Multiscale Structural Topology Optimization

Liang Xia

• Publisher: ISTE Press - Elsevier
• Year: 2016
• Print ISBN: 9781785481000
• eBook ISBN: 9780081011867
• Topic: Technology & Engineering
• Subtopic: Applied Mathematics
• Index: Technology & Engineering

Multiscale Structural Topology Optimization discusses the development of a multiscale design framework for topology optimization of multiscale nonlinear structures. With the intention to alleviate the heavy computational burden of the design framework, the authors present a POD-based adaptive surrogate model for the RVE solutions at the microscopic scale and make a step further towards the design of multiscale elastoviscoplastic structures. Various optimization methods for structural size, shape, and topology designs have been developed and widely employed in engineering applications. Topology optimization has been recognized as one of the most effective tools for least weight and performance design, especially in aeronautics and aerospace engineering. This book focuses on the simultaneous design of both macroscopic structure and microscopic materials. In this model, the material microstructures are optimized in response to the macroscopic solution, which results in the nonlinearity of the equilibrium problem of the interface of the two scales. The authors include a reduce database model from a set of numerical experiments in the space of effective strain. - Presents the first attempts towards topology optimization design of nonlinear highly heterogeneous structures - Helps with simultaneous design of the topologies of both macroscopic structure and microscopic materials - Helps with development of computer codes for the designs of nonlinear structures and of materials with extreme constitutive properties - Focuses on the simultaneous design of both macroscopic structure and microscopic materials - Includes a reduce database model from a set of numerical experiments in the space of effective strain

1

Topology Optimization Framework for Multiscale Nonlinear Structures

Abstract:

This chapter introduces a topology optimization framework for multiscale nonlinear structures. As an extension of the conventional monoscale design, except that the material constitutive law is governed by one or multiple RVEs defined at the microscopic scale, the developed general multiscale design framework is made up of two key ingredients: multiscale modeling for structural performance simulation and topology optimization for structural design. This framework will serve as a basis for the developments presented in the subsequent chapters.

Keywords

BESO updating scheme; FE2 method; Finite element discretization; Model; Multiscale design; Nonlinear heterogeneous structure; Nonlinear homogeneous structure; Periodic boundary conditions; Sensitivity analysis; Topology optimization model

This chapter introduces a topology optimization framework for multiscale nonlinear structures. As an extension of the conventional monoscale design, except that the material constitutive law is governed by one or multiple RVEs defined at the microscopic scale, the developed general multiscale design framework is made up of two key ingredients: multiscale modeling for structural performance simulation and topology optimization for structural design. This framework will serve as a basis for the developments presented in the subsequent chapters.

With regard to the first ingredient, we employ the first-order computational homogenization method FE² [FEY 00] to bridge structural and material scales. By this method, a clear separation of scales is a...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Introduction
• 1: Topology Optimization Framework for Multiscale Nonlinear Structures
• 2: POD-based Adaptive Surrogate for the Design of Multiscale Structures
• 3: Topology Optimization of Multiscale Elastoviscoplastic Structures
• 4: Simultaneous Topology Optimization of Structure and Materials
• 5: Reduced Database Model for Material Microstructure Optimizations
• Conclusion and Perspectives
• Appendix: Design of Extreme Materials in Matlab
• Bibliography
• Index