NUMERICAL ASPECTS FOR FREE-VIBRATION OF THICK PLATES - PART I - FORMULATION AND VERIFICATION

This paper investigates the numerical aspects for free vibration analy sis of a class of thick (relative thickness ratio t/b > 0.2), shear de formable, rectangular plates with all possible combinations of edge co nditions. These thick plate vibration frequencies most probably cannot be accurately determined using the classical thin plate theory or the Mindlin plate theory. The effect of transverse shear strain has been considered by using a higher-order plate theory without the need for a shear correction factor. Unlike some domain discretization methods, t his analysis assumes a single global element for the entire plate. The strain and kinetic energy integrals of the global plate element are f ormulated and the energy functional is minimized to yield the natural frequencies. A set of boundary-compliant admissible shape functions is developed to obtain solutions which are unattainable using the classi cal trigonometric admissible functions. The numerical efficiency of sy mmetry classification is investigated and, on certain computational pl atforms, more than 80% of the execution time can be saved while mainta ining the same level of accuracy. (C) 1998 Elsevier Science S.A.