Two-scale topology of optimization of functionally graded lattice structures with varying volume fraction - 变体分比功能梯度点阵结构两尺度拓扑优化设计

Functionally graded lattice structures enjoy widespread attention due to their lightweight, high specific stiffness/strength, high fracture resistance and other good performances, yet design optimization of these structures is still a challenging task due its cross-scale and spatially graded geometrical characteristics. In this work, a two-step optimization strategy is proposed to design functionally graded lattice structures. In the first step, the Discrete Material Optimization (DMO) is conducted to obtain optimal macro structural configuration and micro structural distribution. In the second step, parametric optimization is conducted to obtain graded lattice structures with varying volume fraction. The advantage of this work includes the adoption of the varying volume fraction operation, which enables the management of complex microstructures, and the pattern of spatially graded microstructure, which further broadens design space and improves structural stiffness, facilitating efficient use of materials. Finally, several numerical examples are presented to verify the effectiveness of the proposed method which significantly expands design space and effectively improve the structural stiffness

A novel bio-inspired design method for porous structures: Variable-periodic Voronoi tessellation

This paper introduces a novel approach, namely Variable-Periodic Voronoi Tessellation (VPVT), for the bio-inspired design of porous structures. The method utilizes distributed points defined by a variable-periodic function to generate Voronoi tessellation patterns, aligning with a wide diversity of artificial or natural cellular structures. In this VPVT design method, the truss-based architecture can be fully characterized by design variables, such as frequency factors, thickness factors. This approach enables the optimal design of porous structures for both mechanical performance and functionality. The varied, anisotropic cell shapes and sizes of VPVT porous structures provide significantly greater design flexibility compared to typical isotropic porous structures. In addition, the VPVT method not only can design micro-macro multiscale materials, but is also applicable for the design of meso-macro scale truss-based porous structures, such as architecture constructions, biomedical implants, and aircraft frameworks. This work employs a Surrogate-assisted Differential Evolution (SaDE) method to perform the optimization process. Numerical examples and experiments validate that the proposed design achieves about 51.1% and 47.8% improvement in compliance performance and damage strength, respectively, than existing studies

Optimisation for ultralight and high-stiffness hierarchical structures with tailored lattice metamaterials

This research aims to develop advanced optimisation frameworks for the optimal design of ultralight and high-stiffness hierarchical structures with tailored lattice metamaterials, with the consideration of manufacturing effects, i.e., additive manufacturing building direction effects, and structural safety, i.e., yield criterion. Lattice structures are a type of bioinspired hierarchical lightweight structures with high stiffness-to-weight ratio and high strength-to-weight ratio. The scale decomposition method is adopted in this research to decompose lattice structures into two hierarchies, being the lower-hierarchical-level structures of lattice cells constructed with networks of struts and the higher-hierarchical-level structures composed of lattice metamaterials with effective material properties (e.g., effective elasticity tensors). To develop the optimisation frameworks, the following studies have been conducted. Firstly, a new framework has been developed to simultaneously optimise the distributions of relative densities, effective elastic moduli, and anisotropy of metamaterials in lattice structures. In this framework, a numerical homogenisation method is adopted to characterise the anisotropic effective elasticity tensors of lattice metamaterials, and neural-network-based surrogate models are developed to bridge the geometric information, i.e., lattice strut radii, of the lower-hierarchical-level lattice cells and the effective material properties of lattice metamaterials at the higher-hierarchical-level. Thus, the tailoring of relative densities, effective elastic moduli, and anisotropy can be enabled by optimising the lattice strut radii. A robust optimisation platform integrating multiple commercial software has been developed to implement the proposed optimisation framework. Case study results confirm that the structural efficiency (the stiffness-to-weight ratio) of graded lattice structures can be effectively improved by tailoring the anisotropy of lattice metamaterials. Secondly, a framework of conformal lattice structural optimisation has been developed to enable the optimisation of orientations of lattice cells to allow them to be not only conformal to the curved boundaries of higher-hierarchical-level structural features to achieve a better approximation of the boundary curvatures but also aligning with the paths of major principal stresses. This framework is implemented into open-source software, FEniCS (finite element solver) and IPOPT (sensitivity solver). Case study results demonstrated that conformal lattice structures can achieve higher structural efficiency than non-conformal lattice structures. Thirdly, the effects of building direction (BD) on the effective Young’s moduli of lattice metamaterials, fabricated using selective laser melting, have been investigated through conducting quasi-static uniaxial compression tests at room temperature. A surrogate model has been developed to describe the BD effects on the effective Young’s moduli of lattice metamaterials as a function of their relative densities and strut overhang angles. This surrogate model has been integrated into the optimisation framework to enable the BD effects to be considered during optimising cell orientations for conformal lattice structures. Finally, yield stress constrained lattice structural optimisation framework has been developed to ensure the structural safety of optimised lattice structures with respect to yield failure. Fillets are introduced to the strut joint regions of lattice cells to effectively enhance the yield stresses of the lattice metamaterials. The effective properties (the effective Young’s moduli, the effective Poisson’s ratios, and the effective yield stresses) of the lattice metamaterials have been experimentally characterised through conducting quasi-static uniaxial compression tests at room temperature. A yield stress constraint for lattice structural optimisation has been derived based on the von Mises yield criterion. Case study results show that by introducing the yield stress constraint, the structural safety of optimised lattice structures with respect to yield failure can successfully be guaranteed. The results also demonstrate that the strength-to-weight ratio of the optimised lattice structures can be effectively improved by introducing fillets to the strut joint regions of lattice cells.Open Acces

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

Fibre-reinforced additive manufacturing: from design guidelines to advanced lattice structures

In pursuit of achieving ultimate lightweight designs with additive manufacturing (AM), engineers across industries are increasingly gravitating towards composites and architected cellular solids; more precisely, fibre-reinforced polymers and functionally graded lattices (FGLs). Control over material anisotropy and the cell topology in design for AM (DfAM) offer immense scope for customising a part’s properties and for the efficient use of material. This research expands the knowledge on the design with fibre-reinforced AM (FRAM) and the elastic-plastic performance of FGLs. Novel toolpath strategies, design guidelines and assessment criteria for FRAM were developed. For this purpose, an open-source solution was proposed, successfully overcoming the limitations of commercial printers. The effect of infill patterns on structural performance, economy, and manufacturability was examined. It was demonstrated how print paths informed by stress trajectories and key geometric features can outperform conventional patterns, laying the groundwork for more sophisticated process planning. A compilation of the first comprehensive database on fibre-reinforced FGLs provided insights into the effect of grading on the elastic performance and energy absorption capability, subject to strut-and surface-based lattices, build direction and fibre volume fraction. It was elucidated how grading the unit cell density within a lattice offers the possibility of tailoring the stiffness and achieving higher energy absorption than ungraded lattices. Vice versa, grading the unit cell size of lattices yielded no effect on the performance and is thus exclusively governed by the density. These findings help exploit the lightweight potential of FGLs through better informed DfAM. A new and efficient methodology for predicting the elastic-plastic characteristics of FGLs under large strain deformation, assuming homogenised material properties, was presented. A phenomenological constitutive model that was calibrated based upon interpolated material data of uniform density lattices facilitated a computationally inexpensive simulation approach and thus helps streamline the design workflow with architected lattices.Open Acces

Anisotropic design and optimization of conformal gradient lattice structures

In this work, we present a novel anisotropic lattice structure design and multi-scale optimization method that can generate conformal gradient lattice structures (CGLS). The goal of optimization is to achieve gradient density, adaptive orientation and variable scale (or periodic) lattice structures with the highest mechanical stiffness. The asymptotic homogenization method is employed for the calculation of the mechanical properties of various lattice structures. And an equation of elastic tensor and relative density of the unit cell is established. The established function above is then considered in the numerical optimization schemes. In the post-processing, we propose a numerical projecting method based on Fourier transform, which can synthesize conformal gradient lattice structure without changing the size and shape of the unit cells. Besides, the algorithm allows us to minimize distortion and prevent defects in the final lattice and keep the lattice structures smooth and continuous. Finally, in comparison with different parameters and methods are performed to demonstrate the superiority of our proposed method. The results show that the optimized anisotropic conformal gradient lattice structures are much stiffer and exhibit better structural robustness and buckling resistance than the uniform and the directly mapped designs