The elastic-plastic straining of some shells of revolution with special reference to expansion bellows

• Main Author: Marcal, Pedro Vincente Fernandes do Couto
• Published: Imperial College London 1963
• Subjects: 621.38
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.602246

This thesis is intended as a contribution to the problem of limited life design of symmetrically loaded shells of revolution. The basic equations governing the behaviour of, a shell of revolution were differentiated implicitly in order to provide a basis for the non-linear numerical analysis of shells of revolution. Incremental generalized stress-strain relations were then introduced which allowed nonlinear stress-strain laws to be taken into account. A later analysis showed that a generalization of the incremental stress-strain relations would enable the Prandtl Reuss equations to be used in writing the three dimensional equations of equilibrium in terms of strains. A computer programme based on the derived shell equations was developed which calculated the elastic-plastic strains in axially loaded bellows. The bellows were assumed to be made of an elastic-perfectly plastic Tresca material of the Reuss type. A method of estimating strains after collapse in beams was adapted for the case of the axially loaded bellows. Calculated and experimental results agreed for the one bellows tested beyond collapse. Tests were performed on four axially loaded bellows to obtain the relationship between maximum strains, load and deflection in the plastic region. The experimental and calculated results were found to be in resonable agreement when they were compared non-dimensionally. The bellows were finally tested in fatigue and the results agreed with the results of fatigue tests on. samples of bellows material.