Abstraction and Modeling Abstraction
• The first step in abstraction is to break the problem into as many functional parts, subproblems, or meaningful units as possible.
• Next, one should try to classify these functional aspects of the problems into more general categories in accordance with their distinctive characteristics.
• Generate as many different alternative designs as possible.
Example: Developing a transportation system
• Objective - Design a method for transporting people from one location to another
• Rather than attempt to generate some specific design for accomplishing this
• Through abstraction, focus on several general methods of “location change”
Methods
• Propel - fluid motion, catapult motion, engine trust
• Carry - by water current (raft), air current (kites, gliders), motorized vehicles, animals
• Attract/repel - magnetism
• Sink/drop - using weight or gravity
• Lift - using the buoyancy of gases
• Slide - reducing friction
• Pull - with ropes
• Abstraction provides us with a perspective of the building blocks than can be used to develop a set of design solutions
• Through abstraction, we view the problem and its possible solution
Models
• Modeling is part of abstraction process
• Models allow us to organize data, structure our thoughts, describe relationships, and analyze proposed designs.
• A model is used to obtain greater insight and understanding about that which is being represented.
• Models can be abstract or concrete
Abstract models - mathematical/symbolic, graphical, and computer based (e.g. simulation, finite element, CAD).
Concrete (physical) models - composed of clay, cardboard, rubber bands, glue, and other materials that are easily available.
Three Types
• Iconic - Equivalent but incomplete 2D or 3D representations - maps and world globes, 3D physical models of proposed bridges, highways, buildings and 3D models generated via CAD.
Example: The statue of liberty - 151 ft Plaster model - 38 ft
• Analogic - Functionally equivalent but incomplete representations Example: Miniature airplanes dynamically tested in wind tunnels
• Symbolic - Higher-level abstractions of reality - equations, physics laws (e,g.
energy conservation, Newton’s laws)
Example: The orbital behavior of planet and its moon, satellites Projectile motion of a cannon ball, rocket motion
Finite Element Models
• A system is described as a collection of interdependent discrete parts.
• The extent of decomposition depends upon the level of detail that one seeks in the analysis.
• More elements of smaller size will generally provide a more precise description of the system and its dynamic behavior.
• Finite elements models are used to describe:
• fluid flow
• heat transfer
• dynamic mechanical responses
• phenomena in systems that would be difficult to analyze in any other way
