MEMBRANE STRESSES IN SKEW CIRCULAR CONES. I. GENERAL THEORY.
THOMPSON RAMO WOOLDRIDGE INC LOS ANGELES CALIF
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The present investigation is concerned with membrane stress states in skew circular cones i.e., surfaces generated by moving a straight line, passing through a fixed point in space, along the circumference of a fixed circle. A right circular cone results as a special case when the line joining the center of the circle and the fixed point is normal to the plane of the circle. The analysis is complicated by the unsymmetric geometry of the cone surface and by the circumstance that a convenient choice of directions of stress and displacements involves a skew coordinate system. In the present paper stress-equilibrium equations, stress strain relationships, and expressions for strains in terms of displacements, and displacements in terms of strains are derived. The application of the theory to various problems will be discussed in a succeeding paper. Author