A simplified technique for shakedown limit load determination of a large square plate with a small central hole under cyclic biaxial loading

Abstract A simplified technique for determining the shakedown limit load of a structure was previously developed and successfully applied to benchmark shakedown problems involving uniaxial states of stress ( Abdalla et al., 2007a , Abdalla et al., 2007b , Abdalla et al., 2007c ). In this paper, the simplified technique is further developed to handle cyclic biaxial loading resulting in multi-axial states of stress within the large square plate with a small central hole problem. Two material models are adopted namely: an elastic-linear strain hardening material model obeying Ziegler's linear kinematic hardening (KH) rule and an elastic-perfectly-plastic (EPP) material model. The simplified technique utilizes the finite element (FE) method and employs small displacement formulation to determine the shakedown limit load without performing lengthy time consuming full elastic–plastic cyclic loading FE simulations or conventional iterative elastic techniques. The simplified technique is utilized to generate the shakedown domain for the plate problem subjected to cyclic biaxial tension along its edges. The outcomes of the simplified technique showed very good correlation with the results of analytical solutions as well as full elastic–plastic cyclic loading FE simulations. Material hardening showed no effect on the shakedown domain of the plate in comparison to employing EPP-material.

[1]  Ted Belytschko.  Plane stress shakedown analysis by finite elements , 1972 .

[2]  Genbao Zhang,et al.  Shakedown with nonlinear strain-hardening including structural computation using finite element method , 1992 .

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

[4]  Hany F. Abdalla,et al.  Comparison of Pipe Bend Ratchetting/Shakedown Test Results With the Shakedown Boundary Determined via a Simplified Technique , 2009 .

[5]  Bingjun Gao,et al.  Ratcheting Study of Pressurized Elbows Subjected to Reversed In-Plane Bending , 2006 .

[6]  Mohammad M. Megahed,et al.  Applications of Iterative Elastic Techniques for Elastic-Plastic Analysis of Pressure Vessels , 1999 .

[7]  J. Bree.  Elastic-plastic behaviour of thin tubes subjected to internal pressure and intermittent high-heat fluxes with application to fast-nuclear-reactor fuel elements , 1967 .

[8]  Leone Corradi,et al.  A linear programming approach to shakedown analysis of structures , 1974 .

[9]  E. Stein,et al.  An analytical method for shakedown problems with linear kinematic hardening materials , 1994 .

[10]  Robert Hamilton,et al.  Evaluating shakedown under proportional loading by non-linear static analysis , 2003 .

[11]  Mohammad M. Megahed,et al.  Influence of hardening rule on the elasto-plastic behaviour of a simple structure under cyclic loading , 1981 .

[12]  R. Seshadri.  The Generalized Local Stress Strain (GLOSS) Analysis—Theory and Applications , 1991 .

[13]  F. A. Leckie,et al.  Shakedown loads for radial nozzles in spherical pressure vessels , 1967 .

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

[15]  C. Polizzotto.  Shakedown theorems for elastic–plastic solids in the framework of gradient plasticity , 2008 .

[16]  Hany F. Abdalla,et al.  Shakedown Limit Loads for 90-Degree Scheduled Pipe Bends Subjected to Constant Internal Pressure and Cyclic Bending Moments , 2008 .

[17]  Hany F. Abdalla,et al.  Shakedown Limits of a 90-Degree Pipe Bend Using Small and Large Displacement Formulations , 2007 .

[18]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[19]  Chi-Yong Park,et al.  Shakedown limit loads for elbows under internal pressure and cyclic in-plane bending , 2008 .

[20]  W. Drugan,et al.  Theory of plasticity , 1987 .

[21]  Martin Muscat,et al.  Elastic-Shakedown Analysis of Axisymmetric Nozzles , 2003 .

[22]  M. Abdel-Karim,et al.  SHAKEDOWN ANALYSIS OF AN INFINITE PLATE WITH A CENTRAL HOLE UNDER BIAXIAL TENSION , 2000 .

[23]  Hany F. Abdalla,et al.  A simplified technique for shakedown limit load determination , 2007 .

[24]  Hany F. Abdalla,et al.  Shakedown Limit Load Determination for a Kinematically Hardening 90-Degree Pipe Bend Subjected to Constant Internal Pressure and Cyclic Bending , 2007 .