Topology Design Methods for Structural Optimization

Osvaldo M. Querin, Mariano Victoria, Cristina Alonso Gordoa, Rubén Ansola, Pascual Martí

• Publisher: Academic Press
• Year: 2017
• Print ISBN: 9780080999821
• eBook ISBN: 9780080999890
• Topic: Technology & Engineering
• Subtopic: Optimization
• Index: Technology & Engineering

Topology Design Methods for Structural Optimization provides engineers with a basic set of design tools for the development of 2D and 3D structures subjected to single and multi-load cases and experiencing linear elastic conditions. Written by an expert team who has collaborated over the past decade to develop the methods presented, the book discusses essential theories with clear guidelines on how to use them.Case studies and worked industry examples are included throughout to illustrate practical applications of topology design tools to achieve innovative structural solutions. The text is intended for professionals who are interested in using the tools provided, but does not require in-depth theoretical knowledge. It is ideal for researchers who want to expand the methods presented to new applications, and includes a companion website with related tools to assist in further study.- Provides design tools and methods for innovative structural design, focusing on the essential theory- Includes case studies and real-life examples to illustrate practical application, challenges, and solutions- Features accompanying software on a companion website to allow users to get up and running fast with the methods introduced- Includes input from an expert team who has collaborated over the past decade to develop the methods presented

Chapter 1

Introduction

Abstract

This chapter presents an overview of structural optimization, explaining briefly the different types which include size, shape, and topology optimization. This book aims to present to the reader the different methods of topology optimization developed by the authors, so this chapter serves as an introduction to topology optimization methods, some of which are then presented in this chapter. Finally the layout of the book is presented.

Keywords

Structural, size, shape and topology optimization; Homogenization; SIMP; Fully Stressed Design; CAO; Soft Kill Option; ESO; BESO

1.1 Structural Optimization (SO)

SO consists of the process of determining the best material distribution within a physical volume domain, to safely transmit or support the applied loading condition(s). To achieving this, the constraints imposed by manufacture and eventual use must also be taken into consideration. Some of these may include increasing stiffness, reducing stress, reducing displacement, altering its natural frequency, increasing the buckling load, manufacture with conventional, or advanced methods.

There are currently three different types of optimization methods which come under the heading of SO, these are: (1) size, (2) shape, and (3) topology optimization[1,2].

In Size optimization [3], the engineer or designer knows what the structure will looks like, but does not know the size of the components which make up that structure. For example, if a cantilever beam was going to be used, its length and position may be known, but not its cross-sectional dimensions (Fig. 1.1A). Another example would be a truss structure where its overall dimensions may be known but not the cross-sectional areas of each truss element (bar), Fig. 1.1B. Yet another example would be the thickness distribution of a shell structure. So basically, any feature of a structure where its size is required, but where all other aspects of the structure are known.

Figure 1.1 Examples of structures where size optimization can be used: (A) cantilever beam of unknown cross-sectional dimensions, (B) truss structure where the area of each bar is unknown.

In Shape optimization, the unknown is the form or contour of some part of the boundary of a structural domain [2,4]. The shape or boundary could either be represented by an unknown equation or by a set of points whose locations are unknown (Fig. 1.2).

Figure 1.2 Structural design domain with the boundary represented as either an equation f(x,y) or as control points which can move perpendicularly (or otherwise) to the boundary.

Topology optimization is the most general form of SO [5]. In discrete cases, such as for a truss structures, it is achieved by allowing the design variables, such as the cross-sectional areas of the tr...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication
• Preface
• Chapter 1. Introduction
• Chapter 2. Growth Method for the Size, Topology, and Geometry Optimization of Truss Structures
• Chapter 3. Discrete Method of Structural Optimization
• Chapter 4. Continuous Method of Structural Optimization
• Chapter 5. Hands-On Applications of Structural Optimization
• Chapter 6. Topology Optimization as a Digital Design Tool
• Chapter 7. User Guides for Enclosed Software
• Index