# An Introduction to Differential Geometry with Applications by Philippe G. Ciarlet

By Philippe G. Ciarlet

This monograph offers the elemental theorems of differential geometry in 3-dimensional area, together with a radical insurance of floor concept. through a sequence of conscientiously chosen and consultant mathematical types this monograph additionally explains at size how those theorems are utilized in three-d elasticity and in shell idea. The presentation is basically selfcontained, with an exceptional emphasis on pedagogy. particularly, no "a priori" wisdom of differential geometry or of elasticity idea is thought, the single requisites are an affordable wisdom of easy research, useful research, and a few acquaintance with usual and partial differential equations.

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Extra info for An Introduction to Differential Geometry with Applications to Elasticity

Example text

This example also illustrates that because the belt speed (in inches per minute) stays the same, the torque on the driven shaft is inversely proportional to the change in speed between the driver and driven pulleys. If the driven shaft turns at a higher speed, its torque is decreased relative to the driver shaft, and vice versa. For every speed change, there is a change in the torque. This relationship can be shown by reviewing the pto horsepower equation: POWER TRAINS hp To x rpm 5252 = 59 (6-3) If the horsepower stays the same.

Problem: Assume that you have a fan and an electric motor, but no pulleys. The fan is designed to operate at 500 rpm, and the electric motor operates at 1725 rpm. What sizes of pulleys will be needed to operate the fan? Solution: First, intuitive reasoning tells us that a large change in speed will require a large difference in pulley diameters. Second, we know that Equation (6-1) includes four Variables, and at this point we only know two, the pulley speeds. To find a solution we must select one of the pulley sizes and then determine the other.

Horsepower is commonly shown mathematically as: FxD hp = T x 33,000 (4-4) This equation requires distance (D) expressed in feet, force (F) in pounds, and time (T) in minutes. 5 minutes? 5 minutes. It becomes necessary to convert seconds to minutes or to use a different conversion factor from power to horsepower. 028 hp PRACTICE PROBLEMS 1. 0 feet? Answer: 300 ft-lb 2. In the first situation a 2000-pound weight is raised vertically through a distance of 20 feet. In the second situation a 3000-pound force moves horizontally through a distance of 10 feet.