1. The Material Selection Strategy

Multiobjective optimization (also known multicriteria optimization) developed in the broad area of multiple criteria decision making, also known as multiple-criteria decision analysis (MCDA). MCDA is a subdiscipline of operations research methodology founded in the UK during World War II explicitly to consider multiple criteria in decision making in highly complex environments like the military. Generalizing the operational research and derivative methods further developed concerns with mathematical optimization problems involving more than one objective function to be optimized simultaneously, so that decision makers could pursue the best choice.

In the case study, the resistance limit of a material is considered to be the resistance to bending fatigue, thus assuming the pan is loaded by this load type. This would not be true in a real case scenario, since the pan is not highly stressed by fatigue loading. In any case in many classroom cases, we prefer to consider some rearranged situation, reflecting on the simple shape and geometry of a component in a state of stress which would be usual in many other structural parts of the object.

This formula is based on a simple proportion as ( unknown value): 3 = ( real value): ( real average value).

Member of the Cambridge University Engineering Department where he holds the post of Royal Society research professor, M. F. Ashby is the academic who has, more than others, devoted his research to material selection strategies. Briefly described here, his approach is today recognized by material specialists as the most brilliant and powerful explicit method for engineering material selection.

For readers with a technical background, readers who are not necessarily material specialists but who wish to go into depth in the matter, we suggest: Ashby, M.F. and Johnson, K. Materials and Design, the Art and Science of Materials Selection in Product Design Butterworth Heinemann, Oxford, 2002.

Different combinations of function, objective, and constraint lead in different engineering cases to different material indexes. Although for the sake of brevity we applied the method to a specific case study (a panel that needs to be as light as possible while it carries a bending moment), the Ashby derivative method is general. Therefore, the material performance index I is characteristic of the proper combination, and thus of the function that the component performs, but it can be calculated in a wide range of problems. Some problems are more complex than the study case we use, and also the equations to derive and to elaborate in the general procedure here described can be of rather greater complexity, even for specialists. Fortunately a wide category of engineering functional problems have been studied by Ashby as master cases. Since it is outside the scope of this book, we suggest that readers who need to select the correct material performance index for their specific case should refer to a fuller catalogue of indices that Ashby has provided in Appendixes in M.F. Ashby, Materials Selection in Mechanical Design, Third Edition, Butterworth Heinemann, Oxford, 2005.

For the complete procedure, refer to: M.F. Ashby, Materials Selection in Mechanical Design, Third Edition, Butterworth Heinemann, Oxford, 2005.

For in-depth studies of other specific cases that Ashby illustrates for varying loading geometries and objective functions, refer to the charts with proper straight parallel guidelines (Ashby 2005).

Engineers and material scientists classify materials quite differently in relation to six broad family groups: metals, polymers, elastomers, ceramics, glasses, and naturals. Unlike architectural classification systems that are determined by how the materials are applied, each of these groupings is determined by certain properties that are common, such as chemical composition, ductility, elasticity, yield strength, tensile strength, compressive strength, and toughness.

Mauro Linari, M.Sc. Mech. Engineering has worked at MSC Software since 1988 and has been involved in support, training, development and services activities, mainly in the aerospace and automotive field industries, as senior project manager. He is an expert in finite element modeling, stress analysis, dynamics, and optimization in the linear and nonlinear field.

Referring to texts and specialized articles dealing with topology optimization for more details, what is important to understand in principle is the way in which the software conducts the analysis: it performs several cycles of automated optimization (in the place of the designer) and, on the basis of simple relations, it builds a map over the design space which in all cases shows the value of a parameter calculated for each element of the mesh (variable in the range from 0 to 1) which can represent the higher or lower importance of each element in collaboration with the global behavior of the structure. Therefore, the software assigns a “quality or importance factor” to each element (generically defined as “element density”). Proceeding with the automated optimization process—and depending on the element density factors—the two design variables on which the software operates—Young modulus and mass density—vary on the basis of the elements, assuming values that are lower or at most equal to those initially defined.