Generalized Variational Principles of the Viscoelastic Body With Voids and Their Applications
-
摘要: 从粘弹性材料的Boltzmann迭加原理和带空洞材料的线弹性本构关系出发,提出了一种损伤粘弹性材料具有广义力场的本构模型．应用变积方法得到了以卷积形式表示的泛函,并建立了损伤粘弹性固体的广义变分原理和广义势能原理．把它们应用于带损伤的粘弹性Timoshenko梁,得到了Timoshenko梁的统一的运动微分方程、初始条件和边界条件． 这些广义变分原理为近似求解带损伤的粘弹性问题提供了一条途径．
-
关键词:
- 损伤粘弹性固体 /
- 变积法 /
- 广义变分原理 /
- 广义势能原理 /
- Timoshenko梁
Abstract: From the Boltzmann's constitutive law of viscoelastic materials and the linear theory of elastic materials with voids,a constitutive model of generalized force fields for viscoelastic solids with voids was given.By using the variational integral method,the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented It can be shown that the variational principles correspond to the did ferential equations and the initial and boundary conditions of viscoela stic body with voids. As an applicanon,a generalized variational prindple of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids. -
[1] 钱伟长.变分法与有限元[M].北京:科学出版社,1980. [2] 钱伟长.广义变分原理[M].北京:知识出版社,1985. [3] Gurtin M E.Variational principles for linear elastodynamics[J].Archive for Rational Mechanics and Analysis,1964,16(1):34—50. [4] 罗恩.关于线弹性动力学中各种Gurtin型变分原理[J].中国科学,A辑,1987,17(9): 936—948. [5] 罗恩.关于线粘弹性动力学中各种变分原理[J].力学学报,1990,22(4):484—489. [6] 罗恩.压电热弹性动力学的一些基本原理[J].中国科学,A辑, 1999,29(9):851—858. [7] 程昌钧,卢华勇.粘弹性Timoshenko梁的变分原理和静动力学行为分析[J].固体力学学报,2002,23(2):190—196. [8] CHENG Chang-jun, ZHANG Neng-hui. Variational principles on static-dynamic analysis of visco~elastic thin plates with applications[J].Int J Solids and Structures,1998,35(33):4491—4505. doi: 10.1016/S0020-7683(97)00262-X [9] 梁立孚,章梓茂.推导弹性力学变分原理和一种凑合法—─反逆法[J].哈尔滨船舶工程学院学报,1985,6(3):86—95. [10] Cowin S C, Nunziato J W. Linear elastic materials with voids[J].J Elasticity,1983,13(2):125—147. doi: 10.1007/BF00041230 [11] 罗祖道,李思简.各向异性材料力学[M].上海:上海交通大学出版社,1994. -
计量
- 文章访问数: 2909
- HTML全文浏览量: 157
- PDF下载量: 670
- 被引次数: 0
下载:
渝公网安备50010802005915号