Numerical Engineering Optimization: Application of the Computer Algebra System Maxim: Application of the Computer Algebra System Maxima

✍ Scribed by Andreas Öchsner, Resam Makvandi

• Publisher: Springer Nature
• Year: 2020
• Tongue: English
• Leaves: 232
• Edition: 1st ed. 2020
• Category: Library

✦ Synopsis

This study aid on numerical optimization techniques is intended for university undergraduate and postgraduate mechanical engineering students. Optimization procedures are becoming more and more important for lightweight design, where weight reduction can, for example in the case of automotive or aerospace industry, lead to lower fuel consumption and a corresponding reduction in operational costs as well as beneficial effects on the environment. Based on the free computer algebra system Maxima, the authors present procedures for numerically solving problems in engineering mathematics as well as applications taken from traditional courses on the strength of materials. The mechanical theories focus on the typical one-dimensional structural elements, i.e., springs, bars, and Euler–Bernoulli beams, in order to reduce the complexity of the numerical framework and limit the resulting design to a low number of variables. The use of a computer algebra system and the incorporated functions, e.g., for derivatives or equation solving, allows a greater focus on the methodology of the optimization methods and not on standard procedures.

The book also provides numerous examples, including some that can be solved using a graphical approach to help readers gain a better understanding of the computer implementation.

✦ Table of Contents

Preface
Contents
1 Introduction
1.1 Optimization Problems
1.2 Maxima—A Computer Algebra System
References
2 Unconstrained Functions of One Variable
2.1 Golden Section Algorithm
2.2 Brute-Force or Exhaustive Search Algorithm
2.3 Newton's Method
2.4 Supplementary Problems
References
3 Constrained Functions of One Variable
3.1 The Exterior Penalty Function Method
3.2 The Interior Penalty Function Method
3.3 Supplementary Problems
References
4 Unconstrained Functions of Several Variables
4.1 General Introduction to the Unconstrained Multidimensional Optimization Problem
4.2 First-Order Methods
4.3 Second-Order Methods
4.4 Supplementary Problems
References
5 Constrained Functions of Several Variables
5.1 General Introduction to the Constrained Multidimensional Optimization Problem
5.2 The Exterior Penalty Function Method
5.3 Supplementary Problems
References
6 Answers to Supplementary Problems
6.1 Problems from Chapter2摥映數爠eflinkchap:Unconstsps1D22
6.2 Problems from Chapter 3摥映數爠eflinkchap:Constsps1D33
6.3 Problems from Chapter 4摥映數爠eflinkchap:UnconstrainedspsFspsv44
6.4 Problems from Chapter 5摥映數爠eflinkchap:ConstrainedspsFspsv55
References
7 Maxima Source Codes
Index