Topology optimization of anisotropic materials and structures under design-dependent loads

Abstract

The traditional structural topology optimization studies the optimal material layout and distribution with pre-defined isotropic material and load conditions. However, it can be challenging when the materials are also considered in optimizations, or the load conditions become design-dependent. This thesis seeks to develop formulations, models, and algorithms for concurrent optimization of structural topology and its anisotropic materials, and topology optimization of structures under design-dependent loading. The concurrent optimization of topology and anisotropic materials is conducted via a two-scale optimization model that simultaneously designs the macro and micro scale topologies and the orientations of microstructures. The orientations are determined by an analytical solution instead of heuristic or gradient-based algorithms. In addition, the optimization problem is studied in a more manufacturable scenario: laminated composite structures, in which concurrent optimization is performed via the laminate topology and fiber orientations. Analytical solutions are proposed to determine material orientations, which are derived for element, patch, and ply orientation, under out-of-plane loadings. Moreover, extended and fully-coupled moving iso-surface threshold (MIST) method and algorithm are developed to solve the two-scale and laminated composite optimization problems. Topology optimization of structures under design-dependent pressure loadings is investigated via an equivalent loading method, which formulates the fluid-structure interface using equivalent virtual strain energy and work for equivalent stiffness matrix and load vector respectively. The exact expression of work equivalent nodal forces is analytically derived and compared to the Gaussian quadrature approximation applied in the literature. Another method that introduces novel topology representation and update model using substructures is developed to model the fluid-structure interface with single-level super-elements. In this method, equivalent stiffness matrices and equivalent load vectors are statically condensed via super-elements. Extended MIST algorithms are employed to implement topology optimization under design-dependent pressure loadings for minimum compliance and compliant mechanism designs, including new components to track and model interface boundaries. Subsequently, topology optimization under design-dependent pressure loads is extended to soft robotic applications. A novel design of pneumatic bending-type soft actuator is developed, and then formulated as compliant mechanisms under design-dependent pressure loadings and optimized. Then, the optimal design is numerically modeled using FEA, and fabricated using 3D printing and experimentally tested.