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Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (4): 381-389.

• 论文 • 上一篇    下一篇

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

盛东发1,2, 程昌钧1, 扶名福2   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Department of Mechanics, Shanghai University, Shanghai 200072, P. R. China;
    2. Graduate School of Engineering Mechanics, Institute of Civil Engineering, Nanchang University, Nanchang 330029, P. R. China
  • 收稿日期:2002-10-25 修回日期:2003-11-06 出版日期:2004-04-18 发布日期:2004-04-18
  • 通讯作者: CHENG Chang-jun(Corresponding author,Tel:+86-21-56331454;E-mail:chjcheng@yc.shu.edu.cn) E-mail:chjcheng@yc.shu.edu.cn
  • 基金资助:
    the National Natural Science Foundation of China(10272069);the Municipal Key Subject Program of Shanghai

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

SHENG Dong-fa1,2, CHENG Chang-jun1, FU Ming-fu2   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Department of Mechanics, Shanghai University, Shanghai 200072, P. R. China;
    2. Graduate School of Engineering Mechanics, Institute of Civil Engineering, Nanchang University, Nanchang 330029, P. R. China
  • Received:2002-10-25 Revised:2003-11-06 Online:2004-04-18 Published:2004-04-18
  • Supported by:
    the National Natural Science Foundation of China(10272069);the Municipal Key Subject Program of Shanghai

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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.

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 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.

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