Abstract
Publisher Summary This chapter describes that if the plate shape is rectangular, the traditional finite difference method (FDM) and generalized differential quadrature (GDQ) method can be readily used to compute the vibration solutions ( Shu and Du 1997a , b ). FDM and GDQ can also be easily applied to plates with circular or circular sectorial domains because these shapes can be readily mapped into rectangles by using the polar coordinate system. However, for irregularly shaped domains, FDM and GDQ cannot be easily applied because their straight mesh lines do not fit the domain boundaries. A better choice is to use mesh-free numerical methods for solving these problems. In this chapter, the least squares-based finite difference (LSFD) method is presented for solving vibration problems of arbitrarily shaped plates. It will be shown that the LSFD method is a powerful mesh-free approach for solving the strong form of PDEs.
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