A Multi-constraints-relaxed Bi-level Optimization Algorithm For Composite Box Beams

Were we to save energy, it is of great significance to realize lightweight design forcar bodies. Replacement of material and structural optimization are the most commonways to realize lightweight. Because of the wide application of box beams in the carbody frame, in this work, I focus on the discussion on how to realize lightweight designfor composite box beams, taking into account the stiffness, strength and modalfrequency constraints. Actually, structural optimization is a mathematic optimizationproblem. For any optimization problems, we can use objectives, constraints and designvariables to describe them. My main contribution in this work is to propose a bi-levelmulti-constraints-relaxed optimization algorithm for laminated structure.This thesis begins with a brief literature review on the optimization methods usedin the design of laminated structure in recent years. I find that problem decomposition isof the most popular methods, for it significantly reduces the complexity of the originalproblem. It is obvious that for each subproblem, it would be much easier for theconvergence of optimization algorithms due to the reduction of the scale. However, itsdisadvantage is also transparent: it separates the original problem into manysubproblems but optimizes them independently. If no proper methods were used tocontrol each sub-optimization, the final result might be far from the global optimum.To overcome this shortcoming, this thesis develops a bi-levelmulti-constraints-relaxed optimization algorithm. This method separates theoptimization of laminated structure into two sub-levels, namely the size optimizationlevel and fiber orientation search level. Unlike the previous works, some auxiliaryparameters are introduced to relax some constraints in size optimization. Then therealization of fiber orientation search is based on the best size dimensions obtained inthe former step. For these auxiliary parameters, they are treated as system designvariables, and they are controlled and optimized in a system level. By properly definingthe system level, we can force the updating of the optimization towards the desireddirection.Since only continuous design variables are considered in size optimization, it iswise to adopt gradient based optimization algorithm. For fiber orientation search, amemory based genetic algorithm is introduced. When it comes to system level optimization, different cases require different optimization algorithm. A bisearch isquite enough for a single constraint relaxed case, because the relationship between thedegree of relaxation and final volume is monotonic. For a multi-constraints-relaxed case,a gradient based algorithm is used. Furthermore, to save time, an artificial neuralnetwork is constructed to reflect the relation between the size dimensions and beststructure performances.Finally, a single-constraint-relaxed case and two multi-constraints-relaxed casesare investigated to demonstrate the efficiency of this algorithm. Because the proposedalgorithm can force the final design’s stiffness responses to be just within the predefinedboundaries, it further explores the potentiality for lightweight design. A discussionrelating to its applicability in a wider field is included.