A constitutively consistent lower bound, direct shakedown and ratchet method

• Main Author: Jappy, Alan
• Published: University of Strathclyde 2014
• Subjects: 629.1
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.618888

When a structure is subject to cyclic loads there is a possibility of it failing due to ratchet or incremental collapse. In many engineering structures the demonstration of non-ratcheting behaviour is a fundamental requirement of the design and assessment process. Whilst it is possible to use incremental finite element analysis to simulate the cyclic response for a given load case to demonstrate shakedown or ratchet, it does not yield any information on the safety factor. In addition, there are several practical problems in using this approach to determine whether or not a component has achieved shakedown. Consequently several direct methods which find the loads at the shakedown and ratchet boundaries have been developed in the past 3 decades. In general, lower bound methods are preferred for design and assessment methodologies. However, to date, the lower bound methods which have been proposed for shakedown and ratchet analysis have not been fully reliable and accurate. In this thesis a lower bound shakedown and ratchet method which is both reliable and accurate is proposed. Previously proposed elastic plastic lower bound ratchet methods are revisited and modified to understand the limitations in current methods. From this, Melan's theorem is reinterpreted in terms of plasticity modelling and shown to have the same form as a non-smooth multi yield surface plasticity model. A new shakedown method is then proposed based on the non-smooth multi yield surface plasticity model. The new shakedown method is extended using a two stage process to determine the ratchet boundary for cyclic loads in excess of the alternating plasticity boundary. Two simplified variants of the ratchet method are also proposed to decrease the computational expense of the proposed ratchet method. Through several common benchmark problems the proposed methods are shown to give excellent agreement with the current upper bound methods which have been demonstrated to be accurate. The flexibility of the shakedown method is demonstrated by extending the method to incorporate temperature dependent yield, hardening and simplified non-linear geometric effects.