COMPLIANCE MINIMIZATION OF STRUCTURES UNDER UNCERTAIN LOADINGS

Abstract

THIS PAPER INVESTIGATES COMPLIANCE OPTIMIZATION OF STRUCTURES UNDER MULTIPLE LOAD CASES. THE PROBLEM CAN BE SOLVED THROUGH A MULTI-CRITERION OPTIMIZATION WHERE THE LOAD CASES ASSOCIATED WITH EACH AND EVERY LOADING CON¯GURATION ARE TREATED AS COMPONENTS OF A MULTIOBJECTIVE FUNCTION VECTOR. ALTERNATIVELY, THE MULTI-OBJECTIVE OPTIMIZATION PROBLEM CAN BE RE-FORMULATED USING A MINIMAX STRATEGY THAT DOES NOT REQUIRE SIMULTANEOUS CONSIDERATION OF ALL THE LOAD CASES AS COMPONENTS OF A MULTI-OBJECTIVE FUNCTION VECTOR. INSTEAD, IT IS SHOWN THAT, FOR COMPLIANCE OPTIMIZATION PURPOSES, IT IS SUFICIENT TO CONSIDER ONLY THOSE LOADS WHICH DE¯NE THE CONVEX HULL OF THE APPLICABLE LOAD SET, THEREBY DRASTICALLY REDUCING THE NUMBER OF LOAD CASES INVOLVED IN THE DESIGN PROCEDURE. THE E±CIENCY OF THE TECHNIQUE PROPOSED IS ILLUSTRATED THROUGH TWO EXAMPLES CONSISTING OF VARIABLE THICKNESS BEAMS AND PLATES SUBJECTED TO UNCERTAIN LOADINGS.