A FULLY NONLINEAR MULTI-PARAMETER ROD MODEL INCORPORATING GENERAL CROSS-SECTIONAL IN-PLANE CHANGES AND OUT-OF-PLANE WARPING

Authors

  • S.P.B. P. M. PIMENTA
  • E. M. B. CAMPELLO

Keywords:

DAMAGE MECHANICS, CONSTITUTIVE MODEL, ANISOTROPY, BIMODULAR MATERIALS

Abstract

THIS WORK PRESENTS A FULLY NONLINEAR GEOMETRICALLY-EXACT MULTI-PARAMETER ROD MODEL THAT INCORPORATES GENERAL IN-PLANE CROSS-SECTIONAL CHANGES AS WELL AS GENERAL OUT-OF-PLANE CROSSSECTIONAL WARPING. THE FORMULATION CONSTITUTES AN EXTENSION OF THE EARLIER WORKS, IN THE SENSE THAT THE RESTRICTIONS TO A RIGID CROSS-SECTION AND TO A SAINT-VENANT-LIKE ELASTIC WARPING ARE NOW REMOVED FROM THE THEORY. THE DE¯NITION OF ENERGETICALLY CONJUGATED CROSS-SECTIONAL RESULTANTS IN TERMS OF GENERALIZED STRESSES AND STRAINS, BASED ON THE CONCEPT OF A CROSS-SECTION IRECTOR, SIMPLI¯ES THE DERIVATION OF EQUILIBRIUM EQUATIONS AND THE ENFORCEMENT OF BOUNDARY CONDITIONS, IN EITHER WEAK OR STRONG SENSES. IN ADDITION, THE CORRESPONDING TANGENT BILINEAR WEAK FORM IS OBTAINED IN A MORE EXPEDIENT WAY, RENDERING ALWAYS SYMMETRIC FOR HYPER-ELASTIC MATERIALS AND CONSERVATIVE LOADINGS. THE DE¯NITION OF A CROSS-SECTION DIRECTOR ALLOWS ALSO THE INTRODUCTION OF INDEPENDENT DEGREES-OF-FREEDOM TO DESCRIBE BOTH THE IN-PLANE CROSS-SECTIONAL CHANGES AND THE OUT-OF-PLANE WARPING. FULLY THREE-DIMENSIONAL ¯NITE STRAIN CONSTITUTIVE EQUATIONS CAN THEREFORE BE EMPLOYED WITH NO SPURIOUS STI®ENING. FINITE ROTATIONS ARE TREATED CONSISTENTLY BY THE EULER-RODRIGUES FORMULA IN A PURE LAGRANGEAN FRAMEWORK. ALTOGETHER, THE PRESENT ASSUMPTIONS ALLOW A CONSISTENT BASIS FOR THE PROPER REPRESENTATION OF PRO¯LE (DISTORTIONAL) DEFORMATIONS, WHICH ARE TYPICAL OF COLD-FORMED THIN-WALLED ROD STRUCTURES. THIS IS ONE OF THE MAIN FEATURES OF THE FORMULATION, AS THE USE OF MORE COMPLEX SHELL MODELS IN ORDER TO CAPTURE SUCH PHENOMENA CAN BE NEEDLESS.

Published

2003-11-01

Issue

Section

Articles