| EXISTENCE THEOREM AND FINITE ELEMENT METHOD FOR STATIC PROBLEMS OF A CLASS OF NONLINEAR HYPERELASTIC SHELLS |
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| 作者姓名： | Li Zhiping |
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| 作者单位： | Department of |
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| 摘 要： | In this paper, various boundary value problems of hyperelastic shells are considered. It is assumed that the storede-nergy function W(x, F) of the material,of which the shell is made, satisfies polyconvex conditions proposed by Ball~(2]).Existence of minimum points of the total energy of the shell in suitably chosen function spaces, and in suitably chosen finite element spaces is proved. Convergence of the finite element solutions is proved under certain regular conditions on the minimum points and some additional assumptions on W(x, F). A Gradient type computing scheme for solving the finite element solutions is given, and global convergent result is obtained.
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| 收稿时间： | 5/8/1986 12:00:00 AM |
EXISTENCE THEOREM AND FINITE ELEMENT METHOD FOR STATIC PROBLEMS OF A CLASS OF NONLINEAR HYPERELASTIC SHELLS |
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| Li Zhiping.EXISTENCE THEOREM AND FINITE ELEMENT METHOD FOR STATIC PROBLEMS OF A CLASS OF NONLINEAR HYPERELASTIC SHELLS[J].Chinese Annals of Mathematics,Series B,1989,10(2):169-189. |
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| Authors: | Li Zhiping |
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| Institution: | Department of Mathematics, Beijing University, Beijing China. |
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| Abstract: | In this paper, various bonndary value problems of hyperelastic shells are considered. It is assumed that the storede-nergy function $\W(x,F)\]$ of the material,of which the shell is made, satisfies polyconvex conditions proposed by $\Bal{l^{2]}}\]$. Existence of minimum points of the total energy of the shell in suitably chosen function spaces, and in suitably chosen finite element spaces is proved. Convergence of the finite element solutions is proved under certain regular conditions on the mininmm points and some addttional assumptions on $\W(x,F)\]$. A Gradient type computing scheme for solving the finite element solutions is given, and global convergent result is obtained |
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