Direct Integration and Work Principle as New Approach in Bending Analyses of Isotropic Rectangular Plates
Ibearugbulem, O. M., Ettu, L. O. and Ezeh, J. C.
2013 The International Journal of Engineering And Science (IJES) Science (IJES), 2(3): 28-36
Rectangular plate; Direct integration; Strain energy; Variational principles; Governing differential equation; Shape function; Equilibrium ofworks; Taylor series
Ibearugbulem, O. M., Ettu, L. O. and Ezeh, J. C., (2013), "Direct Integration and Work Principle as New Approach in Bending Analyses of Isotropic Rectangular Plates", The International Journal of Engineering And Science (IJES) Science (IJES), 2(3): 28-36.
Abstract:
Following the woork of Timoshenko &Woinowsky¨CKrieger(1959) and subsequent researchers, the traditional approaches in analysis of isotropic rectangular plates has been to assume a differential continuous shape function and to employ strain energy and variational principles. Theseapproaches are grossly limited by the difficulty in assuming suitable shape functions, especially for young structural analysts. A new approach to bending analysis of rectangular plates is presented in this paper. Unlike the traditional approaches that first of all assume a shape function, the shape function in this new approach is obtained by direct integration of the governing differential equation for isotropic rectangular plates. This shape function is in the form of Taylor series in two dimensions.Also, rather than the strain energy and variational principles of the traditional approaches, the plate analysis in this new approach is by the simple principle of equilibrium of works performed by the action (load) and resistance (plate),through which equations for deflection and bending moments are obtained. The maximum deflection at the center of SSSS plateand the maximum bending moment in X-direction obtained by this new approach compare favourably with those fromTimoshenko &Woinowsky¨CKrieger(1959) for aspect ratios from 1.0 to 2.0 at 0.1 increments. It is therefore, recommended that this new approach could be ore easily and better used for the analysis of isotropic rectangular plates.
