Optimization Design On Multi-functional Metamaterials Incorporating Tunable Geminations Of Poisson’s Ratio And Coefficient Of Thermal Expansion

Multi-functional metamaterials,which incorporate Poisson’s ratio(PR)and coefficient of thermal expansion(CTE)in tunable geminations such as negative PR & CTE,negative PR &positive CTE,and zero PR & CTE,could offer the promising shape control ability when they are simultaneously suffering the mechanical and temperature loadings,and thus are urgently needed in advance engineering fields such as the aerospace and high-precision instruments.However,most of the existing metamaterials can solely give either tunable PR or CTE.Only a few kinds of such kinds of multi-functional metamaterials have been reported while the systematic design method is still missing,resulting in an obvious restriction to efficiently design novel multi-functional metamaterials.In addition,the realization of the multi-functional metamaterials is also scarce,and experimental characterizations of the corresponding PRs and CTEs are vacant.To this end,this paper proposes a topology-shape integrated design framework for systematically designing the aforementioned multi-functional metamaterials.Basing on the node-variable multi-material interpolation and dynamically-switched partial objective function,the Alternative Active Phase & Objective topology optimization method is established.Besides,the shape optimization method is constructed basing on an enhanced particle swarm optimization algorithm with two core strategies: gradient estimation and multiple subpopulation division.To solidify the effectiveness of the proposed design methods,the additive manufacturing is used to practically fabricate the designed metamaterials,and corresponding PRs and CTEs are experimentally characterized.The main research contents of this thesis are as follows:(1)Aiming at solving the problem of blurred topological configurations with abundant grey elements in the Alternative Active Phase(AAP)topology optimization results,the nodevariable multi-material interpolation model is introduced to establish an improved AAP algorithm.Numerical examples on stiffness-based and stress-based structural optimization problems show that the proposed algorithm could significantly eliminate the ratio of the grey elements from the final results,which lays the foundation for the topology optimization of the multi-functional metamaterials.(2)For systematically designing multi-functional metamaterials incorporating double negative indexes of Poisson’s ratio and thermal expansion,a novel algorithm,named Alternating Active Phase & Objective(AAPO)algorithm,is developed.The dynamicallyswitched partial objective function is proposed to overcome the convergence oscillation arisen from the weighted sums method.Several numerical examples are taken to identify the universal ranges of the key controlling parameters in the AAPO algorithm.A series of multi-functional metamaterials with negative indexes of Poisson’s ratio and thermal expansion are successfully devised.Especially,the category of the consisted base materials is enlarged form bi-material to tri-material,and the inherent topological configuration is extended from the re-entrant to chiral type.(3)Basing on the proposed AAPO algorithm,different partial objective functions and topology optimization formulations are formulated to programmatically design a series of novel multi-functional metamaterials including the re-entrant metamaterials with ZPR & ZTE,NPR& NTE,NPR & PTE,PPR & NTE and PPR & PTE and the chiral metamaterials with NPR &ZTE,NPR & NTE and NPR & PTE.Furthermore,the influences of the base materials’ proportion on the topology-optimized results are identified,and the novel multi-functional deformation mechanisms are revealed in detail through numerical simulation.(4)As the topology optimization results can not be directly imported into manufacturing,the shape optimization method of the multi-functional metamaterials is proposed basing on the parameterized cubic spline.An enhanced particle swarm optimization algorithm with higher efficient and precision is proposed through introducing two core strategies,gradient estimation and multiple subpopulation division.The shape-optimized multi-functional metamaterials are of smooth geometry and high manufacturability.Especially,the corresponding PRs and CTEs are further improved by 13.56% and 54.32%,respectively.(5)Basing on the multi-material additive manufacturing(fused deposition modeling based),engineering polymers are used to practically fabricate the topology-shape optimized multi-functional metamaterials.The mechanical and temperature-rise experiments are conducted to systematically measure and characterize the PRs and CTEs.Related experimental results are in great agreement with the designs,showing that the PR and CTE of the multifunctional metamaterials can be tuned in the range of-0.96～+0.66 and-661.50～+989.58ppm/°C,respectively.The integrated design of the multi-functions is successfully realized,and the effectiveness of the proposed topology-shape optimization methods are solidify verified.In conclusion,this paper systematically solves the optimization design,multi-material additive manufacturing,and experimental characterization of the multi-functional metamaterials.These approaches also provide the fundamentals about designing,manufacturing,and measuring other novel metamaterials with integrated functions.