A Plate Infinite Element Method (PIEM) formulation based on Reissner-Mindlin theory is proposed for the stress analysis of cracked plates under bending and tension. The validity of the proposed formulation is demonstrated by comparing the results obtained for the normalized Stress Intensity Factor (SIF) under various loading conditions with the solutions presented in the literature. Importantly, the proposed formulation enables the effects of different crack lengths to be analyzed without the need to re-mesh the computational domain for each simulation/analysis. Overall, the PIEM formulation provides an accurate and computationally-efficient means of analyzing a wide variety of plate bending problems.

We analyze an isoparametric finite element method to compute thevibration modes of a plate, modeled by Reissner-Mindlin equations,in contact with a compressible fluid, described in terms ofdisplacement variables. To avoid locking in the plate, we considera low-order method of the so called MITC (Mixed Interpolation ofTensorial Component) family on quadrilateral meshes. To avoidspurious modes in the fluid, we use a low-order hexahedralRaviart-Thomas elements and a non conforming coupling is used onthe fluid-structure interface.Applying a general approximation theory for spectral problems,under mild assumptions, we obtain optimal order error estimatesfor the computed eigenfunctions, as well as a double order for theeigenvalues. These estimates are valid with constants independentof the plate thickness. Finally, we report several numericalexperiments showing the behavior of the methods.