GENERAL EVOLUTIONARY PATH FOR FUNDAMENTAL NATURAL FREQUENCIES OF STRUCTURAL VIBRATION PROBLEMS - TOWARDS OPTIMUM FROM BELOW

In this paper, both an approximate expression and an exact expression for the contribution factor of an element to the natural frequency of the finite element discretized system of a structure in general and a membrane in particular have been derived from the energy conservation principle and the finite element formulation of structural eigenvalue problems. The approximate expression for the contribution factor of an element is used to predict and determine the elements to be removed i n an iteration since it depends only on the quantities associated with the old system in the iteration. The exact expression for the contrib ution factor of an element makes it possible to check whether the elem ent is correctly removed at the end of an iteration because it depends on both the old system and the new system in the iteration. Thus, the combined use of the approximate expression and the exact expression a llows a considerable number of elements to be removed in a single iter ation so that the efficiency of the evolutionary structural optimizati on method can be greatly improved for solving the natural frequency op timization problem of a structure. A square membrane with different bo undary supports has been chosen to investigate the general evolutionar y path for the fundamental natural frequency of the structure. The rel ated results indicated that if the objective of a structural optimizat ion is to raise the fundamental natural frequency of the structure to an optimal value, the general evolutionary path during its optimizatio n is that the elements are gradually removed along the direction from the area surrounded by the contour of the highest value to that surrou nded by the contour of the lowest value.