Modular-topology optimization of structures and mechanisms with free material design and clustering

Topology optimization of modular structures and mechanisms enables balancing the performance of automatically-generated individualized designs, as required by Industry 4.0, with enhanced sustainability by means of component reuse. For optimal modular design, two key questions must be answered: (i) what should the topology of individual modules be like and (ii) how should modules be arranged at the product scale? We address these challenges by proposing a bi-level sequential strategy that combines free material design, clustering techniques, and topology optimization. First, using free material optimization enhanced with post-processing for checkerboard suppression, we determine the distribution of elasticity tensors at the product scale. To extract the sought-after modular arrangement, we partition the obtained elasticity tensors with a novel deterministic clustering algorithm and interpret its outputs within Wang tiling formalism. Finally, we design interiors of individual modules by solving a single-scale topology optimization problem with the design space reduced by modular mapping, conveniently starting from an initial guess provided by free material optimization. We illustrate these developments with three benchmarks first, covering compliance minimization of modular structures, and, for the first time, the design of non-periodic compliant modular mechanisms. Furthermore, we design a set of modules reusable in an inverter and in gripper mechanisms, which ultimately pave the way towards the rational design of modular architectured (meta)materials.Comment: 30 page

Synthesis of Frame Field-Aligned Multi-Laminar Structures

In the field of topology optimization, the homogenization approach has been revived as an important alternative to the established, density-based methods because it can represent the microstructural design at a much finer length-scale than the computational grid. The optimal microstructure for a single load case is an orthogonal rank-3 laminate. A rank-3 laminate can be described in terms of frame fields, which are also an important tool for mesh generation in both 2D and 3D. We propose a method for generating multi-laminar structures from frame fields. Rather than relying on integrative approaches that find a parametrization based on the frame field, we find stream surfaces, represented as point clouds aligned with frame vectors, and we solve an optimization problem to find well-spaced collections of such stream surfaces. The stream surface tracing is unaffected by the presence of singularities outside the region of interest. Neither stream surface tracing nor selecting well-spaced surface rely on combed frame fields. In addition to stream surface tracing and selection, we provide two methods for generating structures from stream surface collections. One of these methods produces volumetric solids by summing basis functions associated with each point of the stream surface collection. The other method reinterprets point sampled stream surfaces as a spatial twist continuum and produces a hexahedralization by dualizing a graph representing the structure. We demonstrate our methods on several frame fields produced using the homogenization approach for topology optimization, boundary-aligned, algebraic frame fields, and frame fields computed from closed-form expressions.Comment: 19 pages, 18 figure

Design, Analysis and Experimental Evaluation of 3D Printed Variable Stiffness Structures

The rapid progress of additive manufacturing (AM) introduces new opportunities but also new challenges for design and optimization to ensure manufacturability, testability and accurate representation/prediction of the models. The present dissertation builds a bridge between design, optimization, AM, testing and simulation of advanced optimized variable-stiffness structures. The first part offers an insight on the mechanical, viscoelastic and failure characteristics of AM continuous fiber composites. This understanding was used in the second part to investigate the feasibility of different topology and fiber-orientation optimization methods and the manufacturability of the resulting models. The study also assesses the effects of the manufacturing constraints on the stiffness. In the third part, a framework was used to optimize the topology and orientation of lattice structures subjected to stress constraints. This framework uses homogenized stiffness and strength to expedite the optimization, and Hill’s criterion to express the stress constraint. Those properties are implemented in the macrostructure topology optimization to improve the lattice structure stiffness. The optimized design is projected and post-treated to ensure manufacturability. The framework tested for two case studies producing designs with enhanced yield strength. The last part of this research challenges the capabilities of AM to fabricate, for the first time, an optimized flexible wing model with internal structures. The wing was tested in a low-speed wind tunnel to validate a robust computational model which enables the future study of the aeroelastic performance of different optimized wing models. This dissertation demonstrates that the conjoint use of topology and orientation optimization and AM results in advanced lighter structures with enhanced stiffness and/or strength

Projection-based Topology Optimization Method for Linear and Nonlinear Design

Lighter designs are desirable in many industrial applications and structural optimization is an effective way to generate lightweight structures. Topology optimization is an important tool for investigating the optimal design of engineering structures. Although continuum topology optimization method has already achieved remarkable progress in recent years, there still exist several challenges for conventional density-based method such as manufacturability. Additive manufacturing (AM) is a rapidly developing technology by which the design can achieve more freedom. However, it does not mean that the optimized design generated by topology optimization algorithm can be directly manufactured without any geometry post-processing. Besides AM techniques, the traditional manufacturing methods of machining and casting are also popular in recent years, because the majority of engineering parts are manufactured through these methods. It is difficult for conventional density-based method to account for these manufacturing constraints. The projection-based topology optimization approach is a new trend in this field to properly restrict the optimal solutions by implementing geometric constraints. The nature of projection method is to apply new design variables projected in a pseudo-density domain to find the optimal solutions. In this dissertation, several advanced projection-based topology optimization schemes are proposed to resolve linear and nonlinear design problems and demonstrated through numerical examples. In chapter 2 and 3, a new projection technique is proposed to resolve nonlinear topology optimization problems with large deformation. Chapter 4 describes a novel design method, which combines the TPMS (Triply periodic minimal surface) formulation with standard projection-based method to design functionally graded TPMS lattice. In chapter 5, a projection-based method is combined with moving particles for reverse shape compensation for additive manufacturing technique. Chapter 6 describes a density‐based boundary evolving algorithm based on projection function for continuum‐based topology optimization. In the chapter 7, a novel projection-based method for structural design considering restrictions of multi-axis machining processes is proposed

Topology optimization of cables, cloaks, and embedded lattices

Materials play a critical role in the behavior and functionality of natural and engineered systems. For example, the use of cast-iron and steel led to dramatically increased bridge spans per material volume with the move from compression-dominant arch bridges to tensile-capable truss, suspension, and cable-stayed bridges; materials underlie many of the major technological advancements in the auto and aerospace industries that have made cars and airplanes increasingly light, strong, and damage tolerant; and the great diversity of biological materials and bio-composites enable complex biological and mechanical functions in nature. Topology optimization is a computational design method that simultaneously enhances efficiency and design freedom of engineered parts, but is often limited to a single, solid, isotropic, linear-elastic material. To understand how the material space can be tailored to enhance design freedom and/or promote desired mechanical behavior, several topology optimization problems are explored in this dissertation in which the space of available materials is either relaxed or restricted. Specifically, in a discrete topology optimization setting defined by 1D (truss) elements, tension-only systems are targeted by restricting the material space to that of a tension-only material and tailoring a formulation to handle the associated nonlinear mechanics. The discrete setting is then enhanced to handle 2D (beam) elements in pursuit of cloaking devices that hide the effect of a hole or defect on the elastostatic response of lattice systems. In this case the material space is relaxed to allow for a continuous range of stiffness and the objective is formulated as a weighted least squares function in which the physically-motivated weights promote global stiffness matching between the cloaked and undisturbed systems. Continuous 2D and 3D structures are also explored in a density-based topology optimization setting in which the material space is relaxed to accommodate an arbitrary number of candidate materials in a general continuum mechanics framework that can handle material anisotropy. The theoretical and physical relevance of such framework is highlighted via a continuous embedding scheme that enables manufacturing in the relaxed (or restricted) design space of lattice-based microstructural-materials. Implications of varying the material design space on the mechanics, mathematics, and computations needed for topology optimization are discussed in detail.Ph.D