Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (7): 763-773.

• 论文 • 上一篇    下一篇

TRANSVERSELY ISOTROPIC HYPER-ELASTIC MATERIAL RECTANGULAR PLATE WITH VOIDS UNDER A UNIAXIAL EXTENSION

程昌钧, 任九生   

  1. Shanghai Institute of Applied Mathematics and Mechanics, Department of Mechanics, Shanghai University, Shanghai 200072, P.R.China
  • 收稿日期:2001-10-19 修回日期:2003-02-21 出版日期:2003-07-18 发布日期:2003-07-18
  • 通讯作者: CHENG Chang-jun
  • 基金资助:
    the National Natural Science Foundation of China (10272069)

TRANSVERSELY ISOTROPIC HYPER-ELASTIC MATERIAL RECTANGULAR PLATE WITH VOIDS UNDER A UNIAXIAL EXTENSION

CHENG Chang-jun, REN Jiu-sheng   

  1. Shanghai Institute of Applied Mathematics and Mechanics, Department of Mechanics, Shanghai University, Shanghai 200072, P.R.China
  • Received:2001-10-19 Revised:2003-02-21 Online:2003-07-18 Published:2003-07-18
  • Supported by:
    the National Natural Science Foundation of China (10272069)

摘要: The finite deformation and stress analyses for a transversely isotropic rectangular plate with voids and made of hyper-elastic material with the generalized neo-Hookean strain energy function under a uniaxial extension are studied. The deformation functions of plates with voids that are symmetrically distributed in a certain manner are given and the functions are expressed by two parameters by solving the differential equations.The solution may be approximately obtained from the minimum potential energy principle. Thus, the analytic solutions of the deformation and stress of the plate are obtained. The growth of the voids and the distribution of stresses along the voids are analyzed and the influences of the degree of anisotropy, the size of the voids and the distance between the voids are discussed. The characteristics of the growth of the voids and the distribution of stresses of the plates with one void, three or five voids are obtained and compared.

Abstract: The finite deformation and stress analyses for a transversely isotropic rectangular plate with voids and made of hyper-elastic material with the generalized neo-Hookean strain energy function under a uniaxial extension are studied. The deformation functions of plates with voids that are symmetrically distributed in a certain manner are given and the functions are expressed by two parameters by solving the differential equations.The solution may be approximately obtained from the minimum potential energy principle. Thus, the analytic solutions of the deformation and stress of the plate are obtained. The growth of the voids and the distribution of stresses along the voids are analyzed and the influences of the degree of anisotropy, the size of the voids and the distance between the voids are discussed. The characteristics of the growth of the voids and the distribution of stresses of the plates with one void, three or five voids are obtained and compared.

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