A NONLINEAR ANALYSIS OF STATISTICALLY LOADED PLANE FRAMES USING A DISCRETE ELEMENT MODEL

A DISCRETE ELEMENT ANALYSIS WHICH CONSIDERS GEOMETRIC, MATERIAL, AND SUPPORT NONLINEARITIES OF STATICALLY LOADED PLANE FRAMES IS DEVELOPED. A COMPUTER PROGRAM HAS BEEN WRITTEN TO IMPLEMENT AND VERIFY THE ANALYSIS. FRAME GEOMETRY, LOADS, CROSS SECTIONS, AND SUPPORTS (NONLINEAR CONCENTRATED AND DISTRIBUTED SPRINGS) CAN BE SUFFICIENTLY GENERAL TO WORK PRACTICAL FRAME PROBLEMS. THE METHOD OF ANALYSIS IS BASED ON AN ITERATIVE PROCEDURE CALLED THE TANGENT STIFFNESS METHOD. UNBALANCED NODAL POINT FORCES ARE APPLIED TO A TEMPORARILY LINEAR STRUCTURE WHOSE POSITION DEPENDENT STIFFNESS MATRIX IS THE TANGENT STIFFNESS MATRIX OF THE STRUCTURE. THE FRAME MEMBERS ARE DIVIDED INTO A NUMBER OF DISCRETE ELEMENTS. LOAD-DISPLACEMENT EQUATIONS FOR AN INDIVIDUAL DISCRETE ELEMENT ARE DERIVED WHICH ARE VALID FOR LARGE DISPLACEMENTS. A NUMERICAL TECHNIQUE IS USED TO DETERMINE THE FORCE-DEFORMATION RESPONSE OF A CROSS SECTION WITH NONLINEAR STRESS-STRAIN CURVES. LOADS AND NONLINEAR SUPPORTS ARE INPUT IN NORMAL ENGINEERING TERMS AND CAN BE REFERENCED EITHER TO THE STRUCTURE OR TO THE MEMBER AXES. WHEN NECESSARY, THE LOADS AND NONLINEAR SUPPORTS ARE INTERNALLY TRANSFORMED TO MEMBER COORDINTES AND DISCRETIZED TO CONCENTRATED VALUES AT THE NODAL POINTS. CASTIGLIANO'S FIRST THEOREM IS APPLIED TO DEVELOP MATRIX EXPRESSIONS FOR THE STIFFNESS MATRIX OF A GENERAL DISCRETE ELEMENT AND THESE EXPRESSIONS ARE USED TO OBTAIN THE STIFFNESS MATRIX FOR THE SPECIFIC DISCRETE ELEMENT USED IN THE FRAME SOLUTIONS. A NUMBER OF PROBLEMS ARE WORKED AND COMPARED WITH EXISTING ANALYTICAL OR EXPERIMENTAL SOLUTIONS.