DEVELOPMENT OF SLIDING CONNECTIONS FOR STRUCTURAL ANALYSIS BY A TOTAL LAGRANGIAN FEM FORMULATION

Abstract

IN THIS STUDY A TOTAL LAGRANGIAN 2D FINITE ELEMENT FORMULATION IS USED TO MODEL PLANE FRAMES DEVELOPING LARGE DISPLACEMENTS AND ROTATIONS CONSIDERING SLIDING CONNECTIONS. THIS KIND OF CONNECTIONS IS USUALLY CALLED PRISMATIC AND CYLINDRICAL JOINTS. IN ORDER TO BE SELF-CONTAINING, THE STEPS OF THE DEVELOPMENT OF A FRAME FINITE ELEMENT OF ANY APPROXIMATION ORDER THAT CONSIDERS THE INFLUENCE OF SHEAR STRAIN BY MEANS OF A GENERALIZED REISSNER KINEMATICS IS PRESENTED. THE ADOPTED DEGREES OF FREEDOM ARE POSITIONS AND ROTATIONS. USING POSITIONS AS DEGREES OF FREEDOM SIMPLIFIES THE TOTAL LAGRANGIAN DESCRIPTION AND ENABLES A COMPREHENSIVE PRESENTATION OF THE PROPOSED CONNECTIONS. REVOLUTE CONNECTIONS ARE CONSIDERED BY DIRECT DEGREES OF FREEDOM MATCHING. PRISMATIC CONNECTIONS ARE MODELLED BY THE LAGRANGE MULTIPLIER TECHNIQUE THAT CONSTRAINS POSITIONS AND ROTATION OF A SLIDING NODE TO THE VARYING POSITION AND ROTATION OF A PATH ELEMENT. CYLINDRICAL JOINTS ARE INTRODUCED IN SIMILAR WAY BY LAGRANGE MULTIPLIERS RELEASING THE SLIDING NODE ROTATION. THE PRINCIPLE OF STATIONARY POTENTIAL ENERGY IS USED TO WRITE THE NON-LINEAR EQUILIBRIUM EQUATION INCLUDING THE LAGRANGE MULTIPLIER INFLUENCE. TO SOLVE THE NON-LINEAR EQUATION A TAYLOR EXPANSION IS CARRIED OUT AND THE NEWTON-RAPHSON PROCEDURE IS EMPLOYED. THE FRAME ELEMENT IS CONSIDERED ELASTIC, FOLLOWING THE SAINT-VENANT-KIRCHHOFF CONSTITUTIVE MODEL. SELECTED EXAMPLES ARE USED TO VALIDATE THE FORMULATION AND TO SHOW ITS POSSIBILITIES OF APPLICATION.