An efficient method of analysis for thin-walled beams made with nonlinear elastic materials

Over a period of several decades, engineers have attempted to develop optimum beam shapes in order to use available material in an efficient mariner. It has been determined that the most efficient type, based on weight and strength criteria, is the Thin-Walled Beam (TWB) in which one or more thin plates are combined to form the beam section. These structural elements are used in several engineering disciplines including aeronautical, automotive and structural engineering.; In recent years, engineers have begun to use many materials that are lighter than steel for TWB framing. These materials include some aluminum alloys, reinforced or unfilled polymers, and other types of composites. Many of these new materials display nonlinear behavior thus making the design process more difficult.; In this dissertation, the author has developed an efficient method for analyzing prismatic TWBs with any section configuration made with nonlinear materials. The proposed method treats nonlinear TWBs as a collection of linear short TWB elements that are joined together along the longitudinal axis of the beam. The solution of such single elements is well known. The analysis of an entire beam is obtained by means of an iterative procedure. It is assumed that elements are made with a linear material. The nonlinear behavior is modeled by reducing or increasing various thicknesses of the walls in each element in order to adjust the stiffness. This thickness is determined by considering the resulting stress level and the stress-strain response of the material. In order to verify the accuracy of the proposed method; an experimental program consisting of four tests was performed. In these experiments the material properties were obtained from coupon tests. The test beams were made with steel and the material nonlinear response was obtained by exceeding the material's yield stress. Each test beam was analyzed using two techniques: (1) the proposed method and (2) a standard Finite Element computer program. A comparison of the results of the two techniques has shown close agreement. Analyzing a TWB with the proposed method utilized significantly fewer operations than the Finite Element Method. It was demonstrated that analyzing a beam modeled with one hundred elements requires one hundred times less floating-point operations than the standard Finite Element Method.