功能梯度圆柱壳瞬态动力响应的三维半解析状态空间求解方法（英文）  

A semi-analytical state-space approach for 3D transient analysis of functionally graded material cylindrical shells

作　　者：Xu LIANG Hai-lei KOU Guo-hua LIU Li-zhong WANG Zhen-yu WANG Zhi-jun WU 

机构地区：[1]College of Civil Engineering and Architecture,Zhejiang University [2]School of Civil and Environmental Engineering,Nanyang Technological University [3]School of Civil Engineering and Architecture,Weifang University

出　　处：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》2015年第7期525-540,共16页浙江大学学报（英文版）A辑（应用物理与工程）

基　　金：supported by the National Basic Research Program(973Program) of China(No.2013CB035901);the National Natural Science Foundation of China(Nos.51209185,51079127,51179171,51279180,and 51379185);the International Postdoctoral Exchange Fellowship Program;the China Postdoctoral Science Foundation(No.2013M531462)

摘　　要：目的:研究任意边界条件下功能梯度圆柱壳瞬态动力响应的解析求解方法,并研究荷载、几何以及材料参数对结构瞬态动力响应的影响。创新点:提出一种功能梯度圆柱壳的瞬态动力响应半解析求解方法,并可以考虑任意边界条件。本文考虑四种边界条件:固支-固支、固支-简支、固支-自由和简支-简支。方法:1.提出任意边界条件下功能梯度圆柱壳的瞬态动力响应半解析求解方法;2.采用有限元方法计算成果,验证本方法的正确性;3.将本方法与其他理论方法计算得到的结构固有频率以及文献中试验得到的结构固有频率进行比较;4.研究荷载频率、长径比、内外径比以及功能梯度参数对于结构瞬态动力响应的影响。结论:1.提出一种功能梯度圆柱壳的瞬态动力响应半解析求解方法;2.与其他方法计算成果对比,验证了本方法的正确性;3.收敛性分析表明,随着长度方向采样点数和径向分层数的增加,计算结果迅速收敛。A good understanding of the mechanical behavior of functionally graded material（FGM） cylindrical shells is necessary for designers and researchers. However, the 3D transient response of FGM cylindrical shells under various boundary conditions has not yet been analyzed. In this paper, the problem is addressed by proposing an approach integrating the state space method, differential quadrature method, and Durbin＇s numerical inversion method of Laplace transform. The laminate model is used to obtain the transient solution in the radial direction. At the edges, four kinds of boundary conditions are considered： Clamped-Clamped, Clamped-Simply supported, Clamped-Free, and Simply supported-Simply supported. The results of the proposed method and finite element（FE） method agree with each other excellently. Convergence studies show that the proposed method has a fast convergence rate. The natural frequencies obtained by the proposed method, experiment, and other theoretical methods are in close agreement with each other. The effects of the load frequency and duration, length/outer radius ratio, and the（outer radius-inner radius）/outer radius ratio on the transient response of FGM shells are investigated. Two laws of variation of material properties along the radial direction are considered： the first has material properties varying according to an exponential law along the radial direction, while the second has material properties varying according to a power law. The effect of a functionally graded index on the transient response of FGM shells is investigated in both cases. The results obtained in this paper can serve as benchmark data for further research.

关 键 词：状态空间法 数值Laplace逆变换方法 微分求积法 功能梯度材料 圆柱壳 

分 类 号：O241.8[理学—计算数学] O341[理学—数学]