Pure bending analysis of thin rectangular SSSS plate Using Taylor-Mclaurin series

The bending properties of a plate depend greatly on its thickness as compared with its other dimensions. Previous studies have also made distinction between bending in; thin plates with small deflections, thin plates with large deflections and thick plates. Earlier studies on pure bending of thin rectangular plates were, however, centered on the use of trigonometric series and approximate methods in form of numerical and energy methods. In the present study, an in-depth bending analysis of transversely loaded thin rectangular SSSS plate was carried out. The analysis was accomplished through a theoretical formulation of shape function based on Taylor-McLaurin's series and subsequently used the shape function on Ritz energy method. The Taylor-McLaurin's series shape function was truncated at the fifth terms in x and y before substituting into a total potential energy functional, which was formulated based on Ritz energy approach. Boundary conditions for SSSS plate was first applied to the shape function in order to determine the constants J_m and K_n before substitution into the potential energy functional. The resulting functional equation was minimized and simplified to obtain α. Values of α from the present study were compared with those obtained by other researchers in previous studies. The average percentage difference is about 3.63 and this indicates that the Taylor-McLaurin's shape function is very close to exact displacement shape function of SSSS plate. Therefore, we conclude that the Taylor-McLaurin's shape function is a close approximation of the exact displacement function of a deflected simply supported rectangular thin plate.