Optimality Criteria

• Published in: Optimization Methods in Structural Design Vol. 242; pp. 29 - 53
• Main Author: Rothwell, Alan
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2017; Springer International Publishing
• Series: Solid Mechanics and Its Applications
• Subjects: Circular Tube; Design Variable; Local Buckling; Maximum Stress; Truss Structure
• ISBN: 3319551965; 9783319551968
• ISSN: 0925-0042; 2214-7764
• DOI: 10.1007/978-3-319-55197-5_2

A first optimality criterion, that of the fully stressed design, was already introduced in the previous chapter. The buckling of a circular tube in compression is used to illustrate a second criterion, that of simultaneous buckling modes. In fact, when the tube forms part of a truss structure, this might be seen as a logical extension of the principle of the fully stressed design. This second optimality criterion leads directly to an efficiency formula, expressing the maximum stress that can be achieved in a thin tube or other component in terms of a suitable structural index and the elastic modulus of the material. The concept of the design space, widely used in subsequent chapters, is introduced with the circular tube. A third criterion is developed for the maximum stiffness of a structure, on the basis of a simple truss but taken in principle to apply more widely. It is shown that under certain conditions, a fully stressed design, with maximum strength-to-weight ratio, also has maximum stiffness. A spreadsheet program is presented for the optimization of circular and square tubes in compression, subject to dimensional restrictions and specified maximum allowable stress.