TWO DIMENSIONAL ANALYSIS OF INFLATABLE STRUCTURES BY THE POSITIONAL FEM

Abstract

THIS PAPER PRESENTS A ROBUST TWO DIMENSIONAL FRAME FORMULATION TO DEAL WITH STRUCTURES UNDERGOING LARGE MOTIONS DUE TO DYNAMIC ACTIONS INCLUDING VERY THIN INFLATABLE STRUCTURES, BALLOONS. THE PROPOSED METHODOLOGY IS BASED ON THE MINIMUM POTENTIAL ENERGY THEOREM WRITTEN REGARDING NODAL POSITIONS. VELOCITY, ACCELERATION AND STRAIN ARE ACHIEVED DIRECTLY FROM POSITIONS, NOT DISPLACEMENTS, CHARACTERIZING THE NOVELTY OF THE PROPOSED TECHNIQUE. A NON-DIMENSIONAL SPACE IS CREATED AND THE CHANGE OF CONFIGURATION FUNCTION IS WRITTEN FOLLOWING TWO INDEPENDENT MAPPINGS FROM WHICH THE STRAIN ENERGY FUNCTION IS WRITTEN. THE CLASSICAL NEWMARK EQUATIONS ARE USED TO INTEGRATE TIME. DUMPING AND NON-CONSERVATIVE FORCES ARE INTRODUCED INTO THE MECHANICAL SYSTEM BY A RHEONOMIC ENERGY FUNCTIONAL. THE FINAL FORMULATION HAS THE ADVANTAGE OF BEING SIMPLE AND EASY TO TEACH, WHEN COMPARED TO CLASSICAL COUNTERPARTS. THE BEHAVIOR OF A BENCH-MARK PROBLEM (SPIN-UP MANEUVER) IS SOLVED TO PROVE THE FORMULATION REGARDING HIGH CIRCUMFERENTIAL SPEED APPLICATIONS. OTHER EXAMPLES ARE DEDICATED TO INFLATABLE AND VERY THIN STRUCTURES, IN ORDER TO TEST THE FORMULATION FOR FURTHER ANALYSIS OF THREE DIMENSIONAL BALLOONS.