Research On The Lanczos-based Modal Reanalysis Algorithm And Its Application

The automotive industry is one of the pillar industries of the national economy, which covers almost the entire contents of relevant industrial sector, inseparable from people’s production and life. Product designer can have an understanding of mechanical properties of the product before the trial out of automitive body parts samples by means of finite element analysis, thus shortening the design and development cycle of the product. In order to reach optimal utilization of materials, reduce manufacturing costs and total weight and improve economic efficiency of the vehicle, we can optimize the design on each car assembly structure by CAE method.In structural optimization, structural modifications happen very often. It is very important for improving the efficiency of the entire structure optimization that how to calculate rapidly the the low-order eigenvalues of the revised structures. So in order to improve the optimization design efficiency of the whole structure and accelerate the process of optimizing the design, it is very necessary to research the rapid reanalysis method so that we can decrease the computational amount in the modal reanalysis process. Moreover, that is also the main contents of this paper.To the modal reanalysis problem, this paper proposes a new method which combines Lanczos algorithm, projection techniques and reduced-basis method. The method is fast convergence due to the Lanczos vector and high accuracy of reduced basis due to global approximation at the same time. And a comparative analysis is done with other mainstream approaches. The results of numerical examples demonstrate the high accuracy of the method, which is capable of handling large-scale structural analysis problem in which topological modifications change a lot.We can efficiently reduce the iterative time in the optimization process by applying the modal reanalysis algorithm to the topological optimization design of the structure. Since in the concept design phase od automotive parts, in order to obtain the best layout form, several rounds of design are often needed, we use bidirectional evolutionary structural optimization (BESO) to gradually delete material from the initial structure so that the natural frequency moves towards the expected value. The main basis of structure modification is reducing the amount of estimated values of the frequency changes caused by particular elements. In the confined volume conditions, we often require to maxmize the first order natural frequency of the frame and door to avoid the resonance with other components of the vehicle and further improve the dynamic characteristics. By comparing the optimization results in the software OptiStruct with the numerical example, it is demonstrated that the Lanczos-based modal reanalysis method has great advantages in structural frequency optimization, ensuring precision and saving computation time as well.