Finite element analysis and evaluation of design limits for structural materials in a cyclic state of creep

Abstract

SUMMARYIn this paper a direct non-time stepping method derived from the minimum theorems given by the authors (European Journal of Mechanics -A/Solids 2002; 21:915-925) is outlined. This method can be used in the prediction of the deformation and life assessment of structures subjected to cyclic mechanical and thermal loadings. It produces accurate predictions of failure modes based on material behaviour incorporated into constitutive equations. It also can be used to deÿne limit loads related to certain design criteria.Generally, for complex geometries and load histories, the identiÿcation of load histories that correspond to predeÿned design conditions, in the form of time or number of cycles to failure, can only be achieved by extensive and repeated calculations. For the Linear Matching Method, however, the representation of materially non-linear stress and strain ÿelds by linear behaviour with spatially varying moduli, indicates the possibility that direct evaluation of loads and temperature ranges that correspond to a design restriction may be evaluated directly through the construction of the exact cyclic state and via sequence of approximations. The technique employs the ÿnite element method combined with the cyclic state solution. The description of the material behaviour is given by a non-linear viscous model (Norton's law). It can also apply to any class of material behaviour that includes internal state variables. This technique has been applied successfully to a set of characteristics problems (Bree problem and plate containing a circular hole and subjected to radial temperature gradient).

Analysis of pressure equipment by application of the primal‐dual theory of shakedown

“…Elastic compensation methods are used in the pressure vessel design in some countries for many years. They have been modified to the linear matching method, extended to creep and implemented in the FEM codes ANSYS [6,14] and ABAQUS [15]. The basis reduction method has been extended to bounded kinematic hardening [16,17], applied to fracture mechanics [18] and implemented in the FEM code PERMAS [7,8].…”