J. Sladek, V. Sladek, H.A. Mang:
"Meshless Formulations for Simply Supported and Clamped Plate Problems";
International Journal for Numerical Methods in Engineering,
In this paper, simply supported and clamped thin elastic plates are analysed. The biharmonic differential equation, representing the basis of the Kirchhoff theory, is decomposed into two Poisson equations. Local boundary integral equations are derived for this system of equations. The meshless approximation based on the moving least-squares method is employed for the implementation. In the case of simply supported plates, it is sufficient to use the local boundary integral equations. For the case of clamped plates we propose to use a combination of the local boundary equations and the global ones. Then, two groups of nodal unknowns are computed separately. This leads to a reduced system of algebraic equations.
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