Topology optimization for periodic multi-component structures with stiffness and frequency criteria

Abstract

Design of engineering structures may benefit from reduction in assembly complexity through use of periodic components, in which uniform sub-structures combine to form a relatively simple topology. The benefits of periodic structures include lower manufacture costs as well as ease of assembly. Recent developments in periodic topology optimization have shown its efficacy for addressing a range of design objectives. However, constraints such as assembly conditions and the connection configuration of periodic sub-components present limiting factors in the application of periodic optimization to real-world engineering problems. This study addresses the current knowledge gap in periodic optimization assembly through inclusion of common interfacing connections between periodic components, such as screws, welds, or rivets, thus accounting for real assembly conditions. A bi-directional evolutionary structural optimization (BESO) method and solid isotropic material with penalization (SIMP) method are presented, for stiffness and frequency criteria, which simultaneously optimizes the topology of the periodic components and the joint configuration connecting components. Elemental sensitivities are derived and utilized to drive the design of both the periodic component and the connection layouts. Iterative updating of the topological design, guided by elemental sensitivities, allows for optimization of the periodic topology for given objective functions. To demonstrate the effectiveness of the proposed method, optimized structures are explored through different periodicities. Application of the methodology presented in this study will assist in providing new design capabilities to reduce the costs of manufacturing, transport, and assembly through optimized periodic components.