WIT Press

Analysis Of Von Kármán Plates Using A BEM Formulation


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L. Waidemam & W. S. Venturini


This work deals with non-linear geometrical plates in the context of von Kármán theory. The formulation is written in a way to require only boundary in-plane displacement and deflection integral equation for boundary collocations. At internal points only out of plane rotation, curvature and in-plane internal force representations are used. The non-linear system of algebraic equations to be solved is reduced to internal point collocation relations. The solution is solved by using a Newton scheme for which a consistent tangent operator was derived. Keywords: bending plates, geometrical nonlinearities. 1 Introduction The boundary element method (BEM) applied to solve plate-bending problems has been successfully used many times so far. An important characteristic of the boundary methods applied to plate bending is approximating all boundary values by the same shape function, avoiding therefore using higher order derivatives of displacement approximation to compute internal forces. Thus, bending and twisting moments and also shear forces are precisely evaluated. The method has already proved to be enough accurate and reliable for this kind of application. The plate bending numerical formulation is a very important subject in engineering due to be applied to a large number of complex problems such as aircraft, ship, car, pressure vessel, off shore structures among others. Usually these complex problems require accurate plate bending models as those that take into account the geometrical non-linear effects. In this context, several BEM formulations have already been proposed so far. One of the first works treating this subject is due to Morjaria [1]. Kamiya and Sawaki [2] have proposed a BEM formulation for elastic plates governed by the Berger equation. The first BEM


bending plates, geometrical nonlinearities.