The Analytic Design of Torsion Members.

Abstract

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)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1971
Accession Number
AD0725485

Entities

People

  • Allen S. Henry

Organizations

  • University of Iowa

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Curvature
  • Differential Equations
  • Equations
  • Geometric Forms
  • Geometry
  • Lines (Geometry)
  • Materials
  • Mathematics
  • Military Vehicles
  • Poisson Equation
  • Shear Modulus
  • Theses
  • Vehicles
  • Vibration

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Structural Dynamics.