A FULLY NONLINEAR MULTI-PARAMETER ROD MODEL INCORPORATING GENERAL CROSS-SECTIONAL IN-PLANE CHANGES AND OUT-OF-PLANE WARPING
Keywords:DAMAGE MECHANICS, CONSTITUTIVE MODEL, ANISOTROPY, BIMODULAR MATERIALS
AbstractTHIS 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 DEÂ¯NITION OF ENERGETICALLY CONJUGATED CROSS-SECTIONAL RESULTANTS IN TERMS OF GENERALIZED STRESSES AND STRAINS, BASED ON THE CONCEPT OF A CROSS-SECTION IRECTOR, SIMPLIÂ¯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 DEÂ¯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 Â¯NITE STRAIN CONSTITUTIVE EQUATIONS CAN THEREFORE BE EMPLOYED WITH NO SPURIOUS STIÂ®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 PROÂ¯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.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY] that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).