ALTERNATIVE ACTIVE NONLINEAR TOTAL LAGRANGIAN TRUSS FINITE ELEMENT APPLIED TO THE ANALYSIS OF CABLE NETS AND LONG SPAN SUSPENSION BRIDGE

Abstract

IN THIS STUDY AN ALTERNATIVE GEOMETRICALLY EXACT TOTAL LAGRANGIAN FINITE ELEMENT IS PRESENTED AND APPLIED TO SOLVE CABLE, CABLE NETS AND, WITH PARTICULAR INTEREST, A VERY LONG SUSPENDED BRIDGE IN BOTH THREE AND TWO-DIMENSIONAL SPACES FROM ITS SETTING-UP THROUGH ITS RESPONSE TO AN EARTHQUAKE EXCITATION. THE FORMULATION INCLUDES: DYNAMICS, PSEUDO-DYNAMICS REGULARIZATION, ELASTIC ACTUATORS AND AUTOMATIC STRESS CALIBRATION. THE DYNAMIC FORMULATION AND PSEUDO-DYNAMIC REGULARIZATION ARE USED FOR TWO MAIN PURPOSES: TO PERFORM TRANSIENT STRUCTURAL ANALYSIS AND TO ALLOW THE SETTING-UP OF VERY UNSTABLE STRUCTURES. THE ELASTIC ACTUATORS (ACTIVE ELEMENTS) ALLOW USING PRE-STRESSING STRUCTURAL MEMBERS AS PART OF THE ITERATIVE STRUCTURAL DESIGN AND THE IMPOSITION OF INITIAL NATURAL LENGTH OF CABLES. THE STRATEGY OF AUTOMATIC STRESS CALIBRATION MAKES POSSIBLE TO MODEL CONTINUOUS CABLES IN COMPLICATED STRUCTURES WITHOUT MODELING CUMBERSOME SLIDING CONTACT DEVICES. WITH PARTICULAR INTEREST, IN THIS STUDY, IT IS APPLIED TO MODEL MAIN CABLES OF SUSPENDED BRIDGES PASSING THROUGH SADDLE POINTS.

THE PROPOSED FORMULATION IS BASED ON THE MECHANICAL ENERGY STATIONARY PRINCIPLE FOR GEOMETRICALLY NON LINEAR STRUCTURES IN WHICH THE INERTIAL TERMS ARE INTRODUCED FOLLOWING AN ALTERNATIVE MATHEMATICAL WAY. TWO SIMPLE EXAMPLES ARE USED TO VALIDATE ALL ASPECTS OF THE PROPOSED FORMULATION. FINALLY, A REPRESENTATIVE APPLICATION IS PERFORMED, I.E., THE NUMERICAL DESIGN AND ANALYSIS OF A VERY LONG SPAN SUSPENSION BRIDGE BY THE PROPOSED STRATEGY.