A CONJUGATE MODAL FORCE STRATEGY FOR INSTABILITY ANALYSIS OF THIN-WALLED STRUCTURES: AN UNCONSTRAINED VECTOR POSITIONAL FINITE ELEMENT APPROACH

Abstract

THE IMPORTANCE OF KNOWING CRITICAL LOADS AND POST-CRITICAL BEHAVIOR OF THIN-WALLED STRUCTURES MOTIVATES THE DEVELOPMENT OF SEVERAL SCIENTIFIC AND PRACTICAL STUDIES. MOST REFERENCES ARE CONCERNED WITH STABILITY ANALYSIS FOR SMALL DISPLACEMENTS (FIRST ORDER APPROACH), OR IN SECOND ORDER STABILITY ANALYZES, A LESS PRECISE GEOMETRIC NONLINEAR STRATEGY. HOWEVER, THERE ARE STRUCTURES THAT ARE INITIALLY VERY FLEXIBLE OR THAT PRESENT SMALL LOSS OF STIFFNESS AFTER THE FIRST CRITICAL LOAD IS REACHED. HERE WE DEVELOP A SHELL NUMERICAL FORMULATION CAPABLE OF CARRYING OUT STABILITY ANALYSIS OF THIN-WALLED STRUCTURES DEVELOPING LARGE DISPLACEMENTS. THIS FORMULATION USES GENERALIZED VECTORS AS NODAL PARAMETERS INSTEAD OF ROTATIONS. TO MAKE POSSIBLE A COMPLETE STABILITY ANALYSIS USING UNCONSTRAINED VECTORS, WE PRESENT AN ORIGINAL STRATEGY THAT IMPOSES A CONJUGATE MODAL FORCE AT THE VICINITY OF STRUCTURAL CRITICAL POINTS, ALLOWING AN ACCURATE CHOICE OF POST-CRITICAL PATHS. NON-CONSERVATIVE FORCES ARE ALSO CONSIDERED AND RESULTS ARE COMPARED TO LITERATURE BENCHMARKS DEMONSTRATING THE ACCURACY AND CAPACITY OF THE PROPOSED FORMULATION.