Pascual Martí

Topology design of three-dimensional continuum structures using isosurfaces

Isolines Topology Design (ITD) is an iterative algorithm for the topological design of two-dimensional continuum structures using isolines. This paper presents an extension to this algorithm for topology design of three-dimensional continuum structures. The topology and the shape of the design depend on an iterative algorithm, which continually adds and removes material depending on the shape and distribution of the contour isosurfaces for the required structural behaviour. In this study the von Mises stress was investigated. Several examples are presented to show the effectiveness of the algorithm, which produces final designs with very detailed surfaces without the need for interpretation. The results demonstrate how the ITD algorithm can produce realistic designs by using the design criteria contour isosurface.

Layout optimization of multi-material continuum structures with the isolines topology design method

A heterogeneous or multi-material object is one made from different materials which are distributed continuously or discontinuously. Its properties can be adjusted by controlling the material composition, microstructure and geometry of the object. The development of manufacturing technologies such as rapid prototyping can eliminate the high cost of tooling and offers the possibility to make multi-material structures. However, designing such technologies is not a trivial task and requires the development or modifications of optimization algorithms to take into consideration the different aspects of these problems. This article presents an enhancement to the isolines topology design (ITD) algorithm that allows it to produce multi-material designs. Four examples of the topology design of two-dimensional continuum structures are presented to demonstrate that the ITD algorithm is an efficient and reliable method to achieve the layout optimization of multi-material continuum structures.

liteITD a MATLAB Graphical User Interface (GUI) program for topology design of continuum structures

liteITD (lite version of Isolines Topology Design) software package.Topology optimization of 2D continuum structures using von Mises stress isolines.The liteITD program was completely designed using MATLAB GUI environment.The liteITD can be downloaded from http://www.upct.es/goe/software/liteITD.php. Over the past few decades, topology optimization has emerged as a powerful and useful tool for the design of structures, also exploiting the ever growing computational speed and power. The design process has also been affected by computers which changed the concept of form into the concept of formation and the emergence of digital design. Topology optimization can modify existing designs, incorporate explicit features into a design and generate completely new designs. This paper will show how topology optimization can be used as a digital tool. The liteITD (lite version of Isolines Topology Design) software package will be described with the purpose of providing a tool for topology design. The liteITD program solves the topology optimization of two-dimensional continuum structures using von Mises stress isolines under single or multiple loading conditions, with different material properties in tension and compression, and multiple materials. The liteITD program is fully implemented in the MATrix LABoratory (MATLAB) software environment of MathWorks under Windows operating system. GUIDE (Graphical User Interface Development Environment) was used to create a friendly Graphical User Interface (GUI). The usage of this application is directed to students mainly (educational purposes), although also to designers and engineers with experience. The liteITD program can be downloaded and used for free from the website: http://www.upct.es/goe/software/liteITD.php.

The effects of membrane thickness and asymmetry in the topology optimization of stiffeners for thin-shell structures

Thin-walled shell structures are extensively used in architecture and engineering owing to their light weight and ease of shaping. But they suffer from poor overall stiffness, something addressed by the strategic addition of stiffeners. The optimization of stiffeners is divided between those that include shell membrane in the optimization and those that do not. However, no studies were found that indicate when it is necessary or valid to use either approach. In most cases it was also found that symmetry was forced in the optimization of stiffening layers. These two effects were investigated, and the following conclusions were reached. Membranes with thicknesses less than 20% of the structure do not affect the final topology, whereas membrane thicknesses greater than 20% must be included in the optimization as they have a considerable effect. When bending and membrane loadings are present, symmetry should not be forced, otherwise suboptimal designs are generated.

Topology Optimization as a Digital Design Tool

Topology optimization has emerged as a powerful and useful tool for the design of structures, a contributing factor being the emergence of computational speed and power. The design process has also been affected by computers which have changed the concept of form into the concept of formation and the emergence of digital design. Topology optimization can modify existing designs, incorporate explicit features into a design, and generate completely new designs; however, this has mostly only been appreciated by structural designers and engineers, and not by the wider field of product design. This chapter shows how topology optimization can be used as a digital tool by investigating several examples.

Continuous Method of Structural Optimization

This chapter presents the Isolines/Isosurfaces Topology Design (ITD) method which allows for the continuous optimization of the topology of a structure. For a two-dimensional (2D) domain, ITD uses the isolines, and for a three-dimensional (3D) domain, it uses the isosurfaces of the response used for the optimization of the structure. The topology and hence shape of the design, depends on an iterative process which continually adds and removes material. The material admission and removal process uses the shape and distribution of the contour isolines/isosurfaces of the required structural behaviour.

Hands-On Applications of Structural Optimization

This chapter presents a set of 11 “classical” problems which are commonly used to test topology optimization methods. Both the optimal topologies and where appropriate the nondimensional masses are provided.

User Guides for Enclosed Software

This book presents three topology optimization methods together with examples and explanations of how topology optimization is a powerful tool for the design of structures. It also includes three software tools which allow the reader to try for themselves the three presented topology optimization methods. Two are standalone programs and the third requires the use of MATLAB. The programs are: (1) Truss Topology Optimization (TTO), which implements the Growth method for the optimization of truss structures; (2) The MATLAB set of “SERA.m” programs which allow the reader to try different examples using a basic implementation of the Sequential Element Rejection and Admission (SERA) method as well as explaining how easy it is to change the code for different structural applications; and (3) liteITD which implements the Isolines/Isosurfaces Topology Design (ITD) algorithm. This chapter presents user guides for all programs together with examples of how to use each program.

Discrete Method of Structural Optimization

A wide range of topology optimization methods have been developed for structural topology optimization where the individual finite elements are used as the design variables. Such methods include: Homogenization, Solid Isotropic Microstructure with Penalization Method (SIMP), Computer-Aided Optimization (CAO); Hard-Kill and Soft-Kill; Evolutionary Structural Optimization (ESO), Bi-directional ESO (BESO), Reverse Adaptivity and Metamorphic Development, Sequential Element Rejection and Admission (SERA). This chapter describes the SERA method. Unlike other discrete methods of topology optimization, it uses two separate criteria: one for the “ real material ” and the other for the “ virtual material ” to control the rejection and admission of these elements and hence their movement from the “ real ” to the “ virtual ” domains and vice versa.

Topology Optimization of bidimensional continuum structures by genetic algorithms and stress iso-lines

In these last years, the algorithms based on the biological process of natural evolution have been confirmed as a potent and robust search procedure. Presently work is introduced a new algorithm for the topology optimization of bidimensional continuum structures. The topology and the external shape of the design depend on a genetic algorithm, which, through the stress iso-lines of Von Mises defines the number, forms and distribution of the contours. The analysis of the structure is carried out by a fixed mesh of finite elements. The genetic algorithm (GA) uses the operators: selection (binary tournament), crossover (single point), and mutation (multibit). The procedure has been implemented in the programming language FORTRAN 95, the versatility and flexibility of the algorithm has been proven through several examples, using for it different fitness functions (Fully Stressed Design, compliance, weight, strain energy, etc). The results have been contrasted with the obtained of the most recent bibliography. Due to the scheme of the procedure, the number of evaluations of the fitness function is inferior to the needful for other procedures of similar characteristics, as: Multi-GA, VCL-GA. The produced results confirm the robustness and efficiency of the procedure.