Shakedown analysis of elastic-plastic structures considering the effect of temperature on yield strength: Theory, method and applications

Abstract

According to the extended Melan's static theorem, theoretical and numerical aspects of the stress compensation method (SCM) are presented to perform shakedown analysis of elastic-plastic structures considering the effect of temperature on yield strength. Instead of constructing a mathematical programming formulation, this developed method consists of the two-level iterative scheme. The inner loop constructs the statically admissible self-equilibrating stress field, while the outer loop evaluates a sequence of decreasing load factors to approach to the shakedown limit multiplier. The yield strength considering temperature effect is updated based on the current temperature at each outer iteration, and the yield conditions are checked at all Gauss points. The numerical procedure is well incorporated into ABAQUS finite element code and used for calculating the shakedown limits of structures considering yield strengths as different functions of temperature under complex thermomechanical loading system. The method is validated by some plane stress and axisymmetric numerical examples with theoretical and numerical solutions, and subsequently applied to solve the practical shakedown problem of a pipe with oblique nozzle. The results demonstrate that the developed method is stable, accurate and efficient, and can effectively evaluate the shakedown limit of an elastic-plastic structure where the yield strength of material varies with temperature.

Creep rupture assessment of cyclically heated 3D pressure pipelines with volumetric defects using a direct numerical approach

“…The numerical scheme contains two iterative loops. A sequence of iterative calculations of FE equilibrium equations are carried out in the inner loop to optimise the time-independent residual stress field and the load factor J. is updated through the use of an iterative control scheme in the outer loop to obtain the shakedown limit (18, 21,22]. For the n-th iteration of inner loop.…”

“…For each calculation of creep rupture limit, a specific value of tp is selected and then a load factor ,l is output by the numerical approach procedure. The actual linear elastic stress fields at the two load vertices are (21) (22) It is important to note that the temperature field is also scaled by the load factor ,l after each iteration of load factor, i.e. the actual temperature field O(xk) is O(x,) = ..lOo (x,) (23) After obtaining the creep rupture limits within a series of ratios of inner pressure and temperature load, the creep rupture limit interaction curve is also determined.…”

Ambient multiaxial creep: shakedown analysis of structures using stereo digital image correlation

“…While there are many theoretical and numerical approaches to identify cyclic elastoplastic shakedown behavior that are based on monitoring stress states [53][54][55][56][57][58][59][60][61], the most straightforward and convenient experimental metric is strain-based. From the full-field measurements provided by the DIC described in Sect.…”

Structural topology optimization of elastoplastic continuum under shakedown theory

“…After decades of development, shakedown analysis methods mainly include three types: (1) mathematical programming method, such as the nonlinear Newton-type iteration algorithm, 5,6 the second-order cone programming (SOCP), 7 and various interior-point methods(IPM), [8][9][10] which are directly used to solve mathematical programming problem; (2) basis reduction method [11][12][13][14] which is to reduce the number of bases of self-equilibrated stress field thereby stipulating the number of unknowns and combine some optimization algorithm; and (3) some methods based on mechanics mechanism, which do not depend on the mathematical programming, such as the elastic compensation method (ECM), 15,16 the linear matching method (LMM), 17,18 the residual stress decomposition method for shakedown (RSDM-S), [19][20][21] and the stress compensation method (SCM). [22][23][24] In addition, based on the classical shakedown theory of elastic-perfectly plastic systems, many extensions of shakedown theory are developed for covering various engineering concerns, such as geometric nonlinearities, [25][26][27] creeping effect, 28 frictional contact 6,29 and so forth. In this article, the recently developed PEM method 30 is applied for shakedown analysis of elastic-perfectly plastic continuum.…”