An Extension of Love's Solution for the Axisymmetric Problems of Elasticity

抄録

This paper is concerned with an extension of Love's solution for the axially symmetric problems in the theory of elasticity. The principal results are as follows. (1) Love's solution is generalized such that it may be possible to apply it to the problems accompanied with both torsional deformations and body-forces, because Love's solution in its usual form is inapplicable to the foregoing cases. (2) The generalized Love's solution has the completeness of solution for the axially symmetric problems. The completeness of Love's solution in its usual form is only assured for the cases of torsion-free deformations with no body-force but in z-direction. (3) The torsional solution obtained from the generalized Love's stress function is equivalent to the solutions of other known methods. (4) An attempt is made to investigate a general functional form of Love's stress function which can be applied to any practical problems. (5) The stress function for body-force problems is investigated, and examples of its application are shown.