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Limit problems for plates surrounded by soft material. (English) Zbl 0624.73021

In this paper the authors consider the problem of a clamped elastic plate having a central part \(\Omega\) surrounded by a narrow annulus \(\Sigma_{\epsilon}\) which width \(r_{\epsilon}\) as well as Young modulus \(E_{\epsilon}\) tend to zero when \(\epsilon\) goes to zero. The question is to find the limit problem when \(\epsilon\) goes to zero and to study the convergence of the solution of the plate \({\bar \Omega}\cup \Sigma_{\epsilon}\) to the solution of the limit problem.
For this purpose, the authors study a more general mathematical problem covering the case of the elastic plates. By using the tool of the \(\Gamma\)-convergence they find the limit problem and prove an interesting convergence result on it.
The application of this general result to the elastic plate problem described above gives a very interesting mechanical result. The limit problem ammounts to be a problem of a clamped plate or a simply supported plate or an elastically supported plate depending on the behaviour of \(E_{\epsilon}/r_{\epsilon}\) when \(\epsilon\) goes to zero.
Reviewer: T.Hadhri

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74K20 Plates
49J99 Existence theories in calculus of variations and optimal control
65K10 Numerical optimization and variational techniques
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