Evolutionary Structural Frequency Optimization Using Sensitivity Reanalysis

The much more attention has been paid to the topology optimization of continuum structure in recent years, but limited effort was put into dynamic problems. Lots of engineering structural in using is subject to strong vibration and it is unusable in engineering practice without considering dynamic characteristics. Dynamic design should be considered in structural design.Dynamic optimization design is an important part of structural design and natural frequency of the vibration structure is one of the most important characteristics. The reaction of structure under dynamics load largely extent dependent on the previous natural frequency of the structural. When the dynamic load frequency bands close to natural frequency of the structural, there will be have over-vibration. To avoid over-vibration, natural frequency of the structural should be restricted.Evolutionary structural optimization was based on the simple idea of gradually removing the ineffectively used material from the design domain to achieve an optimal design. Because of the simple idea and effective calculation it was effectively used for structural frequency optimization. In order to obtain the vale of element sensitivity, it was assumed that the eigenvector was the same before and after the removal of that element. There is some error in the calculation of element sensitivity. Lots of elements are removed at each iteration. As more and more elements are removed from the design domain, the eigenvector can not be regard as the same before and after the removal of the element. Because of the big error of element sensitivity, we can not know which element should be removed.In order to update the element sensitivity and improve the effect of the optimization, evolutionary optimization using the sensitivity reanalysis is proposed. Each iteration twice element removal are carried out. The sensitivity reanalysis is conducted between the twice element removal. The sensitivity reanalysis do not need solve the eigenvalue problem twice. It is callused using the previous eigenvector and eigenvalue. In the case that eigenvector do not change significantly before and after the removal of the element, sensitivity reanalysis have a good calculation. It simplifies the sensitivity calculation significantly. Sensitivity Redistribution Method is applied to restrain checkerboard, mesh-independent, local modal and so on. An example is given and shown it is effective. In order to detect exactly which element should be added to the structure, a new element added criterion is proposed. After that, a bi-directional evolutionary structural optimization using sensitivity reanalysis is proposed. The evolutionary iteration procedure of the new approach is given. Some other adder/removal criterion, for example, the positive definite structure criterion, the smooth change criterion and the average value criterion, are introduced to ensure that the modified elements are detected effectively. The main idea of the approach is that elements adder and removal are implement separately. In this new approach a big removal ratio is allowed. It can save time. An example is given and it is shown that it has better performance.Considering the dynamic characteristics and the static characteristics, a new removal criterion is proposed. After that a new evolutionary structural optimization based on stress and frequency is proposed. It is more close to engineering practice. The evolutionary iteration procedure and the mechanical modal was given. An example is given and shown it is effective.