带压电陶瓷片梁的力学分析和二类变量广义变分原理

IMECH-IR > 力学所知识产出(1956-2008)

	带压电陶瓷片梁的力学分析和二类变量广义变分原理
	余青
导师	王克仁
	1999
学位授予单位	中国科学院研究生院
学位授予地点	北京
学位类别	硕士
学位专业	固体力学
关键词	压电陶瓷片智能结构 Euler－bernoulli模型 Hellinger-reissner 二类变分广义余能原理吉尔法结构力学无机材料 Piezoelectric Ceramic Element Intelligent Structure Euler-bernoulli Model HellInger-reissner Generalized Variational PrInciple In Complementary Energy Form Gear Method
英文摘要	对于采用贴有压电陶瓷片作为作动元件的智能结构，在进行自适应控制时，往往要分析压电陶瓷片所引起的结构中的应力、应变和位移。对于带有压电陶瓷片梁的力学分析，文献中大多采用Euler-Bernoulli模型，即不考虑梁中的剪力，且假定梁沿厚度方向满足直法线假定。考虑到压电陶瓷片对梁的作用主要是通过粘贴层以剪力的形式传递到梁上，梁截面上的剪应力和剪应变一般很大，其影响不能忽略。本文采用Hellinger-Reissner二类变分广义余能原理，导出考虑梁截面上剪应力和剪应变影响的方程式，其中采用吉尔法求解非齐次常微分方程组。并将求得的解与相同条件的有限元解进行比较。结果证明该方法很有效。本文还对二类广义变分法进行了一般的讨论，发现，在使用二类广义变分法求解时，随着应力和位移所取项数的增加，结果有时反而变坏。并对二类广义变分法的使用提出了一些建议。; When beam bonded with piezoelectric ceramic elements used as an intelligent structure in a self-adaptive control, it is necessary to accurately find out the stresses and displacements in the structure. The so-called Euler-Bernoulli model is often adopted for the purpose, where shear deformation across the cross section of the beam is neglected. Due to the fact that in that case, shear forces acting on the faces of the beam are the main source for the stresses and strains in the beam, the shear deformation often plays an important role, which can not be neglected. In this paper, Hellinger-Reissner generalized variational principle in complementary energy form is used to derive a new set of equations for the beam, taking account of the shear deformation and other higher order effects, which is then solved by Gear method and whose results are compared with those of finite element method calculations. The final results have proved the validity of our methods. In this paper a general discussion on Hellinger-Reissner generalized variational principle is also made. It is found that while more independent functions are added to the expressions of stresses and displacements in the variational fuctional, the results sometimes get worse instead of improving. Some suggestions are made on that respect.
索取号	29853
语种	中文
文献类型	学位论文
条目标识符	http://dspace.imech.ac.cn/handle/311007/24218
专题	力学所知识产出(1956-2008)
推荐引用方式 GB/T 7714	余青. 带压电陶瓷片梁的力学分析和二类变量广义变分原理[D]. 北京. 中国科学院研究生院,1999.

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