Yi Min Xie

A simple evolutionary procedure for structural optimization

Abstract A simple evolutionary procedure is proposed for shape and layout optimization of structures. During the evolution process low stressed material is progressively eliminated from the structure. Various examples are presented to illustrate the optimum structural shapes and layouts achieved by such a procedure.

Evolutionary topology optimization of continuum structures : methods and applications

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

Static and Dynamic Behaviour of Soils: A Rational Approach to Quantitative Solutions. II. Semi-Saturated Problems

Negative pore pressures existing in semi-saturated conditions provide a substantial ‘cohesion’ of the soil. This cohesion is of importance in the dynamic response of embankments and dams. The paper extends the formulation presented in part I to problems of semi-saturated behaviour with the assumption of free air ingress. An approximate reconstruction of the failure of the lower San Fernando dam during the 1971 earthquake is presented.

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

One of the critical issues in orthopaedic regenerative medicine is the design of bone scaffolds and implants that replicate the biomechanical properties of the host bones. Porous metals have found themselves to be suitable candidates for repairing or replacing the damaged bones since their stiffness and porosity can be adjusted on demands. Another advantage of porous metals lies in their open space for the in-growth of bone tissue, hence accelerating the osseointegration process. The fabrication of porous metals has been extensively explored over decades, however only limited controls over the internal architecture can be achieved by the conventional processes. Recent advances in additive manufacturing have provided unprecedented opportunities for producing complex structures to meet the increasing demands for implants with customized mechanical performance. At the same time, topology optimization techniques have been developed to enable the internal architecture of porous metals to be designed to achieve specified mechanical properties at will. Thus implants designed via the topology optimization approach and produced by additive manufacturing are of great interest. This paper reviews the state-of-the-art of topological design and manufacturing processes of various types of porous metals, in particular for titanium alloys, biodegradable metals and shape memory alloys. This review also identifies the limitations of current techniques and addresses the directions for future investigations.

Evolutionary structural optimisation (ESO) using a bidirectional algorithm

Describes development work to combine the basic ESO with the additive evolutionary structural optimisation (AESO) to produce bidirectional ESO whereby material can be added and can be removed. It will be shown that this provides the same results as the traditional ESO. This has two benefits, it validates the whole ESO concept and there is a significant time saving since the structure grows from a small initial one rather than contracting from a sometimes huge initial one where 90 per cent of the material gets removed over many hundreds of finite element analysis (FEA) evolutionary cycles. Presents a brief background to the current state of Structural Optimisation research. This is followed by a discussion of the strategies for the bidirectional ESO (BESO) algorithm and two examples are presented.

Evolutionary structural optimization for dynamic problems

This paper presents a simple method for structural optimization with frequency constraints. The structure is modelled by a fine mesh of finite elements. At the end of each eigenvalue analysis, part of the material is removed from the structure so that the frequencies of the resulting structure will be shifted towards a desired direction. A sensitivity number indicating the optimum locations for such material elimination is derived. This sensitivity number can be easily calculated for each element using the information of the eigenvalue solution. The significance of such an evolutionary structural optimization (ESO) method lies in its simplicity in achieving shape and topology optimization for both static and dynamic problems. In this paper, the ESO method is applied to a wide range of frequency optimization problems, which include maximizing or minimizing a chosen frequency of a structure, keeping a chosen frequency constant, maximizing the gap of arbitrarily given two frequencies, as well as considerations of multiple frequency constraints. The proposed ESO method is verified through several examples whose solutions may be obtained by other methods.

Evolutionary structural optimization for problems with stiffness constraints

Abstract This paper presents a simple evolutionary procedure based on finite element analysis to minimize the weight of structures while satisfying stiffness requirements. At the end of each finite element analysis, a sensitivity number, indicating the change in the stiffness due to removal of each element, is calculated and elements which make the least change in the stiffness; of a structure are subsequently removed from the structure. The final design of a structure may have its weight significantly reduced while the displacements at prescribed locations are kept within the given limits. The proposed method is capable of performing simultaneous shape and topology optimization. A wide range of problems including those with multiple displacement constraints, multiple load cases and moving loads are considered. It is shown that existing solutions of structural optimization with stiffness constraints can easily be reproduced by this proposed simple method. In addition some original shape and layout optimization results are presented.

Shape and topology design for heat conduction by Evolutionary Structural Optimization

Abstract This paper extends the algorithm of Evolutionary Structural Optimization to shape and topology design problems subjected to steady heat conduction. This extension incorporates an evolutionary iterative process into finite element heat solutions. During each iteration two basic steps are involved. Firstly, a finite element thermal solution is carried out for the current structure. Secondly, a small part of the material which cannot effectively contribute to the functionality of transferring heat is removed. Examples demonstrate the proposed evolutionary procedure being effective in solving heat conduction problems, which conventionally require sophisticated mathematical programming techniques.

Bidirectional Evolutionary Method for Stiffness Optimization

Evolutionary structural optimization (ESO) method was originally developed based on the idea that by systematically removing the inefficient material, the residual shape of the structure evolves toward an optimum. This paper presents an extension of the method called bidirectional ESO (BESO) for topology optimization subject to stiffness and displacement constraints. BESO allows for the material to be added as well as to be removed to modify the structural topology. Basic concepts of BESO including the sensitivity number and displacement extrapolation are proposed and optimization procedures are presented. Integrated with the finite element analysis technique, BESO is applied to several two-dimensional plane stress problems. Its effectiveness and efficiency are examined in comparison with the results obtained by ESO. It is found that BESO is more reliable and computationally more efficient than ESO in most cases. Its capability and limitation are discussed.

Optimal design of multiple load case structures using an evolutionary procedure

The structural optimization presented in this paper is based on an evolutionary procedure, developed recently, in which the low stressed part of a structure is removed from the structure step‐by‐step until an optimal design is obtained. Various tests have shown the effectiveness of this evolutionary procedure. The purpose of this paper is to present applications of such an evolutionary procedure to the optimal design of structures with multiple load cases or with a traffic (moving) load.