Analysis of the von Karman equations by group methods |
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Authors: | KA Ames WF Ames |
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Institution: | 1. Department of Mathematics, Iowa State University, Ames, Ia 50011, U.S.A.;2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A. |
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Abstract: | One of the systems of equations approximating the large deflection of plates consists of two coupled non-linear fourth order partial differential equations, known as the von Karman equations. The full symmetry group for the steady equations is a finitely generated Lie group with ten parameters. For the time-dependent system the full symmetry group is an infinite parameter Lie group. Several subgroups of the full group are used to generate exact solutions of the time-independent and the time-dependent systems. These include the dilatation group (similar solutions), rotation group, screw group and others. Physical implications and applications are discussed. |
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