A finite element code for thin plate dynamics (Q1111816)

The present paper offers a remarkably simple alternative dynamic finite element computational discriptor for thin plate vibrational capability. The spirit for the proposed displacement version finite element formalism rests upon the problem setup procedure of the recently published automated hybrid finite element system of the same author and \textit{H. Alaylioglu} [Int. J. Numer. Methods Eng. 24, 1615-1628 (1987; Zbl 0626.73071)]. The major advantage of this simulator is the minimization of the element integration efforts, such that the number of integrand evaluations is as in the case of a commonly envisaged one-point Gauss integrated model, while the results are free from the hourglass instabilities. Thereby, the scheme circumvents the computational expense involved in a priori or a posteriori anti-hourglassing filter, that is, stabilization of the underintegrated element. The purpose of this paper is threefold: (i) to fully develop powerful algorithms pertaining to the computer automated finite element analysis system that is user-friendly, efficient and reliable, (ii) to apply them to a spectrum of practical vibration mode predictions, and (iii) to compare the solutions with alternative approaches. Two stringent benchmark test problems, consisting of a cantilever and a clamped plate, are used to demonstrate the efficacy of the proposed easy-to-use thin plate simulator based on nonreduced integral implementation.