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Introduction to Numerical Methods Notes

Introduction to Numerical Methods Notes - Chapter 01.01...

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Chapter 01.01 Introduction to Numerical Methods After reading this chapter, you should be able to: 1. understand the need for numerical methods, and 2. go through the stages (mathematical modeling, solving and implementation) of solving a particular physical problem. Mathematical models are an integral part in solving engineering problems. Many times, these mathematical models are derived from engineering and science principles, while at other times the models may be obtained from experimental data. Mathematical models generally result in need of using mathematical procedures that include but are not limited to (A) differentiation, (B) nonlinear equations, (C) simultaneous linear equations, (D) curve fitting by interpolation or regression, (E) integration, and (F) differential equations. These mathematical procedures may be suitable to be solved exactly as you must have experienced in the series of calculus courses you have taken, but in most cases, the procedures need to be solved approximately using numerical methods. Let us see an example of such a need from a real-life physical problem. To make the fulcrum (Figure 1) of a bascule bridge, a long hollow steel shaft called the trunnion is shrink fit into a steel hub. The resulting steel trunnion-hub assembly is then shrink fit into the girder of the bridge. Figure 1 Trunnion-Hub-Girder (THG) assembly. 01.01.1 Trunnion Hub Girder
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01.01.2 Chapter 01.01 This is done by first immersing the trunnion in a cold medium such as a dry- ice/alcohol mixture. After the trunnion reaches the steady state temperature of the cold medium, the trunnion outer diameter contracts. The trunnion is taken out of the medium and slid through the hole of the hub (Figure 2). Figure 2 Trunnion slided through the hub after contracting When the trunnion heats up, it expands and creates an interference fit with the hub.
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