Simultaneous topology and size optimization of a 3D variable-length structure described by the ALE–ANCF

An efficient optimization approach is proposed to simultaneously optimize the topology and geometrical sizes of a three-dimensional (3D) variable-length structure. First of all, in a unified global coordinate system, a flexible multibody system (FMBS) model is established to describe the extension and contraction dynamics of a variable-length structure. The variable-length flexible structure is meshed by the proposed arbitrary Lagrangian–Eulerian (ALE) solid elements of absolute nodal coordinate formulation (ANCF). To consider the variable-length behaviors, the classic equivalent static loads (ESL) is redefined by introducing the concept of virtual design domain. With the help of the ESL, the dynamic response optimization of the variable-length structure is turned into a static one. A simultaneous topology and size optimization approach is initially proposed via the moving morphable components (MMC). By appropriately arranging the initial configuration of the components and linking all or part of the design variables of a component with others’ the variable-length structure can be designed as a homogeneous or heterogeneous periodic structure. The approach is numerically implemented via an additional constraint that modifies the sensitivities with respect to some design variables. Finally, three numerical examples are presented to demonstrate the effectiveness and efficiency of the proposed optimization approach.