GENERALIZED VARIATIONAL PRINCIPLES OF THE VISCOELASTIC BODY WITH VOIDS AND THEIR APPLICATIONS  

作　　者：盛东发 程昌钧 扶名福 

机构地区：[1]Shanghai Institute of Applied Mathematics and Mechanics,Department of Mechanics, Shanghai University [2]Graduate School of Engineering Mechanics, Institute of Civil Engineering, Nanchang University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2004年第4期381-389,共9页应用数学和力学（英文版）

基　　金：theNationalNaturalScienceFoundationofChina ( 1 0 2 72 0 69) ;theMunicipalKeySubjectProgramofShanghai

摘　　要：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 differential equations and the initial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle 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.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 differential equations and the initial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle 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.

关 键 词：viscoelastic solid with void variational integral method generalized variational principle generalized potential energy principle Timoshenko beam 

分 类 号：O343[理学—固体力学]