Upper bound limit and shakedown analysis of shells using the exact Ilyushin yield surface

This paper concerns the development of a kinematic formulation for the finite element limit and shakedown analysis of shells. The technique is based upon an upper bound approach using the re-parameterized exact Ilyushin yield surface and a nonlinear optimization procedure. The solution of the problem is obtained by discretizing the shell into finite elements. Numerical examples are presented to show the validity of the present method.

[1]  M. Robinson,et al.  A comparison of yield surfaces for thin shells , 1971 .

[2]  D. Acker,et al.  DESIGN CRITERIA FOR PIPING COMPONENTS AGAINST PLASTIC COLLAPSE: APPLICATION TO PIPE BEND EXPERIMENTS , 1989 .

[3]  J. E. Griffiths The effect of cracks on the limit load of pipe bends under in-plane bending: Experimental study , 1979 .

[4]  R. Seshadri,et al.  Limit Load Analysis of Pipe Bend Using the R-Node Method , 2005 .

[5]  Manfred Staat,et al.  Numerical methods for limit and shakedown analysis : deterministic and probabilistic problems , 2003 .

[6]  C. D. Bisbos,et al.  Second-Order Cone and Semidefinite Representations of Material Failure Criteria , 2007 .

[7]  H. Nguyen-Dang,et al.  A primal–dual algorithm for shakedown analysis of structures , 2004 .

[8]  Maher Y. A. Younan,et al.  Limit Loads for Pipe Elbows Subjected to In-Plane Opening Moments and Internal Pressure , 1999 .

[9]  C. Burgoyne,et al.  Exact ilyushin yield surface , 1993 .

[10]  D. Chapelle,et al.  The Finite Element Analysis of Shells - Fundamentals , 2003 .

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

[12]  K. Kussmaul,et al.  Pipe Bend Behaviour at Load Levels Beyond Design , 1995 .

[13]  C. R. Calladine,et al.  Limit analysis of curved tubes , 1974 .

[14]  H. Nguyen-Dang,et al.  Direct Finite Element Kinematical Approaches in Limit and Shakedown Analysis of Shells and Elbows , 2000 .

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

[16]  Manfred Staat,et al.  Probabilistic limit and shakedown analysis of thin plates and shells , 2009 .

[17]  Antonio Capsoni,et al.  A FINITE ELEMENT FORMULATION OF THE RIGID–PLASTIC LIMIT ANALYSIS PROBLEM , 1997 .

[18]  Jayanta Chattopadhyay,et al.  Closed-Form Collapse Moment Equations of Elbows Under Combined Internal Pressure and In-Plane Bending Moment , 2000 .

[19]  Jayanta Chattopadhyay,et al.  Limit Load of Elbows under Combined Internal Pressure and Bending Moment , 1999 .

[20]  Spyros A. Karamanos,et al.  Ultimate Bending Capacity and Buckling of Pressurized 90 deg Steel Elbows , 2006 .

[21]  Maher Y. A. Younan,et al.  Limit-Load Analysis of Pipe Bends Under Out-of-Plane Moment Loading and Internal Pressure , 2002 .

[22]  Manfred Staat,et al.  FEM-computation of load carrying capacity of highly loaded passive components by direct methods , 1999 .

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

[24]  Alan R.S. Ponter,et al.  A general approximate technique for the finite element shakedown and limit analysis of axisymmetrical shells. Part 1: Theory and fundamental relations , 1997 .

[25]  Alan R.S. Ponter,et al.  A general approximate technique for the finite element shakedown and limit analysis of axisymmetrical shells. Part 2: Numerical applications , 1997 .

[26]  Hany F. Abdalla,et al.  Determination of Shakedown Limit Load for a 90-Degree Pipe Bend Using a Simplified Technique , 2006 .

[27]  Maher Y. A. Younan,et al.  Limit Loads for Pipe Elbows With Internal Pressure Under In-Plane Closing Bending Moments , 1998 .

[28]  Syed Mizanur Rahman Finite Element Analysis and Related Numerical Schemes for Ratcheting Simulation , 2006 .