A plate is considered to be a thin plate if the ratio of the plate thickness to the smaller span length is less than 1/20; it is considered to be a thick plate if this ratio is larger than 1/20 [1].

The behavior of thick plates has been investigated by several researchers. Reissner [2] derived expressions for moments and shear forces for isotropic elastic plates including the effects of shear deformation, rotatory inertia, and vertical stress sigma_z by using a variational principle. Later Mindlin [3] derived equations of motion for isotropic elastic plates including the effects of shear deformation and rotatory inertia and obtained the equations to calculate stresses of a plate. Ayvaz [4] derived the equations of motions for orthotropic elastic plates using Hamilton's principle, but did not present any results. Özdemir and Ayvaz [5] analyzed thick slabs with four-node finite element by using Mindlin's theory. No references have been found in the literature on the analysis of thick plates subjected to earthquakes by using higher order displacement shape function.

The purpose of this paper is to study shear locking-free analysis of thick plates using Mindlin's theory and to determine the effects of the thickness/span ratio, the aspect ratio and the boundary conditions on the linear responses of thick plates subjected to earthquake excitations. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the program, the finite element method is used for spatial integration and the Newmark-beta method is used for time integration. In the analysis, 8- and 17-node finite elements are used to construct the stiffness and mass matrices.

It is concluded that, by using 17-node finite element, the mesh size required to produce the desired accuracy can be approximately reduced to 1/4 of those of the 8-node finite elements, and that the effects of the thickness to span ratios on the absolute maximum displacement and bending moments are also larger for larger values of the aspect ratios than for smaller values of the aspect ratios.

1

S. Timoshenko, S. Woinowsky-Krieger, "Theory of Plates and Shells", Second edition, McGraw-Hill, New York, 1959.

2

E. Reissner, "On Bending of Elastic Plates", Quarterly of Applied Mathematics, 5(1), 55-68, 1947.

3

R.D. Mindlin, "Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates", Journal of Applied Mechanics, 18(1), 31-38, 1951.

4

Y. Ayvaz, "Parametric Analysis of Reinforced Concrete Slabs Subjected to Earthquake Excitation", PhD Thesis, Graduate School of Texas Tech University, Lubbock, Texas, 1992.

5

Y.I. Özdemir, Y. Ayvaz, "Analysis of Clamped and Simply Supported Thick Plates Using Finite Element Method", in Proceedings of the 6th International Conference on Advances in Civil Engineering, Istanbul, 652-661, 2004.

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