Chapter 4 - Solutions of Element Models

Abstract

An element model describes the relations of nodal variables and loads in the element. An element model is used to determine nodal variables based on given loads on nodes. Element models are basic building blocks to a system model. This chapter is to (1) formulate a boundary value problem as a mathematic model to represent the physical behaviors of elements and (2) introduce the techniques to solve mathematic models for discretized elements. Generally, an engineering problem can be modeled by partial differential equations (PDEs). Therefore, the solutions to PDEs are applicable to a broad scope of engineering problems. The governing equations of various engineering problems are reviewed. Accordingly, engineering problems are classified into equilibrium problems, eigenvalue problems, and transient problems. Weighted residual methods are applied to develop element models for these PDEs.