Multilevel computer-aided optimum design of structural systems using multiple basis vectors.

摘要

A new alternative multilevel structural optimization method using multiple basis vectors for each substructure is presented. The system level design task is formulated using multiple design space basis vectors for each substructure and the corresponding participation coefficients (system level design variables). In the system level design problem the total structural weight is minimized, subject to the system level constraints, namely static displacement limitations and natural frequency constraints. At the end of a system level optimization stage, the weight of each substructure is evaluated and used to establish an updated upper bound weight cap constraint for each upcoming substructure optimization procedure. At the subsystem level the structure is decomposed into a number of small substructures each one of which contains multiple design space basis vectors. A buffer (slack) variable is selected as the objective function for each substructure. Stress and member buckling constraints are incorporated at the subsystem level. The design modification problem at the subsystem level is formulated in a manner such that maximization of the buffer variable drives the substructure design vector away from all of the constraints except the side constraints. After completing the subsystem level optimization task, the final values of buffer variables, local behavior constraints, and local design variables are obtained and used to evaluate lower limit values for the upcoming system level design variables. At both the system level and the subsystem level, design modification is carried out by solving a sequence of explicit approximate problems. The new alternative multilevel method which introduces multiple basis vectors for each substructure leads to greater flexibility when constructing and solving design optimization models for large structural systems.