A GENERALIZED EVOLUTIONARY METHOD FOR NATURAL FREQUENCY OPTIMIZATION OF MEMBRANE VIBRATION PROBLEMS IN FINITE-ELEMENT ANALYSIS

From the energy conservation principle, the contribution factor of an element to the:natural frequency of the finite element discretized sys tem of a membrane vibration problem is presented in this paper. Since the contribution factor of an element is derived from the general fini te element formulation of structural eigenvalue problems, it can be us ed for solving the natural frequency optimization problem of any struc ture. Therefore, the method associated with it is called as a generali zed evolutionary Method. Using the contribution factor of an element, the relevant evolutionary criterion which bridges between the structur al optimization and the,conventional finite element analysis can be ea sily established for the evolutionary natural frequency optimization o f a structure. Physically, the contribution factor of an element impli es the direct contribution of an element to the natural frequency of t he structure. A square membrane with four sides fixed has been chosen as an example to show the usefulness and robustness of the generalized evolutionary method for natural frequency optimization of membrane vi bration problems in the finite element analysis. (C) 1997 Elsevier Sci ence Ltd.