带孔隙损伤的弹性固体的广义变分原理  

Generalized Variational Principle of Elastic Body with Void Damage

作　　者：齐荣庆 程家幸 盛冬发 QI Rongqing;CHENG Jiaxing;SHENG Dongfa(Civil Engineering Institute,Southwest Forestry University,Kunming 650224,Yunnan,China;Civil Engineering Institute,Southeast University,Nanjing 210000,Jiangsu,China)

机构地区：[1]西南林业大学土木工程学院,云南昆明650224 [2]东南大学土木工程学院,江苏南京210000

出　　处：《力学季刊》2021年第3期604-612,共9页Chinese Quarterly of Mechanics

基　　金：云南省科技厅青年项目(2018FD049);国家自然科学基金(11862023)。

摘　　要：应用弹性微结构理论,建立了具广义力场带孔隙损伤线弹性固体的基本模型.应用变积方法,同时分别建立了带孔隙损伤弹性固体四类和两类变量的广义变分原理,这些变分原理对应着带孔隙损伤弹性固体微分方程和初值边值条件.应用弹性微结构理论,建立了带孔隙损伤的弹性Timoshenko梁的基本方程,得到带孔隙损伤的弹性Timoshenko梁两类变量的广义变分原理.这些广义变分原理为近似求解带孔隙损伤的弹性问题提供了有效途径.Based on the theory of elastic body with microstructure,the constitutive model with generalized force fields for elastic body with void damage is established.By using the variational integral method,the generalized variational principles with four and two kinds of variables for elastic body with void damage are developed.It shows that the variational principles are referring to the differential equations and the initial and boundary conditions of elastic body with void damage.Based on the theory of elastic body with microstructure,the basic equations of the generalized motion of elastic Timoshenko beam with void damage are established.Additionally,the generalized variational principle with two kinds of variables for elastic Timoshenko beam with void damage is obtained.These generalized variational principles can provide an effective approach for approximately solving the mechanical problems of elastic body with void damage.

关 键 词：带孔隙损伤弹性固体 变积方法 广义变分原理 TIMOSHENKO梁 

分 类 号：O343[理学—固体力学]