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 intitial 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 intial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids.
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Contributed by CHENG Chang-jun and FU Ming-fu
Foundation items: the National Natural Science Foundation of China (10272069); the Municipal Key Subject Program of Shanghai
Biographies: SHENG Dong-fa(1966≈), Doctor
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Dong-fa, S., Chang-jun, C. & Ming-fu, F. Generalized variational principles of the viscoelastic body with voids and their applications. Appl Math Mech 25, 381–389 (2004). https://doi.org/10.1007/BF02437521
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DOI: https://doi.org/10.1007/BF02437521
Key words
- viscoelastic solid with void
- variational integral method
- generalized variational principle
- generalized potential energy principle
- Timoshenko beam