Analysis and design of trussed structures made of elastic/stiffening materials

Abstract

An extremum problem formulation for the equilibrium analysis of general structures made of stiffening material is applied to the analysis of trussed structures. The nonlinear material is modelled in a way to simulate an arbitrary, polygonal stress-strain relation; material properties may vary over the truss. The form of this convex nonlinear programming problem statement is convenient for the prediction of the evolution (over the truss system) of local member stiffening under increasing proportional load. Computational solutions are obtained directly on the basis of the extremum problem statement, using commercial minimizer software. The formulation for analysis is extended to model a design problem for the prediction of the optimal modification of certain material properties, namely the bounds that reflect the onset of stiffening in the material. Computational results for this optimal material design problem are also provided.