Shakedown analysis of nozzles in the knuckle region of torispherical heads under multiple thermo-mechanical loadings

Abstract The load-bearing capacity of cylindrical pressure vessels closed by Klopperboden torispherical drumheads with piping nozzle connections placed in the head's knuckle region is determined by using shakedown analysis. The pressure vessels under consideration are subjected to internal pressure, an axial force in the direction of the nozzle, in-plane bending moment at the nozzle, and temperature loading, all of which may vary independently. In particular, the interactions are investigated in several combinations of two and three of these loads, leading to two- and three-dimensional loading domains. The corresponding elastic and shakedown limits are computed based on Melan's statical shakedown theorem. The obtained results are compared to those taken from literature where available.

[1]  D G Moffat,et al.  Nozzles in the knuckle region of a torispherical head: Stress levels and load interaction effects , 2000 .

[2]  Kristian Krabbenhoft,et al.  A general non‐linear optimization algorithm for lower bound limit analysis , 2003 .

[3]  Jose Luis Silveira,et al.  An algorithm for shakedown analysis with nonlinear yield functions , 2002 .

[4]  D G Moffat,et al.  Nozzles in the knuckle region of a torispherical head : limit load interaction under combined pressure and piping loads , 2000 .

[5]  Jan A. König,et al.  Shakedown of Elastic-Plastic Structures , 1987 .

[6]  Johannes Groβ-Weege.  On the numerical assessment of the safety factor of elastic-plastic structures under variable loading , 1997 .

[7]  S. Paul,et al.  Cyclic plastic deformation response at fatigue crack tips , 2013 .

[9]  Robert J. Vanderbei,et al.  Global convergence of a primal-dual interior-point method for nonlinear programming , 2008, Algorithmic Oper. Res..

[10]  D N Moreton,et al.  Limit loads for knuckle-encroaching nozzles in torispherical heads: Experimental verification of finite element predictions , 2002 .

[11]  Manfred Staat,et al.  Upper bound limit and shakedown analysis of shells using the exact Ilyushin yield surface , 2008 .

[12]  Dieter Weichert,et al.  Progress in shakedown analysis with applications to composites , 2005 .

[13]  Helmut Saal,et al.  Flexibility factors for nozzles in the knuckle region of dished pressure vessel heads , 1997 .

[14]  Tianbai Li,et al.  On the shakedown analysis of welded pipes , 2011 .

[15]  M. Eslami,et al.  Thermal and mechanical cyclic loading of thick spherical vessels made of transversely isotropic materials , 2013 .

[16]  Jorge Nocedal,et al.  An interior algorithm for nonlinear optimization that combines line search and trust region steps , 2006, Math. Program..

[17]  Scott W. Sloan,et al.  Lower bound limit analysis using non‐linear programming , 2002 .

[18]  Zhangzhi Cen,et al.  Limit analysis based on a modified elastic compensation method for nozzle-to-cylinder junctions , 2005 .

[19]  Dieter Weichert,et al.  Inelastic Analysis of Structures under Variable Loads , 2000 .

[20]  Christian Wielgosz,et al.  In-plane limit moment for an elbow. Lower-bound analytical solution and finite element processing by elastic compensation method , 1997 .

[21]  Jaan-Willem Simon,et al.  Shakedown Analysis Combined With the Problem of Heat Conduction , 2012 .

[22]  Haofeng Chen,et al.  The Bree problem with different yield stresses on-load and off-load and application to creep ratcheting , 2014 .

[23]  Bingjun Gao,et al.  Recent progresses in experimental investigation and finite element analysis of ratcheting in pressurized piping , 2013 .

[24]  R. Bradford,et al.  The Bree problem with primary load cycling in-phase with the secondary load , 2012 .

[25]  M. H. Wright.  The interior-point revolution in optimization: History, recent developments, and lasting consequences , 2004 .

[26]  J. Simon,et al.  Numerical lower bound shakedown analysis of engineering structures , 2011 .

[27]  Erling D. Andersen,et al.  On implementing a primal-dual interior-point method for conic quadratic optimization , 2003, Math. Program..

[28]  J. Simon,et al.  Interior-Point Method for Lower Bound Shakedown Analysis of von Mises-Type Materials , 2013 .

[29]  Ernst Melan,et al.  Zur Plastizität des räumlichen Kontinuums , 1938 .

[30]  Manfred Staat,et al.  Analysis of pressure equipment by application of the primal-dual theory of shakedown , 2006 .

[31]  Lorenz T. Biegler,et al.  Line Search Filter Methods for Nonlinear Programming: Motivation and Global Convergence , 2005, SIAM J. Optim..

[32]  Jaan-Willem Simon,et al.  Shakedown analysis of engineering structures with limited kinematical hardening , 2012 .

[33]  Etienne Loute,et al.  Limit analysis decomposition and finite element mixed method , 2010, J. Comput. Appl. Math..

[34]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[35]  P. Wriggers,et al.  An interior‐point algorithm for elastoplasticity , 2007 .

[36]  J. Simon,et al.  Shakedown analysis with multidimensional loading spaces , 2012 .

[37]  Jaan-Willem Simon,et al.  Direct evaluation of the limit states of engineering structures exhibiting limited, nonlinear kinematical hardening , 2013 .

[38]  D Plancq,et al.  Limit analysis based on elastic compensation method of branch pipe tee connection under internal pressure and out-of-plane moment loading , 1998 .

[39]  P. Fuschi,et al.  A numerical approach for limit analysis of orthotropic composite laminates , 2007 .

[40]  Gang Chen,et al.  Ratcheting behavior of pressurized elbow pipe with local wall thinning , 2013 .

[41]  Haofeng Chen,et al.  Creep-fatigue life assessment of cruciform weldments using the linear matching method , 2013 .

[42]  Le Thi Hoai An,et al.  Application of lower bound direct method to engineering structures , 2007, J. Glob. Optim..

[43]  E. Loute,et al.  Mixed method and convex optimization for limit analysis of homogeneous Gurson materials: a kinematical approach , 2009 .