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Homogenization and Structural Topology Optimization

Theory, Practice and Software

verfasst von: Behrooz Hassani, MSc, PhD, Ernest Hinton, BSc, MSc, PhD, DSc, CEng, MIStructE, MBCS

Verlag: Springer London

Enthalten in: Professional Book Archive

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Über dieses Buch

Structural topology optimization is a fast growing field that is finding numerous applications in automotive, aerospace and mechanical design processes. Homogenization is a mathematical theory with applications in several engineering problems that are governed by partial differential equations with rapidly oscillating coefficients Homogenization and Structural Topology Optimization brings the two concepts together and successfully bridges the previously overlooked gap between the mathematical theory and the practical implementation of the homogenization method. The book is presented in a unique self-teaching style that includes numerous illustrative examples, figures and detailed explanations of concepts. The text is divided into three parts which maintains the book's reader-friendly appeal.

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Inhaltsverzeichnis

Frontmatter

Introduction

1. Introduction

Abstract

The objective of this chapter is to give an overview of structural topology optimization. The mathematical description of a general optimization problem is explained. The types of structural optimization are briefly reviewed and some aspects of the structural topology optimization are introduced, Finally, the layout of the book is outlined.

Behrooz Hassani, Ernest Hinton

Homogenization

Frontmatter

2. Homogenization Theory for Media with Periodic Structure

Abstract

In this chapter an overview of the theory of homogenization for composites with regulär structure is presented. Periodicity and asymptotic expansion are deßned and an application of homogenization to the simple case of a one dimensional elasticity problem is given. Derivation of the basic formulas for the general case of a boundary value problem in strong form is discussed. Finally, the homogenization equations for the elasticity problems in weak form for perforated media are derived.

Behrooz Hassani, Ernest Hinton

3. Solution of Homogenization Equations for Topology Optimization

Abstract

In this chapter motives for using the homogenization theory for topological structural optimization are brießy explained. Different material models are descrihed and the analytical Solution of the homogenization equations, derived in the last section of Chapter 2, for the so called ‘rank laminate composites’ is presented. The ßnite element formulation is explained for the material model based on a microstruciure consisting of an isotropic material with rectangular voids. Using the periodicity assumption, the boundary conditions are derived and the homogenization equation is solved. The results to be used in topology optimization are presented.

Behrooz Hassani, Ernest Hinton

Topology Optimization

Frontmatter

4. Structural Topology Optimization using Optimality Criteria Methods

Abstract

In this chapter, the basic concepts related to the optimality criteria methods are introduced. Then the mathematical model for the structural topology optimization problem is constructed. The optimality conditions are explained and an optimization procedure based on optimality criteria methods is presented. Resizing schemes for updating design variables are explained. The issue of the optimal orientation for the homogenized orthotropic material is discussed. The algorithm of the Computer program PLATO is explained and a few illustrative examples are presented.

Behrooz Hassani, Ernest Hinton

5. Experiences In Topology Optimization of Plane Stress Problems

Abstract

The outcome of the topology optimization process is inßuenced by several factors: different material models, resizing schemes, finite element discretizations and element types. The optimal layout may also be affected by the resizing parameters. This chapter is mainly devoted to the study of the inßuence of the above parameters. To demonstrate the usefulness of the method, several examples of a more practical nature are provided.

Behrooz Hassani, Ernest Hinton

6. Topological Layout and Reinforcement Optimization of Plate Structures

Abstract

In this chapter the homogenization method for plane stress problems is extended to deal with the creation of optimal layout and reinforcement topologies of plate structures. In this formulation the problem is to determine the stiffest plate strueture with a volume constraint for the reinforcement material. Introducing plate microcell models, a formulation for homogenization of plates based on the first order thick plate theory is presented. To solve the optimization problem the optimality criteria method is used. Using different material models some examples are provided.

Behrooz Hassani, Ernest Hinton

Other Methods and Integrated Structural Optimization

Frontmatter

7. Alternative Approaches to Structural Topology Optimization

Abstract

This chapter is devoted to intuitive methods which are simple to implement and may be used as an alternative to topology optimization by the homogenization method. A method for Simulation of functional adaptation of bone mineralization in vertebrates is introduced and an algorithm based on effective stresses is presented. The evolutionary fully stressed method is also briefly explained.

Behrooz Hassani, Ernest Hinton

8. Integrated Structural Optimization

Abstract

An overview of the concept and modules of a three phase integrated structural optimization system is the subject of this Chapter. The topology optimization module provides Information about the Optimum layout and topology. In the image processing module by employing Computer vision techniques a structural model with smooth boundaries is extracted. In the third phase, using the conventional size and shape optimization methods the final optimal design is obtained. By constructing integrated design and optimization systems considerable improvement may be achieved by cutting development time and design costs.

Behrooz Hassani, Ernest Hinton

Backmatter

Titel: Homogenization and Structural Topology Optimization
verfasst von: Behrooz Hassani, MSc, PhD
Ernest Hinton, BSc, MSc, PhD, DSc, CEng, MIStructE, MBCS
Copyright-Jahr: 1999
Verlag: Springer London
Electronic ISBN: 978-1-4471-0891-7
Print ISBN: 978-1-4471-1229-7
DOI: https://doi.org/10.1007/978-1-4471-0891-7