PSI - Issue 8

G. Fargione et al. / Procedia Structural Integrity 8 (2018) 566–572 Author name / Structural Integrity Procedia 00 (2017) 000–000

569

4

• Requirements related to environmental conditions – They regard the behavior of the component in relation to the conditions in which the system performs its functions.

2.2. System composition

At the end of System Design phase, system composition is obtained. It is represented by:

• the set of components {C}, that collects the n c components constituting the system {C 1 , ..., C i , ..., C nc }; • the set of constraints between components in the whole system {CbC}, that describe the network of correlation between components in the design process, which means they are correlated in terms of requirements, functionality, geometric parameters, materials. The constraints between components on geometric parameters are the most common. Another common potential constraint between components could take places on materials (e.g. because of incompatible materials). If a component is related to another component at functional level (some requirements are shared among components), objective and constraint functions will depend on properties of both components. The set of requirements {R}, previously defined by the requirements specification phase (Section 2.1), can be translated into requirements on system components {C}. The set {R} i specifies the requirements concerning the i-th component C i . Each component C i must be defined by design, choosing the parameters G i , that specify the shape and sizes, and its material M i . Based on the set of ascribed requirements, for each component the design problem can be formulated identifying objectives, constraints, variables. The objectives of the design problem can be expressed by Objective or Performance Functions, to be minimized or maximized, in the basic form [ ] F V T R f G ,G ,M P PF 1 = (1) that is a function of groupings of variables: specifications on geometry G F and G V (fixed and variable geometric parameters); properties of material M T P R . The minimization (or maximization) of PF is subject to constraints on requirements R, geometric parameters G F and G V , and material properties M T P R . Constraints on requirements R can be expressed as constraint equations in the generalized form [ ] F V T R R f G ,G ,M P 2 ≤ (2) The first term in equation type (2) stands for the “generalized stresses” to which the component must resist (that quantifies the requirement), the second term stands for the “generalized resistances” of component to this stresses. Therefore, constraint equations (2) can be also formulated in the form of Constraint Ratio CR, as the ratio between component resistance and the stress to which it is subjected, that should be higher than 1: [ ] 1 2 ≥ = R f G ,G ,M P CR F V T R (3) 2.3. Components characterization

2.4. System characterization

The previous formalization of objectives, constraints, and variables of the design problem refers to the case where the component is independent of the other components in the system, which means that the set {CbC} i collecting the constraints between i-th component C i , and all the other components of the system between, is empty.