NUMERICAL ANALYSIS OF HIGHLY DEFORMABLE ELASTOPLASTIC BEAMS

Authors

  • JOÃO PAULO PASCON MATERIALS ENGINEERING DEPARTMENT LORENA SCHOOL OF ENGINEERING UNIVERSITY OF SãO PAULO

Keywords:

FINITE BENDING DEFORMATIONS, THIN BEAMS, ELASTOPLASTIC MATERIAL, POST-BUCKLING BEHAVIOR, FOURTH-ORDER RUNGE-KUTTA INTEGRATION, NONLINEAR SHOOTING METHOD.

Abstract

THE OBJECTIVE OF THE PRESENT STUDY IS TO DEVELOP A NUMERICAL FORMU-LATION TO PREDICT THE BEHAVIOR OF HIGHLY DEFORMABLE ELASTOPLASTIC THIN BEAMS. FOLLOWING THE EULER-BERNOULLI BENDING, THE AXIAL AND SHEAR EFFECTS ARE NEGLECTED, AND THE NONLINEAR SECOND-ORDER DIFFERENTIAL EQUATION REGARDING THE ANGLE OF ROTATION IS DEFINED BASED ON THE SPECIFIC MOMENT-CURVATURE RELATIONSHIP. ALTHOUGH THE FORMULATION CAN BE USED FOR GENERAL MATERIALS, THREE CONSTITUTIVE MODELS ARE EMPLOYED: LINEAR-ELASTIC, BILINEAR ELASTOPLASTIC, AND LINEAR-ELASTIC WITH SWIFT ISOTROPIC HARDENING. THE RESULTANT BOUNDARY VALUE PROB-LEM IS SOLVED BY MEANS OF THE FOURTH-ORDER RUNGE-KUTTA INTEGRATION PROCEDURE AND THE ONE-PARAMETER NONLINEAR SHOOTING METHOD. THE PERFORMANCE OF THE PRESENT FORMULATION IS INVESTIGATED VIA THREE NUMERICAL PROBLEMS INVOLVING FINITE BENDING OF SLENDER BEAMS COM-POSED OF ELASTOPLASTIC MATERIALS. FOR THESE PROBLEMS, NUMERICAL SOLUTIONS REGARDING ROTATIONS, DISPLACEMENTS AND STRAINS FOR THE LOADING, UNLOADING AND RELOADING PHASES ARE PROVIDED. FINALLY, IT IS SHOWN THAT THE PRESENT METHODOLOGY CAN ALSO BE USED TO DETERMINE THE POST-BUCKLING BEHAVIOR OF ELASTOPLASTIC THIN BEAMS.

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Published

2015-05-02

Issue

Vol. 12 No. 8 (2015)

Section

Articles

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