Mathematical Modeling for Structural Analysis
The dictionary defines a model as “a miniature representation of something; a pattern of something to be made; an example for imitation or emulation; a description or analogy used to help visualize something (e.g., an atom) that cannot be directly observed; a system of postulates, data and inferences presented as a mathematical description of an entity or state of affairs.” This definition suggests that modeling is an activity, a cognitive activity in which one thinks about and makes models to describe how devices or objects of interest behave. Thus, it is important to remember that when we describe or formulate a problem in words, draw a sketch (e.g., a free-body diagram), write down or derive a formula, and crank through to get some numbers, we are modeling something. In each of these activities we are formulating and representing a model of the problem in a modeling language. And as we go from words to pictures to formulas to numbers, we must be sure that we are translating our problem correctly and consistently. We have to maintain our assumptions, and at the right level of detail.