Topological Optimization Of Complex Heterogeneous Materials And Structures

The application of new materials and of structural optimization technologies play an important role to design lightweight vehicles Topology optimization aims to define the op-timal structural or material geometry with regards to specific objectives(e.g.maximal stiff-ness)under mechanical constraints like equilibrium and boundary conditions.The essential idea of automobile lightweight design is to achieve the best use of materials and reduce the weight of the body structure,which is coincide with the purpose of the topology optimiza-tion.Therefore,with the help of effective structural optimization technology,the automotive design cycle can be greatly shortened and its lightweight design can be accurately guided.In addition,high-performance composite materials have been increasingly used in vehicles.Rapid advancement of processing technologies allows manufactures now have the ability to control material architecture or topology,at unprecedented length scales.This opens up the design space and provides exciting opportunities for topology optimization.Further-more,the fatigue or fracture resistance of vehicles,aerospace and civil structures greatly affects their service life.How to improve the durability and fracture resistance of actual engineering structures while ensuring the same amount of materials will be very important in the conceptual design stage of these structures.In this thesis,we have studied the topo-logical optimization of complex heterogeneous materials and structures comprehensively and systematically,including topology optimization of mono-scale structures,multi-scale topological optimization with and without scale separation and topological optimization for maximizing fracture resistance.The innovations of the thesis are as follows.First,topology optimization in mono-scale structures is developed.We primarily present a new evolutionary topology optimiza-tion method for design of continuum structures with smoothed boundary representation and high robustness.In addition,we propose two topology optimization frameworks in design of material microstructures for extreme effective elastic modulus or negative Poisson's ratio.Next,we investigate multiscale topology optimization within the non-separated framework giving,for the first time,towards a feasible realization of the finite-scale lattice structures with current resolution of additive manufacturing technologies.Finally,we proposea first attempt for the use of topology optimization in the context of fracture resistance of hetero-geneous structures and materialsThe specific content of the thesis is as follows.In the framework of topology optimization of mono-scale structures,we have primar-ily develop an evolutionary topology optimization(ETO)method for topology optimization design of continuum structures with smooth boundary representation.The projection re-lationship between the design model and the FEA model is established.The analysis of the design model is replaced by the FEA model with various elemental volume fractions,which are determined by the auxiliary LSF.The filter scheme is adopted to transfer sensi-tivity numbers from elements to nodes.Level-set value which is calculated iteratively by using the bi-section method so as to satisfy the target material volume at each iteration.It has been shown that the developed ETO method is capable of generating a clear and smooth boundary representation;meanwhile the resultant designs are less dependent on the initial guess design and the finite element mesh resolution.In addition,we develope two topo-logical design models of material microstructures for extreme effective elastic modulus or negative Poisson's ratio.Strain energy is firstly adopted with a simple expression of its sen-sitivity with respect to the material density within the bi-directional evolutionary structural optimization framework.Then,cellular automata model is conducted for the evolution of material design in the process of optimizing bulk and shear moduli,and for maximizing the negative Poisson ratio.In the framework of topology optimization of multi-scale structures,we extend the ma-terial design model to concurrent design of composite structures and the underlying multi-phase material microstructures.This model allows designers to determine not only the best material layout at the microscale,but also the optimal use of the designed material at the macro scale offering more design freedom on the two scales.In addition,we first develop a multiscale topology optimization procedure for periodic structures based on the classical homogenization theory,however in the context of non-separated scales.Size effect of the periodic unit cell is investigated to analysis the effectiveness of the homogenization-based topology optimization.In addition,we develop a new multiscale topology optimization procedure,by using a nonlocal filter-based homogenization scheme,for heterogeneous ma-terials such that lattice materials in the context of non-separated scales.We have shown that taking into account strain gradient effects can lead to a significant increase in the stiffness of the lattice associated with the optimized topology.Subsequently,we present the topological optimization of mesostructures with fixed microscopic unit cells without scale separations.The microscopic substructure/RVE can be selected through existing materials,artificial def-initions,or optimally designs.For practice engineering structures,the substructure may has been fixed due to certain specific requirements.This research is important for how to use the fixed substructure to optimize the geometry of the entire structure.Nonlinear optimization design of composite materials accounting for fracture resis-tance remains relatively unexplored so far,mainly due to the lack of robust numerical meth-ods for fracture propagation in presence of complex heterogeneous media and interfaces,until recently.A phase field method for fracture capable of describing interactions between bulk brittle fracture and interfacial damage is adopted within a diffuse approximation of dis-continuities.This formulation avoids the burden of remeshing problem during crack prop-agation and is well adapted to topology optimization purpose.Efficient design sensitivity analysis is performed by using the adjoint method,and the optimization problem is solved by an extended bi-directional evolutionary structural optimization method.The sensitivity formulation accounts for the whole fracturing process involving crack nucleation,propaga-tion,and merging of micro cracks until complete failure of the specimen.We demonstrate through several examples that the fracture resistance of the composite can be significantly increased at constant volume fraction of inclusions by the topology optimization process.The optimization model can be directly extended to various optimization problems con-sidering the interfacial effect,which has positive significance for fracture resistance of the industry structres,such as vehicles,aerospace and civil engineering structures.