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

This review paper provides an overview of different level-set methods for structural topology optimization. Level-set methods can be categorized with respect to the level-set-function parameterization, the geometry mapping, the physical/mechanical model, the information and the procedure to update the design and the applied regularization. Different approaches for each of these interlinked components are outlined and compared. Based on this categorization, the convergence behavior of the optimization process is discussed, as well as control over the slope and smoothness of the level-set function, hole nucleation and the relation of level-set methods to other topology optimization methods. The importance of numerical consistency for understanding and studying the behavior of proposed methods is highlighted. This review concludes with recommendations for future research.

Level-set methods for structural topology optimization: a review

A level set method for structural topology optimization and its applications

A survey of manufacturing oriented topology optimization methods

A review of topology optimization for additive manufacturing: Status and challenges

Combining the vector level set model, the shape sensitivity analysis theory with the gradient projection technique, a level set method for topology optimization with multi-constraints and multi-materials is presented in this paper. The method implicitly describes structural material interfaces by the vector level set and achieves the optimal shape and topology through the continuous evolution of the material interfaces in the structure. In order to increase computational efficiency for a fast convergence, an appropriate nonlinear speed mapping is established in the tangential space of the active constraints. Meanwhile, in order to overcome the numerical instability of general topology optimization problems, the regularization with the mean curvature flow is utilized to maintain the interface smoothness during the optimization process. The numerical examples demonstrate that the approach possesses a good flexibility in handling topological changes and gives an interface representation in a high fidelity, compared with other methods based on explicit boundary variations in the literature.

A level set method for structural topology optimization with multi-constraints and multi-materials

Using automatic localization to ensure sufficient machining allowance or derive reliable evaluation results of machining quality, it is possible to cope with the case where the coordinate system in a part design specification is different from that for machining or measuring the part. To achieve workpiece localization and machining quality evaluation, it is essential to find the optimum Euclidean transformation that aligns the nominal mode to the sample points from a workpiece. This paper describes a unified algorithm for workpiece localization and quality evaluation. The optimum alignment model is firstly established with minimax criteria, and then sequential quadratic programming (SQP) is proposed to solve the optimization problem. A computational algorithm of point-to-surface distance and a linear differential motion model of the objective function with respect to alignment parameters are subsequently provided. The results show that the SQP-based workpiece localization and quality evaluation method is computationally more efficient than those based on direct search algorithms. It is found that the proposed method is effective in machining localization and quality evaluation even with a large set of sample points.

Machining localization and quality evaluation of parts with sculptured surfaces using SQP method

A novel mode of space-aero bistatic SAR, in which the spaceborne transmitter is side-look and the airborne receiver is forward-look, is studied. The characteristics of the traditional forward-look SAR is discussed to compare with the special space-aero bistatic forward-look SAR. Because the range direction of the transmitter is the azimuth direction of the receiver in this mode, the' forward-look SAR does not like the traditional forward-look SAR, it can acquire high azimuth resolution by using the range compression. Through the analysis of Doppler characteristic and echo signal model, the equidistance line of this mode is quite similar to that of squint SAR is pointed out, which enables the transplantation of existed well-rounded imaging algorithm of squint SAR to this mode. The imaging algorithm and simulation experiment are presented

Wang Xiaoming

Papers

A level set method for structural topology optimization and its applications

A level set method for structural topology optimization with multi-constraints and multi-materials

Machining localization and quality evaluation of parts with sculptured surfaces using SQP method

Space-aero Bistatic Forward-look SAR