Lower and Upper Bound Shakedown Analysis of Structures With Temperature-Dependent Yield Stress
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TL;DR: In this article, a linear matching method (LMM) lower bound procedure was proposed for shakedown analysis of structures with temperature-dependent yield stress, which is implemented into ABAQUS using the same procedure as for upper bounds.
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Abstract: Based upon the kinematic theorem of Koiter, the Linear Matching Method (LMM) procedure has been proved to produce very accurate upper bound shakedown limits. This paper presents a recently developed LMM lower bound procedure for shakedown analysis of structures with temperature-dependent yield stress, which is implemented into ABAQUS using the same procedure as for upper bounds. According to the Melan's theorem, a direct algorithm has been carried out to determine the lower bound of shakedown limit using the best residual stress field calculated during the LMM upper bound procedure with displacement-based finite elements. By checking the yield condition at every integration point, the lower bound is calculated by the obtained static field at each iteration, with the upper bound given by the obtained kinematic field. A number of numerical examples confirm the applicability of this procedure and ensure that the upper and lower bounds are expected to converge to the theoretical solution after a number of iterations.
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Citations
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I. W. Goodall,R. A. Ainsworth +1 more
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TL;DR: This paper describes extensive work within Nuclear Electric, to develop a procedure which assembles knowledge in structural mechanics and materials science for assessment of components operating in the creep range.
401
Shakedown and limit analyses for 3-D structures using the linear matching method
Haofeng Chen,Alan R.S. Ponter +1 more
TL;DR: In this article, the shakedown and limit loads of a holed plate subjected to biaxial loading are calculated by implementing the upper bound linear matching method into the commercial FE code ABAQUS.
165
Shakedown Limits for a General Yield Condition: Implementation and Application for a Von Mises Yield Condition
TL;DR: In this article, a nonlinear programming approach was proposed for the evaluation of limit loads and shakedown limits for a body subjected to cyclic loading, where the local gradient of the upper bound functional and the potential energy of the linear problem were matched at a current strain rate or during a strain rate history.
132
A method for the evaluation of a ratchet limit and the amplitude of plastic strain for bodies subjected to cyclic loading
Haofeng Chen,Alan R.S. Ponter +1 more
TL;DR: In this paper, an extension of the upper bound shakedown theorem to load histories in excess of shakedown has been presented, where the minimisation process described therein is applied to the solutions of the ratchet limit as well as shakedown and limit load for a range of simple problems.
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