A 213-line topology optimization code for geometrically nonlinear structures

Structural and Multidisciplinary Optimization - This paper presents a 213-line MATLAB code for topology optimization of geometrically nonlinear structures. It is developed based on the density...     

A 99 line topology optimization code written in Matlab

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. Received October 22, 1999     

A discrete level-set topology optimization code written in Matlab

This paper presents a compact Matlab implementation of the level-set method for topology optimization. The code can be used to minimize the compliance of a statically loaded structure. Simple code modifications to extend the code for different and multiple load cases are given. The code is inspired by a Matlab implementation of the solid isotropic material with penalization (SIMP) method for topology optimization (Sigmund, Struct Multidiscipl Optim 21:120–127, 2001). Including the finite element solver and comments, the code is 129 lines long. The code is intended for educational purposes, and in particular it could be used alongside the Matlab implementation of the SIMP method for topology optimization to demonstrate the similarities and differences between the two approaches.     

A filter-based level set topology optimization method using a 62-line MATLAB code

Structural and Multidisciplinary Optimization - The present paper proposes a fast and easy to implement level set topology optimization method that is able to adjust the complexity of resulting...     

PolyMat: an efficient Matlab code for multi-material topology optimization

Structural and Multidisciplinary Optimization - We present a Matlab implementation of topology optimization for compliance minimization on unstructured polygonal finite element meshes that...     

A sequential element rejection and admission (SERA) topology optimization code written in Matlab

Structural and Multidisciplinary Optimization - This paper presents the Matlab implementation of the Sequential Element Rejection and Admission (SERA) method for topology optimization of structures...     

Further elaborations on topology optimization via sequential integer programming and Canonical relaxation algorithm and 128-line MATLAB code

Structural and Multidisciplinary Optimization - This paper provides further elaborations on discrete variable topology optimization via sequential integer programming and Canonical relaxation...     

Constrained-manufacturable stacking sequence design optimization using an improved global shared-layer blending method and its 98-line Matlab code

An improved global shared-layer blending method (GSLB) is suggested to address the constrained-manufacturable stacking sequence design optimization problem of tapered composite structures. First, the mathematical model for tapered composite structures design problem is constructed and the effect of blending constraint on the design space is analyzed. By introducing the set theory, the original GSLB method is improved by aggregating a shape prediction algorithm and a thickness evaluation procedure. The shape prediction algorithm takes advantage of the set computation procedure, which simplifies the process for detecting the shared layers’ boundaries. The maximum blending shared layers are evaluated by the improved GSLB in terms of the thickness distribution of multiple ply orientations. Subsequently, the obtained shared-layers are served as integrated variables for stacking sequence design, in which complex manufacturing constraints are involved. Three multi-panel structures and a wing box structure are adopted to verify the improved GSLB method and stacking sequence design strategy, and perfectly blended solutions are found without violation of manufacturing constraints and mechanical requirements. Finally, the 98 line Matlab code of the improved GSLB method is provided for the convenience of engineering application. This research has two purposes: providing a technique for tailoring design of tapered composite structures and giving reference solutions for constrained-manufacturable stacking sequence design optimization problem.

     

A 2589 line topology optimization code written for the graphics card

We investigate topology optimization based on the solid isotropic material with penalization approach on compute unified device architecture enabled graphics cards in three dimensions. Linear elasticity is solved entirely on the GPU by a matrix-free conjugate gradient method using finite elements. Due to the unique requirements of the single instruction, multiple data stream processors, special attention is given to the procedural generation of matrix?Cvector products entirely on the graphics card. The GPU code is found to be extremely efficient, being faster than a 48 core shared memory CPU system. CPU and GPU implementations show different performance bottlenecks. The sources are available at http://www.mathematik.uni-trier.de/~schmidt/gputop.     

A simple and compact Python code for complex 3D topology optimization

This paper presents a 100-line Python code for general 3D topology optimization. The code adopts the Abaqus Scripting Interface that provides convenient access to advanced finite element analysis (FEA). It is developed for the compliance minimization with a volume constraint using the Bi-directional Evolutionary Structural Optimization (BESO) method. The source code is composed of a main program controlling the iterative procedure and five independent functions realizing input model preparation, FEA, mesh-independent filter and BESO algorithm. The code reads the initial design from a model database (.cae file) that can be of arbitrary 3D geometries generated in Abaqus/CAE or converted from various widely used CAD modelling packages. This well-structured code can be conveniently extended to various other topology optimization problems. As examples of easy modifications to the code, extensions to multiple load cases and nonlinearities are presented. This code is useful for researchers in the topology optimization field and for practicing engineers seeking automated conceptual design tools. With further extensions, the code could solve sophisticated 3D conceptual design problems in structural engineering, mechanical engineering and architecture practice. The complete code is given in the appendix section and can also be downloaded from the website: www.rmit.edu.au/research/cism/.     

A Pareto-optimal genetic algorithm for warehouse multi-objective optimization

The automated warehouse management requires to fulfill objectives that are usually conflicting with each other. The decisions taken must ensure optimized usage of resources, cost reduction and better customer service. The warehouse replenishment task is a typical example of multi-objective optimization. In this paper, a genetic algorithm with a new crossover operator is developed to solve the replenishment problem. This algorithm is applied to real warehouse data and produces Pareto-optimal permutations of the stored products. A fuzzy rule-base is proposed to increase the diversity of the optimal solutions.     

Alternating active-phase algorithm for multimaterial topology optimization problems: a 115-line MATLAB implementation

Structural and Multidisciplinary Optimization - A new algorithm for the solution of multimaterial topology optimization problems is introduced in the present study. The presented method is based on...     

Concurrent topology optimization of multiscale composite structures in Matlab

Structural and Multidisciplinary Optimization - This paper presents the compact and efficient Matlab codes for the concurrent topology optimization of multiscale composite structures not only in 2D...     

Efficient topology optimization in MATLAB using 88 lines of code

The paper presents an efficient 88 line MATLAB code for topology optimization. It has been developed using the 99 line code presented by Sigmund (Struct Multidisc Optim 21(2):120–127, 2001) as a starting point. The original code has been extended by a density filter, and a considerable improvement in efficiency has been achieved, mainly by preallocating arrays and vectorizing loops. A speed improvement with a factor of 100 is obtained for a benchmark example with 7,500 elements. Moreover, the length of the code has been reduced to a mere 88 lines. These improvements have been accomplished without sacrificing the readability of the code. The 88 line code can therefore be considered as a valuable successor to the 99 line code, providing a practical instrument that may help to ease the learning curve for those entering the field of topology optimization. The paper also discusses simple extensions of the basic code to include recent PDE-based and black-and-white projection filtering methods. The complete 88 line code is included as an appendix and can be downloaded from the web site .     

Matlab的图形处理器并行计算及其在拓扑优化中的应用

针对传统并行计算方法实现结构拓扑优化快速计算的硬件成本高、程序开发效率低的问题,提出了一种基于Matlab和图形处理器(GPU)的双向渐进结构优化(BESO)方法的全流程并行计算策略。首先,探讨了Matlab编程环境中实现GPU并行计算的三种途径的优缺点和适用范围;其次,分别采用内置函数直接并行的方式实现了拓扑优化算法中向量和稠密矩阵的并行化计算,采用MEX函数调用CUSOLVER库的形式实现了稀疏格式有限元方程组的快速求解,采用并行线程执行(PTX)代码的方式实现了拓扑优化中单元敏度分析等优化决策的并行化计算。数值算例表明,基于Matlab直接开发GPU并行计算程序不仅编程效率高,而且还可以避免不同编程语言间的计算精度差异,最终使GPU并行程序可以在保持计算结果不变的前提下取得可观的加速比。     

A topological derivative method for topology optimization

We propose a fictitious domain method for topology optimization in which a level set of the topological derivative field for the cost function identifies the boundary of the optimal design. We describe a fixed-point iteration scheme that implements this optimality criterion subject to a volumetric resource constraint. A smooth and consistent projection of the region bounded by the level set onto the fictitious analysis domain simplifies the response analysis and enhances the convergence of the optimization algorithm. Moreover, the projection supports the reintroduction of solid material in void regions, a critical requirement for robust topology optimization. We present several numerical examples that demonstrate compliance minimization of fixed-volume, linearly elastic structures.     

A surface reconstruction algorithm for topology optimization

For mechanical structural design, topology optimization is often utilized. During this process, a topologically optimized model must be converted into a parametric CAD solid model. The key point of conversion is that a discretized shape of a topologically optimized model must be smoothed, but features such as creases and corners must be retained. Thus, a surface reconstruction algorithm to produce the parametric CAD solid model from a topologically optimized model is proposed in this paper. Our presented algorithm consists of three parts: (1) an enclosed isosurface geometry from which the topologically optimized model is generated, (2) features detected and (3) the parametric CAD solid model reconstructed as biquartic surface splines. In order to generate an enclosed isosurface model effectively, we propose an algorithm based upon the marching cubes method to detect elements intersected by an isosurface. After generating an enclosed isosurface model, we produce biquartic surface splines. By applying our algorithm to an enclosed isosurface model, it is possible to produce smoothed biquartic surface splines with features retained. Some examples are shown and the effectiveness of our algorithm is discussed in this paper.