小参数展开法解圆柱扭转的有限位移问题

THE SOLUTION TO THE FINITE DISPLACEMENT PROBLEM OF A CIRCULAR CYLINDER UNDER TORSION BY USING THE METHOD OF SMALL PARAMETER EXPANSIONS

By using the method of small parameter expansions the present boundary-value problem is solved. We thus obtain the formulae in the second approxima-tion for the displacement, strain, and stress fields. The second-order theory reveals that after deformation, any cross-section of the circular cylinder must be displaced into a plane section perpendicular to its central axis, and neither the normal strains nor the normal stresses vanish throughout the cylinder. These effects are abient from the classical elasticity theory.