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Unformatted text preview: Section 4.1 Solid Mechanics Part II Kelly 55 4.1 Cylindrical and Polar Coordinates 4.1.1 Geometrical Axisymmetry A large number of practical engineering problems involve geometrical features which have a natural axis of symmetry , such as the solid cylinder, shown in Fig. 4.1.1. The axis of symmetry is an axis of revolution ; the feature which possesses axisymmetry (axial symmetry) can be generated by revolving a surface (or line) about this axis. Figure 4.1.1: a cylinder Some other axisymmetric geometries are illustrated Fig. 4.1.2; a frustum, a disk on a shaft and a sphere. Figure 4.1.2: axisymmetric geometries Some features are not only axisymmetric they can be represented by a plane, which is similar to other planes right through the axis of symmetry. The hollow cylinder shown in Fig. 4.1.3 is an example of this plane axisymmetry . axis of symmetry create cylinder by revolving a surface about the axis of symmetry Section 4.1 Solid Mechanics Part II Kelly 56 Figure 4.1.3: a plane axisymmetric geometries Axially Non-Symmetric Geometries Axially non-symmetric geometries are ones which have a natural axis associated with them, but which are not completely symmetric. Some examples of this type of feature, them, but which are not completely symmetric....
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- Fall '11