Second Order Sensitivity For Evolutionary Structural Frequency Optimization: The Concept & Application

Frequency optimization is of great interest in structural design. The dynamic response of a structure depends, to a large extent, on the first few natural frequencies of the structure. To avoid severe vibration, frequency optimum design should be conducted to steer them away from the frequency range of the dynamic loads.Evolutionary structural optimization (ESO) is an algorithm for topology optimization. It is based on the idea of gradually removing redundant material to achieve an optimal design. Studies have shown that this method can be effectively used for structural frequency optimization, however, the problem of low performance resulted from the failure of sensitivity number exists in actual application.In this thesis, based on the sensitivity number of the standard ESO method, the concept of second order sensitivity is proposed, the equation for its calculation is given out, and its relative error is analyzed. After that, a method improved from the standard ESO algorithm, called re-deleting procedure, is presented. This method adopts the second order sensitivity to update the sensitivity number, and examples show that it has better performance than the standard algorithm.ESO can be explained in the scope of optimization theory, and it has been pointed out that this method is actually a kind of sequential linear programming method. This thesis adopts the scale factor of element thickness as optimization variables and explains theoretically the ESO method for frequency optimization; then the theoretical aspect of second order sensitivity is explained, and the three possible expressions of second order sensitivity are studied for their relative errors. It is shown that the expression presented at first in the thesis is the most efficient form.Within the scope of optimization theory, the re-deleting procedure is explained in this thesis and it is generalized to the extent of multi-deleting procedure; then through examples, the expression of second order sensitivity according to the objective function is discussed.Examples in this thesis are programmed with VC++6.0 for the main structure. The dynamic finite element analysis is carried out using MSC.Nastran. Calculations for sensitivity numbers and second order sensitivities, along with the drawing of the FEA model, are conducted through Matlab.