Isogeometric topology optimization for auxetic metamaterials and structures

University of Technology Sydney. Faculty of Engineering and Information Technology.It is known that topology optimization is located at the conceptual design phase, which can effectively determine the numbers, connectivity and existence of holes in the structural design domain and evolve design elements to improve the concerned performance. General speaking, topology optimization works as an important tool to seek for the optimal material distribution, which has been identified as one of the most promising sub-field of structural optimization due to its superior features occurring in the conceptual design stage without prior knowledge of the design domain. In the current work, the main intention is to propose a novel numerical method for the topology optimization with more effectiveness and efficiency for the single-material structures and structures with multiple materials. Meanwhile, the proposed topology optimization method is also applied to implement the rational design of auxetic metamaterials and auxetic composites. In Chapter 1, we provide a brief description for the main intention of the current work. In Chapter 2, the comprehensive review about the developments of topology optimization, isogeometric topology optimization and the rational design of auxetic materials is provided. In Chapter 3, a more effective and efficient topology optimization method using isogeometric analysis is proposed for continuum structures using an enhanced density distribution function (DDF). The construction of the DDF mainly involves two steps: (1) the smoothness of nodal densities is improved by the Shepard function; (2) the higher-order NURBS basis functions are combined with the smoothed nodal densities to construct the DDF with the continuity. A topology optimization formulation to minimize the structural mean compliance is developed using the DDF and isogeometric analysis (IGA) is applied to solve structural responses. An integration of the geometry parametrization and numerical analysis offer several benefits for the optimization. The Chapter 4 intends to develop a Multi-material Isogeometric Topology Optimization (M-ITO) method. Firstly, a new Multi-material Interpolation model is established with the use of NURBS (Non-uniform Rational B-splines), termed by the “N-MMI” model, which mainly involves three components: (1) Multiple Fields of Design Variables (DVFs); (2) Multiple Fields of Topology Variables (TVFs); (3) Multi-material interpolation. Two different M-ITO formulations are developed using the N-MMI model to address the problems with multiple volume constraints and the total mass constraint, respectively. The decoupled expression and serial evolving of the DVFs and TVFs can effectively eliminate numerical difficulties in the multi-material problems. In Chapter 5, the proposed ITO method is applied for the systematic design of both 2D and 3D auxetic metamaterials. An energy-based homogenization method (EBHM) to evaluate the macroscopic effective properties is numerically implemented by IGA, with the imposing of periodic boundary formulation on material microstructure. An ITO formulation for 2D and 3D auxetic metamaterials is developed using the DDF, where the objective function is defined as a combination of the homogenized elastic tensor. A relaxed optimality criteria (OC) method is used to update the design variables, due to the non-monotonic property of the problem. In Chapter 6, the proposed M-ITO method is applied for the systematic design of both 2D and 3D auxetic composites. The homogenization, that evaluates macroscopic effective properties of auxetic composites, is numerically implemented by IGA, with the imposing of the periodic boundary formulation on composite microstructures. The developed N-MMI model is applied to describe the multi-material topology and evaluate the multi-material properties. A topology optimization formulation for the design of both two-dimensional (2D) and three-dimensional (3D) auxetic composites is developed. Finite element simulations of auxetic composites are discussed using the ANSYS to show different deformation mechanisms. Finally, conclusions and prospects are given in Chapter 7

Computational Based Investigation of Lattice Cell Optimization under Uniaxial Compression Load

Structural optimization is a methodology used to generate novel structures within a design space by finding a maximum or minimum point within a set of constraints. Topology optimization, as a subset of structural optimization, is often used as a means for light-weighting a structure while maintaining mechanical performance. This article presents the mathematical basis for topology optimization, focused primarily on the Bi-directional Evolutionary Structural Optimization (BESO) and Solid Isotropic Material with Penalization (SIMP) methodologies, then applying the SIMP methodology to a case study of additively manufactured lattice cells. Three lattice designs were used: the Diamond, I-WP, and Primitive cells. These designs are all based on Triply Periodic Minimal Surfaces (TPMS). Individual lattice cells were subjected to a uniaxial compression load, then optimized for these load conditions. The optimized cells were then compared to the base cell designs, noting changes in the stress field response, and the maximum and minimum stress values. Overall, topology optimization proved its utility under this loading condition, with each cell seeing a net gain in performance when considering the volume reduction. The I-WP lattice saw a significant stress reduction in conjunction with the mass and volume reduction, marking a notable increase in cell performance

Dynamic multiscale topology optimization for multi-regional micro-structured cellular composites

© 2018 Elsevier Ltd In this paper, a new dynamic multiscale topology optimization method for cellular composites with multi-regional material microstructures is proposed to improve the structural performance. Firstly, a free-material distribution optimization method (FMDO) is developed to generate the overall configuration for the discrete element densities distributed within a multi-regional pattern. The macrostructure is divided into several sub regions, and each of them consists of a number of elements but with the same densities. Secondly, a dynamic topology optimization formulation is developed to perform the concurrent design of the macrostructure and material microstructures, subject to the multi-regional distributed element densities. A parametric level set method is employed to optimize the topologies of the macrostructure and material microstructures, with the effective macroscopic properties evaluated by the homogenization. In the numerical implementation, the quasi-static Ritz vector (QSRV) method is incorporated into the finite element analysis so as to reduce the computational cost in numerical analysis, and some kinematical connectors are introduced to make sure the connectivity between adjacent material microstructures. Finally, 2D and 3D numerical examples are tested to demonstrate the effectiveness of the proposed dynamic multiscale topology optimization method for the material-structural composites

Topology optimization for multiscale design of porous composites with multi-domain microstructures

© 2018 Elsevier B.V. This paper proposes a new multiscale topology optimization method for the design of porous composites composed of the multi-domain material microstructures considering three design elements: the topology of the macrostructure, the topologies of multiple material microstructures and their overall distribution in the macrostructure. The multiscale design involves two optimization stages: the free material distribution optimization and the concurrent topology optimization. Firstly, the variable thickness sheet (VTS) method with the regularization mechanism is used to generate multiple element density distributions in the macro design domain. Hence, different groups of elements with the identical densities can be uniformly arranged in their corresponding domains, and each domain in the space will be periodically configured by a unique representative microstructure. Secondly, with the discrete material distributions achieved in the macro domain, the topology of the macrostructure and topologies of multiple representative microstructures are concurrently optimized by a parametric level set method combined with the numerical homogenization method. Finally. Several 2D and 3D numerical examples are provided to demonstrate the effectiveness of the proposed multiscale topology optimization method

Topological design of continuum structures with global stress constraints considering self-weight loads

This paper proposes an approach for the topological design of continuum structures with global stress constraints considering self-weight loads. The rational approximation of material properties is employed to describe the material distribution for overcoming the parasitic effect for low densities. The structure volume is used as the objective function to be minimized. The local stress constraints for all elements are aggregated into a global stress constraint using the improved P-norm method. A model for the stress-constrained topology optimization of continuum structures considering the self-weight loads is established. The projection filtering method is adopted to avoid numerical instability, and the topology optimization problems are solved using the method of moving asymptotes. Several numerical examples are presented to demonstrate the validity of the proposed method. The structures obtained by the proposed method can have better performance. The effects of different norm parameters, stress constraints and mesh densities on the topological structures are analyzed

Assessing the Versatility and Robustness of Pore Network Modeling to Simulate Redox Flow Battery Electrode Performance

Porous electrodes are core components that determine the performance of redox flow batteries. Thus, optimizing their microstructure is a powerful approach to reduce system costs. Here we present a pore network modeling framework that is microstructure and chemistry agnostic, iteratively solves transport equations in both half-cells, and utilizes a network-in-series approach to simulate the local transport phenomena within porous electrodes at a low computational cost. In this study, we critically assess the versatility and robustness of pore network models to enable the modeling of different electrode geometries and redox chemistries. To do so, the proposed model was validated with two commonly used carbon fiber-based electrodes (a paper and a cloth), by extracting topologically equivalent networks from X-ray tomograms, and evaluated for two model redox chemistries (an aqueous iron-based and a non-aqueous TEMPO-based electrolyte). We find that the modeling framework successfully captures the experimental performance of the non-aqueous electrolyte but is less accurate for the aqueous electrolyte which was attributed to incomplete wetting of the electrode surface in the conducted experiments. Furthermore, the validation reveals that care must be taken when extracting networks from the tomogram of the woven cloth electrode, which features a multiscale microstructure with threaded fiber bundles. Employing this pore network model, we elucidate structure-performance relationships by leveraging the performance profiles and the simulated local distributions of physical properties and finally, we deploy simulations to identify efficient operation envelopes

Topology Optimization of Micro-Structured Materials Featured with the Specific Mechanical Properties

© 2020 World Scientific Publishing Company. Micro-structured materials consisting of an array of microstructures are engineered to provide the specific material properties. This present work investigates the design of cellular materials under the framework of level set, so as to optimize the topologies and shapes of these porous material microstructures. Firstly, the energy-based homogenization method (EBHM) is applied to evaluate the material effective properties based on the topology of the material cell, where the effective elasticity property is evaluated by the average stress and strain theorems. Secondly, a parametric level set method (PLSM) is employed to optimize the microstructural topology until the specific mechanical properties can be achieved, including the maximum bulk modulus, the maximum shear modulus and their combinations, as well as the negative Poisson's ratio (NPR). The complicated topological shape optimization of the material microstructure has been equivalent to evolve the sizes of the expansion coefficients in the interpolation of the level set function. Finally, several numerical examples are fully discussed to demonstrate the effectiveness of the developed method. A series of new and interesting material cells with the specific mechanical properties can be found