Topology Optimization and Analysis of Thermal and Mechanical Metamaterials

To take advantage of multi-material additive manufacturing technology using mixtures of metal alloys, a topology optimization framework is developed to synthesize high-strength spatially periodic metamaterials possessing unique thermoelastic properties. A thermal and mechanical stress analysis formulation based on homogenization theory is developed and is used in a regional scaled aggregation stress constraint method, and a method of worst-case stress minimization is also included to efficiently address load uncertainty. It is shown that the two stress-based techniques lead to thermal expansion properties that are highly sensitive to small changes in material distribution and composition. To resolve this issue, a uniform manufacturing uncertainty method is utilized which considers variations in both geometry and material mixture. Test cases of high stiffness, zero thermal expansion, and negative thermal expansion microstructures are generated, and the stress-based and manufacturing uncertainty methods are applied to demonstrate how the techniques alter the optimal designs. Large reductions in stress are achieved while maintaining robust strength and thermal expansion properties. An extensive analysis is also performed on structures made from two-dimensional lattice materials. Numerical homogenization, finite element analysis, analytical methods, and experiments are used to investigate properties such as stiffness, yield strength, and buckling strength, leading to insights on the number of cells that must be included for optimal mechanical properties and for homogenization theory to be valid, how failure modes are influenced by relative density, and how the lattice unit cell can be used to build macrostructures with performance superior to structures generated by conventional topology optimization

Set-based Design Method for Multi-objective Structural Design with Conflicting Performances Under Topological Change

In car manufacturing, sustainable structural design with multiple conflicting objectives like weight reduction for less CO2 emission, strength and rigidity is essential. This research focuses on topological optimization method with which greater weight reduction is expected to be achieved. In view of the application of preference set-based design (PSD) method, topologically satisfied design is considered. We applied PSD method to the design of topological model. This study indicates the efficacy of PSD method to topological design problems including weight reduction aspect

Stacking sequences in composite laminates through design optimization

AbstractComposites are experiencing a new era. The spatial resolution at which is to date possible to build up complex architectured microstructures through additive manufacturing-based and sintering of powder metals 3D printing techniques, as well as the recent improvements in both filament winding and automated fiber deposition processes, are opening new unforeseeable scenarios for applying optimization strategies to the design of high-performance structures and metamaterials that could previously be only theoretically conceived. Motivated by these new possibilities, the present work, by combining computational methods, analytical approaches and experimental analysis, shows how finite element Design Optimization algorithms can be ad hoc rewritten by identifying as design variables the orientation of the reinforcing fibers in each ply of a layered structure for redesigning fiber-reinforced composites exhibiting at the same time high stiffness and toughening, two features generally in competition each other. To highlight the flexibility and the effectiveness of the proposed strategy, after a brief recalling of the essential theoretical remarks and the implemented procedure, selected example applications are finally illustrated on laminated plates under different boundary conditions, cylindrical layered shells with varying curvature subjected to point loads and composite tubes made of carbon fiber-reinforced polymers, recently employed as structural components in advanced aerospace engineering applications

Optimal shape and topology of multi-material microstructures in min-max stress design problems

The present dissertation seeks to optimize the unit cell of a two-dimensional cellular material, pursuing the minimization of the peak equivalent stress in the microstructure. This class of materials is particularly relevant to the design of lightweight structures. By minimizing the peak stress in the microstructure, it is possible to use material in a more rational way. Given the periodic nature of the problem, asymptotic homogenization is employed to compute the stress distribution in the microstructure when a macroscopic load is applied, since periodicity boundary conditions are imposed. With this being a purely conceptual study, only three macroscopic loads are considered: the hydrostatic, biaxial, and pure shear ones. Initially, the single-material problem is solved through shape optimization. Then, the potential to reduce the peak equivalent stress through the introduction of additional material phases is explored. Also with shape optimization, the in uence of one additional material phase is studied. Additionally, topology optimization is used to discover the functionally graded material that minimizes the peak stress in the microstructure. The obtained results show that an increased design exibility always leads to milder stress states. The known theoretical results were successfully replicated, with minimal error measures associated. By increasing the number of material phases in the microstructure, peak stress reduction are attainable. A uniformly stressed microstructure is possible to obtain, by means of a functionally graded material

Minimization of the stress concentration in Formed Parts through Non-Parametric Optimization

Parametric and non-parametric are the main optimization methods that are used in various industrial fields. In non-parametric optimization, the process of manipulating the node locations (shape optimization) or removing mass without changing the node locations (topology optimization) is adopted to achieve a desired objective. This structural optimization is formulated as a non-parametric problem, and for analysis purposes, ABAQUS/CAE software is adopted for this approach. Manufacturing process like forming is always linked with stress concentration, especially in the sharp ends and variable cross sections like holes and fillets. The problems of representation and finding the optimal and better structural design of some known quantities such as reactions, loads and masses is not easy. A large deflection may be induced in a structure when experiencing severe mechanical loads. In this work, the numerical method has been presented to investigate a method for optimization of formed parts geometry. Numerical examination confirmed that high-stress concentrations are generated in many places. Material distribution is highly influenced by nonlinearity and the new layout will result in intermediate densities. In such cases, the nonlinear elasticity like nonlinear strain must be considered. As a result, the non-parametric optimization can offer good design flexibility to use the existing model with ease of setup and without the need for parameterization. It can provide a conceptual design that can reduce the structure's weight to the maximum extent in the early design stage. This work is going to optimize the design of the formed plates by reducing the volume while maximizing its stiffness. As a recommendation, in order to provide an attractive approach with suitable levels of structural performance, the combination of both optimization methods is the short way to achieve this aim

Engineering 3D architected metamaterials for enhanced mechanical properties and functionalities.

Compared with conventional materials, architected metamaterials have shown unprecedented mechanical properties and functionalities applications. Featured with controlled introduction of porosity and different composition, architected metamaterials have demonstrated unprecedent properties not found in natural materials. Such design strategies enable researchers to tailor materials and structures with multifunctionalies and satisfy conflicting design requirements, such as high stiffness and toughness; high strength with vibration mitigation properties, etc. Furthermore, with the booming advancement of 3D printing technologies, architected materials with precisely defined complex topologies can be fabricated effortlessly, which in turn promotes the research significantly. The research objectives of this dissertation are to achieve the enhanced mechanical properties and multifunctionalities of architected metamaterials by integrative design, computational modeling, 3D printing, and mechanical testing. Phononic crystal materials are capable of prohibiting the propagation of mechanical waves in certain frequency ranges. This certain frequency ranges are represented by phononic band gaps. Formally, band gaps are formed through two main mechanisms, Bragg scattering and local resonance. Band gaps induced by Bragg scattering are dependent on periodicity and the symmetry of the lattice. However, phononic crystals with Bragg-type band gaps are limited in their application because they do not attenuate vibration at lower frequencies without requiring large geometries. It is not practical to build huge models to achieve low frequency vibration mitigation. Alternatively, band gaps formed by local resonance are due to the excitation of resonant frequencies, and these band gaps are independent of periodicity. Therefore, lower frequency band gaps have been explored mostly through the production of phononic metamaterials that exploit locally resonant masses to absorb vibrational energy. However, despite research advances, the application of phononic metamaterials is sill largely hindered by their limited operation frequency ranges. Designing lightweight phononic metamaterials with low-frequency vibration mitigation capability is still a challenging topic. On the other hand, conventional phononic crystals usually exhibit very poor mechanical properties, such as low stiffness, strength, and energy absorption. This could largely limit their practical applications. Ideally, multifunctional materials and structures with both vibration mitigation property and high mechanical performance are demanded. In this work, we propose architected polymer foam material to overcome the challenges. Beside altering the topological architecture of metamaterials, tailoring the composition of materials is another approach to enhance the mechanical properties and realize multifunctionalities. Natural materials have adopted this strategy for long period of time. Biological structural materials such as nacre, glass sea sponges feature unusual mechanical properties due to the synergistic interplay between hard and soft material phases. These exceptional mechanical performance are highly demanded in engineering applications. As such, intensive efforts have been devoted to developing lightweight structural composites to meet the requirements. Despite the significant advances in research, the design and fabrication of low-cost structural materials with lightweight and superior mechanical performance still represent a challenge. Taking inspiration from cork material, we propose a new type of multilayered cellular composite (MCC) structure composed of hard brittle and soft flexible phases to tackle this challenge. On the other hand, piezoelectric materials with high sensitivity but low energy absorption have largely limited their applications, especially during harsh environment where external load could significantly damage the materials. Enlightened by the multiphase composite concept, we apply this design motif to develop a new interpenetrating-phased piezoelectric materials by combining PZT material as skeleton and PDMS material as matrix. By using a facial camphene-templated freeze-casting method, the co-continuous composites are fabricated with good quality. Through experiment and simulation studies, the proposed composite demonstrates multifunction with exceptional energy absorption and high sensitivity. Based on the above experimental studies, we further propose to use topology optimization framework to obtain the composites with the best performance of multifunctionalities. Specifically, we will use the solid isotropic material with penalization (SIMP) approach to optimize the piezoelectric materials with multi-objectives of 1) energy absorption and 2) electric-mechanical conversion property. The materials for the optimization design will be elastic PZT as skeleton and elatic material PDMS as matrix. To enable the gradient search of objective function efficiently, we will use adjoint method to derive the shape sensitivity analysis