性梁在温度荷载下发生的前屈曲和后屈曲问题.在辛空间中,前屈曲问题和后屈曲问题分别归结于系统的零本征值问题和非零本征值问题,而结构屈曲的临界温度和屈曲模态对应Hamilton体系的广义本征值和本征解.采用辛本征解展开方法对非线性大变形的后屈曲问题进行了深入探讨,揭示了从前屈曲到后屈曲变化的整个过程.结果发现梁在屈曲变形过程中向一个特殊的模式过渡,并最终发展为梁在某一平衡位置作周期振荡.The Hamiltonian system is introduced for pre-buckling and post-buckling of elastic beams under the thermal load.In the symplectic space,the problems of the pre-buckling and the post-buckling of beams are deduced respectively into the subjects of the zero eigenvalues and non-zero eigenvalues of the system.The critical temperatures and buckling modes can be obtained by generalized eigenvalues and eigensolutions of Hamiltonian system.Using the expanding method of symplectic eigensolutions,the post-buckling problem is discussed,in which the non-linear problem of the large deformation is considered.The whole process from the pre-buckling to the post-buckling of the beam is revealed.Results show that there is a transitional mode in the process of the buckling deformation and the last phase of the buckling is a periodic vibration of the beam on a balanceable station.

关 键 词：HAMILTON体系 弹性梁 热屈曲 大变形 

分 类 号：O343.9[理学—固体力学]