Biomechanics

Optimization, Uncertainties and Reliability

Ghias Kharmanda, Abdelkhalak El Hami

• Publisher: Wiley-ISTE
• Year: 2017
• Print ISBN: 9781786300256
• eBook ISBN: 9781119379119
• Edition: 1
• Topic: Biological Sciences
• Subtopic: Biotechnology
• Index: Biological Sciences

In this book, the authors present in detail several recent methodologies and algorithms that they developed during the last fifteen years. The deterministic methods account for uncertainties through empirical safety factors, which implies that the actual uncertainties in materials, geometry and loading are not truly considered. This problem becomes much more complicated when considering biomechanical applications where a number of uncertainties are encountered in the design of prosthesis systems. This book implements improved numerical strategies and algorithms that can be applied to biomechanical studies.

1
Introduction to Structural Optimization

1.1. Introduction

Structural optimization is a topic which affects many different physical domains – particularly solid mechanics – and which it is tricky to characterize, as its formulations may have a number of different aspects. Firstly, a distinction regarding the way in which geometries are parameterized is presented, and secondly, a distribution pertaining to the intrinsic nature of optimization algorithms is established.

Determining the appropriate shape for structural components is a crucially important problem for engineers. In all areas of structural mechanics, the impact of proper design of a part is very significant in terms of its strength, its lifetime and its usage. This is a challenge faced on a daily basis in the sectors of spatial research, aeronautics, the automobile industry, naval competition, fine mechanics, precision mechanics or artwork in civil engineering, and so on. To develop the art of the engineer requires enormous effort to continuously improve techniques for designing structures. Optimization is of primary importance in improving the performance and reducing the weight of aerospace- and automobile machinery, providing substantial energy savings. The different development of computer-aided design (CAD) techniques and optimization strategies is part of this context. There has been keen interest in structural optimization for over thirty years. Whilst it is still too infrequently applied in the conventional techniques used by research centers, it is becoming more widely used as its reliability improves. Having begun with the simplest of problems, the field of application of structural optimization today extends to new and ever more interesting challenges.

To illustrate the evolution of structural optimization techniques, we can arbitrarily split structural optimization into three major groups (or families). In historical terms, each of them has been addressed in order of increasing difficulty and generality.

With sizing optimization, we are only able to modify the dimensions of an object whose shape and topology are fixed. There can be no modification of the geometric model. We speak of a homeomorphic transformation.

Shape optimization involves making changes of shape which are compatible with a predetermined topology. Typical shape optimization modifies the parametric representation of the boundaries of the domain. By moving the boundaries of the domains, we can seek the best solution out of all the structures obtained by homeomorphic transformation of the original object. In this case, it is clear that we can make a change to the transverse dimensions as well as a modification to the object’s configuration, but it is certainly not acceptable to modify its connectivity or its nature – in particular, the number of components that it has. The optimal object exhibits the same topology as the original object.

With topology optimization, we can fundamentally change the nature of the object. The “topology” refers to the number and position of the components of the domains. Here, the object’s geometry is presented with no prerequisites as to the connectivity of the domains or the components present in the solution. We take no initial information about the topology of the optimal shape.

1.2. History of structural optimization

It was in the early 1960s that Schmit [SCH 60] and Fox [FOX 65] laid the foundations for a modern theory of structural optimization, based on the concepts of mathematical programming and sensitivity analysis. Paradoxically, at the time, “fully stressed design” was the only widely used technique in practice, although it lacked any theoretic...

Table of contents

• Cover
• Table of Contents
• Title
• Copyright
• Preface
• Introduction
• List of Abbreviations
• 1 Introduction to Structural Optimization
• 2 Integration of Structural Optimization into Biomechanics
• 3 Integration of Reliability into Structural Optimization
• 4 Reliability-based Design Optimization Model
• 5 Reliability-based Topology Optimization Model
• 6 Integration of Reliability and Structural Optimization into Prosthesis Design
• Appendices
• Bibliography
• Index
• End User License Agreement