Ciarlet, PG and Kesavan, S (1981) Two-dimensional approximations of 3-dimensional eigenvalue problems in plate-theory. In: Computer Methods in Applied Mechanics and Engineering, 26 (2). pp. 145-172.
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The eigenvalues and eigenfunctions corresponding to the three-dimensional equations for the linear elastic equilibrium of a clamped plate of thickness 2ϵ, are shown to converge (in a specific sense) to the eigenvalues and eigenfunctions of the well-known two-dimensional biharmonic operator of plate theory, as ϵ approaches zero. In the process, it is found in particular that the displacements and stresses are indeed of the specific forms usually assumed a priori in the literature. It is also shown that the limit eigenvalues and eigenfunctions can be equivalently characterized as the leading terms in an asymptotic expansion of the three-dimensional solutions, in terms of powers of ϵ. The method presented here applies equally well to the stationary problem of linear plate theory, as shown elsewhere by P. Destuynder.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Elsevier Science.|
|Date Deposited:||08 Feb 2012 09:44|
|Last Modified:||08 Feb 2012 09:44|
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