Topology optimization is the process of determining the optimal layout of material and connectivity inside a design domain. This paper surveys topology optimization of continuum structures from the year 2000 to 2012. It focuses on new developments, improvements, and applications of finite element-based topology optimization, which include a maturation of classical methods, a broadening in the scope of the field, and the introduction of new methods for multiphysics problems. Four different types of topology optimization are reviewed: (1) density-based methods, which include the popular Solid Isotropic Material with Penalization (SIMP) technique, (2) hard-kill methods, including Evolutionary Structural Optimization (ESO), (3) boundary variation methods (level set and phase field), and (4) a new biologically inspired method based on cellular division rules. We hope that this survey will provide an update of the recent advances and novel applications of popular methods, provide exposure to lesser known, yet promising, techniques, and serve as a resource for those new to the field. The presentation of each method's focuses on new developments and novel applications.

/pdf/a-survey-of-structural-and-multidisciplinary-continuum-3lbeegkisv.pdf

A survey of structural and multidisciplinary continuum topology optimization: post 2000

Topology optimization has become an effective tool for least-weight and performance design, especially in aeronautics and aerospace engineering. The purpose of this paper is to survey recent advances of topology optimization techniques applied in aircraft and aerospace structures design. This paper firstly reviews several existing applications: (1) standard material layout design for airframe structures, (2) layout design of stiffener ribs for aircraft panels, (3) multi-component layout design for aerospace structural systems, (4) multi-fasteners design for assembled aircraft structures. Secondly, potential applications of topology optimization in dynamic responses design, shape preserving design, smart structures design, structural features design and additive manufacturing are introduced to provide a forward-looking perspective.

Topology Optimization in Aircraft and Aerospace Structures Design

With the fast development of computational mechanics and the capacity as well as the speed of modern computers, simulation-based structural optimization has become an indispensable tool in the design process of competitive products. This paper presents a brief description of the current status of structural optimization by reviewing some significant progress made in the last decades. Potential research topics are also discussed. The entire literatures of the field are not covered due to the limitation of the length of paper. The scope of this review is limited and closely related to the authors’ own research interests.

Recent development in structural design and optimization

Coupling lattice structure topology optimization with design-dependent feature evolution for additive manufactured heat conduction design

Level set-based topology optimization with overhang constraint: Towards support-free additive manufacturing

The purpose of this paper was to study the layout design of the components and their supporting structures in a finite packing space. A coupled shape and topology optimization (CSTO) technique is proposed. On one hand, by defining the location and orientation of each component as geometric design variables, shape optimization is carried out to find the optimal layout of these components and a finite-circle method (FCM) is used to avoid the overlap between the components. On the other hand, the material configuration of the supporting structures that interconnect components is optimized simultaneously based on topology optimization method. As the FE mesh discretizing the packing space, i.e., design domain, has to be updated itertively to accommodate the layout variation of involved components, topology design variables, i.e., density variables assigned to density points that are distributed regularly in the entire design domain will be introduced in this paper instead of using traditional pseudo-density variables associated with finite elements as in standard topology optimization procedures. These points will thus dominate the pseudo-densities of the surrounding elements. Besides, in the CSTO, the technique of embedded mesh is used to save the computing time of the remeshing procedure, and design sensitivities are calculated w.r.t both geometric variables and density variables. In this paper, several design problems maximizing structural stiffness are considered subject to the material volume constraint. Reasonable designs of components layout and supporting structures are obtained numerically.

Simultaneous design of components layout and supporting structures using coupled shape and topology optimization technique

The demonstration of the self-crystallization nucleation process from an amorphous precursor in a solid is crucial for understanding of interactions between atoms. We report a study of dynamic crystallization process of iron oxides by virtue of in situ measurement of transmission electron microscopy. At first, semiordered chainlike structures are observed with the increase of concentration, and when sufficient chains form, the crystalline lattice begins to grow. The two-step nucleation pathway has also been confirmed by performing a molecular dynamics simulation, where Lennard-Jones and magnetic dipole-dipole interaction potentials are both taken into account and take effect individually predominantly in different ranges of distance between atoms. Furthermore, the total free energy profile in the crystallization nucleation process is calculated to evidence the stabilization of intermediate state. This work advances our understanding of nonclassical nucleation theory.

Dynamic Observation of Anisotropic Chainlike Structures during Nonclassical Two-Step Nucleation in Solid-State Iron Oxide Crystallization.

Collective excitation modes in a general 3D homogenous spin-3/2 Fermi gas with spin-dependent contact interactions are investigated by two-particle Green’s functions and diagram techniques. Energy spectra for two branches of charge-density waves and three branches of transverse spin-density waves are obtained within the random-phase approximation. All spectra are gapless and linear in the small wave vector q, with their slopes dependent on the interaction parameters. It is also found that the spin-mixing interaction has effects on the transverse spin-density waves, but not on the charge-density modes. When the system satisfies SU(4) symmetry, the two charge-density modes become degenerate and two of the three transverse spin-density modes are degenerate, too. Furthermore, static spin susceptibilities are discussed in detail. It is found that susceptibilities increase with the enhancement of all interaction parameters, and become divergent at certain points. This phenomenon is analogous to the Stoner transition in spin-1/2 fermion gas.

Zhongze Guo

Papers

Simultaneous design of components layout and supporting structures using coupled shape and topology optimization technique

Dynamic Observation of Anisotropic Chainlike Structures during Nonclassical Two-Step Nucleation in Solid-State Iron Oxide Crystallization.

Collective excitations of a general spin-3/2 Fermi gas