A finite element model has been introduced for static bending analysis of THICK PLATES based on mixed plate variational formulation. refined Reissner' s mixed variational theoy is employed to derive the governing equations in terms of the introduced transverse normal stress and displacement variables. The in-plane displacement components of the plate are described by combination of polynomial and exponential terms. Concerning the transverse displacement component, first-order polynomial is adopted. second-order expansion is considered for the variations of the transverse normal component of the stress tensor along the THICKness direction of the plate. The boundary conditions of shear and normal tractions on the top and bottom surfaces of the plate are exactly satisfied. Based on the proposed mixed plate theory, 􀂃 four nodded compatible Hermitian rectangular element which ensures C1-type continuity of all unknown parameters of the plate along in-plane directions is employed. An arbitrary free parameter, called the splitting factor, appears in the functional of the proposed variational formulation. In the numerical part of the present paper, simple formulation has been proposed for selecting the splitting factor which leads to the results of higher precision. Comparison of present bending results for thin and THICK PLATES with results of the three-dimensional theory of elasticity and other plate theories available in literature reveals efficiency of the proposed parametrized mixed plate theory. Moreover, the proposed model has high convergence rate and is computationally low cost.

Due to their continuous material variation and eliminating the mismatch stress field in the THICKness direction, Functionally Graded Materials (FGMs) have found wide applications in aerospace and mechanical engineering. This article presents closed-form solution for THICK functionally graded plate based on three-dimensional elasticity theory. To this end, first, the characteristic equation of FG plate is derived and general closedform is obtained analytically. Both positive and negative discriminant of characteristic equation is considered and solved. The presented method is validated with finite element results by considering isotropic THICK plate. Several parametric studies are carried out to investigate the effect of geometric and material parameters. The aim of this research is to present analytical solution form for THICK FG plate and work out the problem of inconsistency for corresponding displacements field. The presented solution can be used to examine accuracy of various plate theories such as first-order, third order shear deformation theories and other equivalent plate theories.

In this study, the buckling response of homogeneous circular PLATES with variable THICKness subjected to radial compression based on the first-order shear deformation plate theory in conjunction with von-Karman nonlinear strain-displacement relations is investigated. Furthermore, optimal THICKness distribution over the plate with respect to buckling is presented. In order to determine the distribution of the prebuckling load along the radius, the membrane equation is solved using the shooting method. Subsequently, employing the pseudo spectral method that makes use of Chebyshev polynomials, the stability equations are solved. The influence of the boundary conditions, the THICKness variation profile and aspect ratio on the buckling behavior is examined. The comparison shows that the results derived, using the current method, compare very well with those available in the literature.

In this paper a variationally consistent trigonometric shear deformation theory is presented for the free vibration of THICK isotropic square and rectangular plate. In this displacement based theory, the in-plane displacement field uses sinusoidal function in terms of THICKness coordinate to include the shear deformation effect. The cosine function in terms of THICKness coordinate is used in transverse displacement to include the effect of transverse normal strain. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Results of frequency of bending mode, THICKness-shear mode and THICKness-stretch mode are obtained from free vibration of simply supported isotropic square and rectangular PLATES and compared with those of other refined theories and frequencies from exact theory. Present theory yields exact dynamic shear correction factor p2/12 from THICKness shear motion of the plate.

An analysis of buckling for THICK anisotropic PLATES subjected to arbitrary loading is presented. The analysis employs the complex finite strip method which utilizes complex harmonic functions in the longitudinal direction, a cubic polynomial in the transverse direction and a parabolic distribution of the transverse shear strains through the THICKness of the THICK plate based on the higher-order shear deformation theory. The method is programmed to investigate local buckling of square and long THICK PLATES subjected to compression bending and shear stresses. Examples of the accuracy of the method with an increasing number of strips are presented. The method is then applied to study the local instability of THICK orthotropic PLATES under compression and shear with different boundary conditions. Local instability interaction between compression and shear, and bending and shear in THICK orthotropic PLATES is investigated

Dynamic analysis of rectangular THICK PLATES on elastic foundations under partially distributed and centrally concentrated impulsive load is presented using Winkler foundation model. An 8-noded (PBQ8) Mindlin plate element are adopted for modeling the plate to account the transverse shear deformation effects neglected in the classical thin plate theory. Selective reduced integration technique is used to avoid shear locking problem which occurs as THICKness/span ratio decreases. The results obtained from the study are compared with the solutions obtained by SAP2000 software to show the validity of the elements. The variation of the maximum displacement with various values of subgrade reaction modulus, aspect ratios, the ratio of plate THICKness to shorter span of the plate and loaded area are investigated. Numerical examples show the applicability of the 8-noded element to dynamic analysis of THICK PLATES on elastic foundation subjected to external loads using Winkler model.