Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsoe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary” and several others. The paper gives an overview, comparison and critical review of the different approaches, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.

Topology optimization approaches: A comparative review

The mechanical properties of ordinary materials degrade substantially with reduced density because their structural elements bend under applied load. We report a class of microarchitected materials that maintain a nearly constant stiffness per unit mass density, even at ultralow density. This performance derives from a network of nearly isotropic microscale unit cells with high structural connectivity and nanoscale features, whose structural members are designed to carry loads in tension or compression. Production of these microlattices, with polymers, metals, or ceramics as constituent materials, is made possible by projection microstereolithography (an additive micromanufacturing technique) combined with nanoscale coating and postprocessing. We found that these materials exhibit ultrastiff properties across more than three orders of magnitude in density, regardless of the constituent material.

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Ultralight, ultrastiff mechanical metamaterials

Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: A review.

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.

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

This review comprises a detailed survey of ongoing methodologies for soft actuators, highlighting approaches suitable for nanometer- to centimeter-scale robotic applications. Soft robots present a special design challenge in that their actuation and sensing mechanisms are often highly integrated with the robot body and overall functionality. When less than a centimeter, they belong to an even more special subcategory of robots or devices, in that they often lack on-board power, sensing, computation, and control. Soft, active materials are particularly well suited for this task, with a wide range of stimulants and a number of impressive examples, demonstrating large deformations, high motion complexities, and varied multifunctionality. Recent research includes both the development of new materials and composites, as well as novel implementations leveraging the unique properties of soft materials.

Soft Actuators for Small-Scale Robotics.

Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method

Preface 1 Introduction 1.1 Structural Optimization 1.2 Topology Optimization of Continuum Structures 1.3 ESO/BESO and the Layout of the Book References 2 Evolutionary Structural Optimization Method 2.1 Introduction 2.2 ESO Based on Stress Level 2.3 ESO for Stiffness or Displacement Optimization 2.4 Conclusion References 3 Bi-directional Evolutionary Structural OptimizationMethod 3.1 Introduction 3.2 Problem Statement and Sensitivity Number 3.3 Filter Scheme and Improved Sensitivity Number 3.4 Element Removal/Addition and Convergence Criterion 3.5 Basic BESO Procedure 3.6 Examples of BESO Starting from Initial Full Design 3.7 Examples of BESO Starting from Initial Guess Design 3.8 Example of a 3D Structure 3.9 Mesh-independence Studies 3.10 Conclusion References 4 BESO Utilizing Material Interpolation Scheme withPenalization 4.1 Introduction 4.2 Problem Statement and Material Interpolation Scheme 4.3 Sensitivity Analysis and Sensitivity Number 4.4 Examples 4.5 Conclusion References Appendix 4.1 5 Comparing BESO with Other Topology OptimizationMethods 5.1 Introduction 5.2 The SIMP Method 5.3 Comparing BESO with SIMP 5.4 Discussion on Zhou and Rozvany (2001) Example 5.5 Conclusion References 6 BESO for Extended Topology Optimization Problems 6.1 Introduction 6.2 Minimizing Structural Volume with a Displacement orCompliance Constraint 6.3 Stiffness Optimization with an Additional DisplacementConstraint 6.4 Stiffness Optimization of Structures with MultipleMaterials 6.5 Topology Optimization of Periodic Structures 6.6 Topology Optimization of Structures with Design-dependentGravity Load 6.7 Topology Optimization for Natural Frequency 6.8 Topology Optimization for Multiple Load Cases 6.9 BESO Based on von Mises Stress 6.10 Conclusion References 7 Topology Optimization of Nonlinear ContinuumStructures 7.1 Introduction 7.2 Objective Functions and Nonlinear Analysis 7.3 Sensitivity Analysis and Sensitivity Number for ForceControl 7.4 Sensitivity Analysis and Sensitivity Number for DisplacementControl 7.5 BESO Procedure for Nonlinear Structures 7.6 Examples of Nonlinear Structures under Force Control 7.7 Examples of Nonlinear Structures under DisplacementControl 7.8 Conclusion References 8 Optimal Design of Energy Absorption Structures 8.1 Introduction 8.2 Problem Statement for Optimization of Energy AbsorptionStructures 8.3 Sensitivity Number 8.4 Evolutionary Procedure for Removing and Adding Material 8.5 Numerical Examples and Discussions 8.6 Conclusion References 9 Practical Applications 9.1 Introduction 9.2 Akutagwa River Side Project in Japan 9.3 Florence New Station Project in Italy 9.4 Sagrada Familia Church in Spain 9.5 Pedestrian Bridge Project in Australia 9.6 Conclusion References 10 Computer Program BESO2D 10.1 Introduction 10.2 System Requirements and Program Installation 10.3 Windows Interface of BESO2D 10.4 Running BESO2D from Graphic User Interface 10.5 The Command Line Usage of BESO2D 10.6 Running BESO2D from the Command Line 10.7 Files Produced by BESO2D 10.8 Error messages Index

Evolutionary Topology Optimization of Continuum Structures: Methods and Applications

There are several well-established techniques for the generation of solid-void optimal topologies such as solid isotropic material with penalization (SIMP) method and evolutionary structural optimization (ESO) and its later version bi-directional ESO (BESO) methods. Utilizing the material interpolation scheme, a new BESO method with a penalization parameter is developed in this paper. A number of examples are presented to demonstrate the capabilities of the proposed method for achieving convergent optimal solutions for structures with one or multiple materials. The results show that the optimal designs from the present BESO method are independent on the degree of penalization. The resulted optimal topologies and values of the objective function compare well with those of SIMP method.

Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials

Evolutionary Structural Optimization (ESO) and its later version bi-directional ESO (BESO) have gained widespread popularity among researchers in structural optimization and practitioners in engineering and architecture. However, there have also been many critical comments on various aspects of ESO/BESO. To address those criticisms, we have carried out extensive work to improve the original ESO/BESO algorithms in recent years. This paper summarizes latest developments in BESO for stiffness optimization problems and compares BESO with other well-established optimization methods. Through a series of numerical examples, this paper provides answers to those critical comments and shows the validity and effectiveness of the evolutionary structural optimization method.

Xiaodong Huang

Papers

Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method

Evolutionary Topology Optimization of Continuum Structures: Methods and Applications

Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials

A further review of ESO type methods for topology optimization

Topological design of microstructures of cellular materials for maximum bulk or shear modulus