Rational Estimate For Move Limits In Structural Optimization And Its Application

In this dissertation, a new estimate method for the rational move limits is presented, which aims at ensuring reliability of approximate model for the approximate optimization technology. Approximate optimization technology is not only applied to reduce computation and analysis for the structural optimization design effectively, but also combined design of experiments can facilitate the structural optimization modeling. The approximate optimization method has been researched and applied more and more in structural optimization design. The approximate model which constructed with the approximate optimization technology can only approximate the original model at a certain extent, accuracy can not be ensured when distance between the start point and the current point increasing. One method for resolving such issues is that imposing reasonable limits to the design variables to ensure reliability of the approximate model.The computation of the move limits in traditional methods is mostly based on the position of design point and the boundary of design variables by a certain criteria. The strategy of giving move limits belongs to perceptual estimate method. They are rough sometimes. Some methods can change their move limits adapting with the position of design point. However, these methods only fit for a particular algorithm. The rational move limits in this dissertation aims at overcoming deficiency of the traditional move limits. The main contents are included as follows:(1) An evaluate model is constructed by iterative information. An approximate explicit function of constraint second-order estimation for the accumulated information is constructed by the zero-order and first-order information of linear approximation in current step and first-order information of the linear approximation in previous step. A rational estimate function for move limits is established by specified the error limit, which is greater than the absolute value of relative error about the first-approximation of the constraints and the evaluation function, to substitute the accurate function of the constraint condition as an evaluation function. Move limits are obtained by computing their inequalities that is converted from the rational estimate function of move limits. Therefore, the move limits estimation is promoted from perceptual to rationality for cumulative information of the linear approximation to constraint functions.(2) Combining the rational move limits with sequential quadratic programming algorithm, a new SQPRML (sequential quadratic programming with rational move limits) algorithm is presented. A large number of examples are compared using SQPRML and other algorithms, those numerical results show that the proposed algorithm is reliable and effective.(3) In addition, rational move limits are adopted in the shape optimization based on MSC.PATRAN/NASTRAN for two-dimensional continuum structure. A friendly user interface is developed with PCL for the program, which is proved feasible and effective by achieved optimal shapes for several classical structures.