Προσθήκη στα αγαπημένα
This book provides theories on non-parametric shape optimization problems, systematically keeping in mind readers with an engineering background. Non-parametric shape optimization problems are defined as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined. In these problems, optimum shapes are obtained from an arbitrary form without any geometrical parameters previously assigned. In particular, problems in which the optimum shape is sought by making a hole in domain are called topology optimization problems. Moreover, a problem in which the optimum shape is obtained based on domain variation is referred to as a shape optimization problem of domain variation type, or a shape optimization problem in a limited sense. Software has been developed to solve these problems, and it is being used to seek practical optimum shapes. However, there are no books explaining such theories beginning with their foundations.
Preface.- Notation.- Chapter 1: Basics of Optimal Design.- Chapter 2: Basics of Optimization Theory.- Chapter 3: Basics of Mathematical Programming.- Chapter 4: Basics of Variational Principles and Functional Analysis.- Chapter 5: Boundary Value Problems of Partial Differential Equations.- Chapter 6: Fundamentals of Numerical Analysis.- Chapter 7: Abstract Optimum Design Problem.- Chapter 8: Topology Optimization Problem of Density Variation Type.- Chapter 9: Shape Optimization Problems of Domain Variation Type.- Answers to Practice Problems.- Afterword.- References.- Index.
Περιγραφή
This book provides theories on non-parametric shape optimization problems, systematically keeping in mind readers with an engineering background. Non-parametric shape optimization problems are defined as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined. In these problems, optimum shapes are obtained from an arbitrary form without any geometrical parameters previously assigned. In particular, problems in which the optimum shape is sought by making a hole in domain are called topology optimization problems. Moreover, a problem in which the optimum shape is obtained based on domain variation is referred to as a shape optimization problem of domain variation type, or a shape optimization problem in a limited sense. Software has been developed to solve these problems, and it is being used to seek practical optimum shapes. However, there are no books explaining such theories beginning with their foundations.
