Influence of shear deformations in plate bending

Abstract

The influence of shear deformations in plate bending becomes significant when the ratio of the thickness to span is relatively large. However, the effects of transverse shear strains are neglected normally in classical theory and therefore, Kirchhoff thin plate theory is not adequate for providing accurate deflections, shear and bending moment values in both static and dynamic conditions. In order to include the influence of shear strains, the shear deformation theories, such as the first order shear deformation theory of Mindlin, is used. Normally, for the analyses of relatively thick plates special category of solid finite elements incorporating the shear deformations are used. In this study, however, a new version of Hrennikoff lattice model has been introduced for the analysis of thick plates. The flexural stiffness properties of the individual members of the lattice model have been appropriately modified to take into account the influence of shear deformations. Thus, the complicated expressions and the extensive theoretical derivations involved in following the Mindlin’s thick plate theory, are avoided. Further, the task of computer programming as well as the speed of computations have been simpler and much faster. For purposes of illustration, a number of thick plates of square, rectangular and elliptical shapes and with different support conditions are analysed under the action of UDL and point load for varying thickness to span ratios. The results of analyses corresponding to a) the closed form solutions, b) the 2D and 3D solid finite elements, and c) the lattice model technique have been presented in a comparative fashion. It has been demonstrated that the newly introduced lattice model technique provides relatively very high degree of accuracy for thick plates, by using appropriate shape factors.