Abstract
This chapter discusses polar coordinates. Many structural parts can be idealized as plates bounded by circular arcs and radial lines. It was previously found that stresses and displacements could be found by differentiating various scalar functions. It is now necessary to rewrite the first and second derivatives with respect to x and y in terms of new coordinates (r, θ). These describe the position of a point at radius r and angular position θ measured from some radial datum line. The strains may be integrated to obtain displacements if the strains happen to be known. This may be done by writing down for each component of displacement a likely expression containing a number of unknown constants. Differentiation then gives expressions for strains that can be compared with the known values. Internal stresses in a stationary disc cannot be directly described by these equations. This is because the strain compatibility equation is no longer satisfied because of dislocations of some kind being introduced when the internal stresses are set up.
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