A survey of current continuous nonlinear multi-objective optimization (MOO) concepts and methods is presented. It consolidates and relates seemingly different terminology and methods. The methods are divided into three major categories: methods with a priori articulation of preferences, methods with a posteriori articulation of preferences, and methods with no articulation of preferences. Genetic algorithms are surveyed as well. Commentary is provided on three fronts, concerning the advantages and pitfalls of individual methods, the different classes of methods, and the field of MOO as a whole. The Characteristics of the most significant methods are summarized. Conclusions are drawn that reflect often-neglected ideas and applicability to engineering problems. It is found that no single approach is superior. Rather, the selection of a specific method depends on the type of information that is provided in the problem, the user’s preferences, the solution requirements, and the availability of software.

Survey of multi-objective optimization methods for engineering

A level set method for structural topology optimization

The paper presents a compact Matlab implementation of a topology optimization code for compliance minimization of statically loaded structures. The total number of Matlab input lines is 99 including optimizer and Finite Element subroutine. The 99 lines are divided into 36 lines for the main program, 12 lines for the Optimality Criteria based optimizer, 16 lines for a mesh-independency filter and 35 lines for the finite element code. In fact, excluding comment lines and lines associated with output and finite element analysis, it is shown that only 49 Matlab input lines are required for solving a well-posed topology optimization problem. By adding three additional lines, the program can solve problems with multiple load cases. The code is intended for educational purposes. The complete Matlab code is given in the Appendix and can be down-loaded from the web-site http://www.topopt.dtu.dk.

/pdf/a-99-line-topology-optimization-code-written-in-matlab-ww0712da5i.pdf

A 99 line topology optimization code written in Matlab

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

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

Long before FEA was developed, people were participating in sports and as competition intensified is became clear that for many sports, the equipment plays as important a part in performance as does the athlete. With the use of modern materials and manufacturing processes there is always scope for maximizing the performance of sporting equipment. Traditionally improvements were incremental, as athletes fed-back suggestions to manufacturers and new prototypes were built and tested. Given the cost of tooling for many of the current manufacturing methods, carbon fibre with resin infusion to mention one, it is clear that such build and test iterations are not as preferable given the potential of limited success and high cost.Modern simulation techniques are capable of examining a “day–in–the-life” of an object and from an examination of the envelope of response the most sensitive regions can be detected. Iteration on the design variables, provided they remain within any constraints, be they physical or otherwise, can be incorporated to investigate their effect on performance.In this paper non-linear transient dynamic (NLTD) FEA is undertaken on a 3 iron golf club impacting a golf ball. During the less than 0.5 millisecond impact the whole outcome of the shit is established. Design changes that can lead to improved performance are studied. From the FEA simulation information on ball top spin, side spin, take off velocity are investigated.

Simulating the Contact of Golf Club to Ball for Improved Performance

The solution to a finite element analysis involving an eigenvalue/eigenvector extrapolation generally requires the eigenvalue solution as the design parameter. The eigenvector solution merely gives a visual representation of the deforming structure. Buckling and free vibration analyses are of this type, where the eigenvalue is related to the buckling load factor and natural frequency of the structure respectively. The eigenvector shows the buckled or vibrating shape of the structure.

Error Estimation for General Finite Element Eigenvalue Problems

Many structures are subjected to different load cases at different times, and some structures are held or supported in different ways at different times. The former is referred to as structures with multiple load cases, and the later multiple support environments. The ESO procedures for the optimal design of structures with multiple load cases and multiple support environments are the topics of this chapter. Original research on these topics was first reported by Xie and Steven (1994) and Steven et al. (1995).

ESO for Multiple Load Cases and Multiple Support Environments

In this study, three-dimensional finite element (FE) models were developed for determining the stress and displacement distributions in a direct composite dental bridge reinforced with high density etched polyethylene fibres. The accuracy of the FE model was established via a convergence study and an appropriately fine FE mesh with around 21,000 degrees-of-freedom (dof) was adopted for the investigations. Model variations were made by changing the number of the fibre spans and the bond conditions on the proximal surface between the artificial and the abutment teeth. The significance of modelling with and without an adhesive layer was also investigated. The results, based on the finite element analysis, are expected to provide dental clinicians with some structural implications, which will aid the implementation of such composite cantilever dental bridges.

Grant P. Steven

Papers

Simulating the Contact of Golf Club to Ball for Improved Performance

Error Estimation for General Finite Element Eigenvalue Problems

ESO for Multiple Load Cases and Multiple Support Environments

Three Dimensional Finite Element Analysis for Direct Fibre - Reinforced Composite Dental Bridge

Phase field fracture model for additively manufactured metallic materials