APPLICATION OF THE COMPLEX VARIABLE SEMI-ANALYTICAL METHOD FOR IMPROVED DISPLACEMENT SENSITIVITY EVALUATION IN GEOMETRICALLY NONLINEAR TRUSS PROBLEMS

Abstract

THE APPLICATION OF GRADIENT-BASED METHODS TO STRUCTURAL OPTIMIZATION PROBLEMS USUALLY REQUIRES THE DETERMINATION OF DISPLACEMENT SENSITIVITIES WITH RESPECT TO DESIGN VARIABLES. IN THIS REGARD, IT IS IMPORTANT TO HAVE AT HAND COMPREHENSIVE METHODS FOR SENSITIVITY ANALYSIS, WHICH SHOW STABILITY, EFFICIENCY AND ACCURACY. PARTICULARLY, APPLICATION OF THE SEMI-ANALYTICAL METHOD FOR LINEAR AND NONLINEAR PROBLEMS IS GENERALLY A GOOD TRADE-OFF BETWEEN FORMULATION SIMPLICITY AND ACCURACY. IN SPITE OF THAT, SEMI-ANALYTICAL METHODS ARE KNOWN TO BEHAVE PATHOLOGICALLY FOR SHAPE DESIGN VARIABLES WHEN THE STRUCTURE IS SUBJECTED TO RIGID ROTATIONS. A LARGE NUMBER OF SOLUTIONS FOR THIS PROBLEM HAVE BEEN PRESENTED IN LAST YEARS, ALTHOUGH THE FORMULATION INVOLVED IS GENERALLY NOT TRIVIAL, ESPECIALLY IN THE NONLINEAR CASE. A RECENT METHOD, WHICH ADOPTS THE SEMI-ANALYTICAL APPROACH AND USES COMPLEX VARIABLES HAS RENDERED VERY PROMISING RESULTS FOR ALL THE AFOREMENTIONED ASPECTS: STABILITY, EFFICIENCY AND ACCURACY. ADDITIONALLY, IT IS SIMPLE TO CODIFY. THE PRESENT CONTRIBUTION IS CONCERNED WITH THE APPLICATION OF THIS SENSITIVITY ANALYSIS METHOD TO GEOMETRICALLY NONLINEAR TRUSS PROBLEMS. TO THIS END, A FINITE ELEMENT FORMULATION IS PRESENTED AND DISPLACEMENT SENSITIVITIES ARE EVALUATED WITH RESPECT TO MATERIAL AND SHAPE DESIGN VARIABLES. THE RESULTS ARE COMPARED TO THOSE OBTAINED USING THE SEMI-ANALYTICAL METHOD WITH REAL VARIABLES AND TO GLOBAL FINITE DIFFERENCES. AN EXAMPLE DEMONSTRATES THE POTENTIALITY OF THIS NEW APPROACH.