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.

This paper deals with automatic generation of optimal strut-and-tie models in prestressed concrete beams by the performance-based optimization (PBO) method. In the present approach, developing strut-and-tie models in prestressed concrete members is transformed to the topology optimization problem of continuum structures. By treating prestressing forces as external loads, prestressed concrete beams can be analyzed, optimized and dimensioned with strut-and-tie models like reinforced concrete beams. Optimal strut-and-tie models in non-prestressed, partially-prestressed and fully-prestressed concrete beams are investigated by using the performance-based optimization technique. It is demonstrated that the magnitude of prestressing forces significantly affects the layouts of optimal strut-and-tie models in prestressed concrete members. The performance-based optimization method is shown to be effective in developing reliable strut-and-tie models for the design of prestressed concrete beams.

/pdf/generating-optimal-strut-and-tie-models-in-prestressed-4z7o155oeb.pdf

Generating optimal strut-and-tie models in prestressed concrete beams by performance-based optimization

PURPOSE This study examined the effects of using four different core-ceramic materials on the stresses that developed in a single all-ceramic first premolar crown. MATERIALS AND METHODS This was done by analyzing models constructed in an axisymmetric fashion with finite element analyses. The model had a 600-N vertical load applied uniformly over a circular area on top of the crown. Particular emphasis was placed on the tensile stresses that developed. RESULTS For this particular type of model and loading configuration, radial tensile stresses were predominant in magnitude. Peak hoop and axial tensile stresses were approximately 80% and 2% of this value, respectively. The peak radial and hoop tensile stresses were located on the inside of the coping and scaled with the elastic modulus of the coping. For the axial component, the peak was located in the veneer ceramic on its outermost perimeter. CONCLUSION Under normal loading, a near-uniform tensile stress field developed within the coping, directly beneath the contact area. The magnitude of this stress for realistic bite forces using current design recommendations was significantly lower than the fracture strength of the four ceramic materials investigated. The stresses developed within the porcelain were in all instances well below typical strength values.

Grant P. Steven

Papers

Generating optimal strut-and-tie models in prestressed concrete beams by performance-based optimization

Finite element analysis studies of an all-ceramic crown on a first premolar.

Buckling mode transition in hat-stiffened composite panels loaded in uniaxial compression

Optimisation of columns and frames against buckling

Evolutionary structural optimization for stress minimization problems by discrete thickness design