Development of a discrete Reissner–Mindlin element on Winkler foundation

Bending of a fiber-reinforced viscoelastic composite plate resting on elastic foundations

“…8, 9, 10, 11 and 12. The stressesσ x ,σ y , andσ xy are tensile at the top surface and compressive at the bottom one (see Figs. 8,9,10). The maximum values of the transverse shear stressesσ yz andσ xz occur at a point on the mid-plane of the plate as shown in Figs.…”

“…Wen [8] derived the fundamental solutions in the Laplace domain for a moderate thick plate (Mindlin's theory) resting on the two-parameter model (Pasternak's theory) by using three potential functions. The Discrete Reissner-Mindlin element was extended to solve problems of thin and thick plates resting on Winkler-type foundation by Abdalla and Ibrahim [9]. Large deflection, buckling responses and bending behavior of functionally graded rectangular plates resting on an elastic foundation were investigated in [10][11][12].…”

Effect of transverse shear strains on plates resting on elastic foundation using modified Vlasov model

“…The important point here is that the modulus of subgrade reaction, k, and the second parameter, 2t, which represents the shear deformation of the soil, are both dependent on the vertical deformation function f and the depth of the soil, H, as can be seen in Eq. (7) and (8). Furthermore the value of g varies with the displacement of the plate and the depth of the subsoil.…”

“…These values are used for the computation of the values of subgrade reaction, k, and soil shear parameter, 2t, from Eqs. (7) and (8). With these values of k and 2t, the total coefficient matrix of the plate-soil system is constructed and the set of simultaneous equations is solved to find the displacements at discrete points in the plate.…”

“…Liu [7] developed differential quadrature element method for the static analysis of homogenous isotropic rectangular plates on Winkler foundation on the basis of first-order shear deformation theory. Abdalla and Ibrahim [8] developed a discrete Reissner-Mindlin triangular plate element for analysis of thick plates on Winkler foundation. Wang et al [9] used a semianalytical and semi-numerical method for the analysis of plates on layered foundation.…”