A cascadic multilevel optimization algorithm for the design of composite structures with curvilinear fiber based on Shepard interpolation

A hierarchy of parameterizations of fiber angle arrangement are constructed by using the Shepard interpolation. From the top level to the bottom level of the hierarchy, the number and density of design points for the Shepard interpolation increase, thus the design freedom and the resolution of parameterization increase as well. Also, a hierarchy of optimization problems are formulated, and they are solved successively from the coarsest level to the finest level. After the optimization problem at a coarse level is solved, one goes to its neighboring finer level, using the solution of the former one to compute an initial design for the latter one. Again, the Shepard interpolation is used for the computation of initial design. In the cascadic multilevel optimization, it is not necessary to devote too much effort to find an accurate solution for the optimization at a coarse level, and the optimization is allowed to stop when it comes near a local optimal solution. Only at the finest level, it is meaningful to seek an accurate solution which is usually also a local optima. Therefore, a guideline for the selection of parameters that affect efficiency of the optimization at all the levels is proposed.