The Analytic Design of Torsion Members.
IOWA UNIV IOWA CITY DEPT OF MECHANICS AND HYDRAULICS
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The classical torsion analysis of a prismatic bar reduces to the solution of a linear boundary-value problem posed in terms of either the Laplace or Poisson equation on the region representing the cross-section of the bar. Material properties are represented by a single physical constant, the shear modulus. The effect of this constant can be simply treated by the introduction of non-dimensional variables. Thus, within the linear theory, the only design changes of possible interest are those involving changes in the geometry of the corss-section. This dissertation is concerned with an analytical method for improving the design of a restricted class of cross-sections namely, those bounded by a closed curve having a continuous unit normal vector and piece-wise continuous curvature. Regions whose boundary contours possess exterior corners are treated as a a limiting case of the above class. At the heart of the technique is a representation of the change in the solution to the boundary-value problem in terms of a small change in the boundary contour. This representation is exploited using a numerical method to improve the design of the cross-section. Author
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