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.

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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.

The results of a combined experimental and numerical study of hat-stiffened co-cured carbon-fibre composite panels loaded in uniaxial compression are presented. All panels consisted of two integrated stiffeners separated by an eight-ply thick skin bay of lay-up [*45/0190], . The effects of a 100 mm circular cutout in the skin was also investigated. The ultimate strength of all panels was governed by the load carrying capacity of the stiffeners. A change in the skin's buckling mode-shape was also observed for all panels loaded deep in the postbuckling region. The strains induced at the interior free-edge were not found to be critical. Non-linear finite element results correlated well with the prebuckling and initial postbuckling strain and displacements results obtained by experiment.

Postbuckling behaviour of hat-stiffened thin-skinned carbon-fibre composite panels

Purpose – To describe the mathematics, mechanics and computer code that are involved in deriving the mechanical properties of a 3D composite material with a complicated internal architecture. To inform the reader how an application programming interface (API) can be used with a commercial FEA code to undertake the task. Finally to validate the process an demonstrate the versatility of the process.Design/methodology/approach – The complex architecture of the composite is imported to an FEA environment and meshed. The special code is written in Pascal that applies six sets of constraints to simulate unit strain vectors on a cell of the composite. After six separate analyses are undertaken, the forces necessary to achieve the boundary constraints are summed to provide stresses and hence the necessary coefficients in the stress to strain relationship for the composite. After global FEA the strains in the homogenized material are used as input to the inverse homogenizer so that stress and strain levels in the ...

Homogenization and inverse homogenization for 3D composites of complex architecture

A-posteriori error estimator/corrector for natural frequencies of thin plate vibration problems

In order to make an exact estimation of discretization error for finite/infinite element methods, it is necessary to develop analytical solutions for some transient mass transport problems in infinite media These transient mass transport problems may be viewed as the benchmark problems for the discretization error estimation of a new numerical method so that they generally have the following characteristics: (1) their initial and boundary conditions can be exactly modelled by the finite/infinite element method; (2) their solutions can be rigorously expressed in a closed form In this paper, several of the aforementioned problems have been constructed and solved mathematically for transient mass transport problems in both 1D and 2D infinite media

Grant P. Steven

Papers

Postbuckling behaviour of hat-stiffened thin-skinned carbon-fibre composite panels

Homogenization and inverse homogenization for 3D composites of complex architecture

A-posteriori error estimator/corrector for natural frequencies of thin plate vibration problems

Analytical solutions of mass transport problems for error estimation of finite/infinite element methods

Error estimation for natural frequency finite element analysis