Dynamic stiffness design of plate/shell structures using explicit topology optimization

Abstract

The aim of this article is to present a novel and viable topological design approach for minimizing dynamic compliance of stiffened plate/shell structures subjected to time-harmonic loading with prescribed excitation frequency. In this method, the generalized incremental frequency technique (GIF) is introduced to transform the optimization problem into several sub-problems by making the prescribed excitation frequency located within different sub-intervals constructed by adjacent resonance frequencies. Based on this, a set of local optimum designs are identified by associating with the smallest value of dynamic compliance in each sub-interval, and then the optimized solution is selected from among these candidate solutions. Furthermore, the GIF technique is integrated into a Lagrangian-based topology optimization framework, where the stiffening topologies are represented explicitly by a set of geometric primitives such as line segments. In order to get an optimal layout solution, a special interpolation scheme called stiffness and mass transformation approach (SMTA) is presented to separate the line segments from the underlying FEM grids, so that they can move freely within the design domain. To demonstrate the benefits this method affords for dynamic design problems, three numerical examples are validated in detail. In each of the cases the optimization enables a significant reduction in the dynamic compliance. The proposed method allows for more flexibility in topology optimization, which is applicable for large-scale practical dynamic design problems.