Chapter 2 - Mathematical modeling of physical systems

Abstract

The goal of this chapter is to briefly demonstrate mathematical equations that govern the deformation of linear elastic solids and thermal energy transfer and storage in solid bodies. While more detailed discussion of these topics can be found in the specialized references, we demonstrate how to obtain mathematical representations (models) of physical systems by using the fundamental laws of physics. We show that deformation of elastic solids can be described by using Newton's laws of motion, resulting in equations of motion represented as partial differential equations. Equations of motion of linear elastic solids in one, two, and three dimensions are derived. The principle of conservation of energy is used to describe effects of heat transfer in a continuum.