Lewis P. Felton

Optimum design of structures with random parameters

Abstract A general formulation of the minimum-weight optimization problem for indeterminate structures with random parameters is presented. The formulation enables the designer to specify maximum allowable probability of system failure and maximum allowable probabilities of occurrence of individual failure modes. All random parameters are characterized by their mean values and coefficients of variation, with the latter assumed to be amenable to realistic estimation at the outset. The standard deviations of response quantities are then obtained in a straightforward manner for use in the constraint equations, which generally resemble those for deterministic optimization problems. Several examples of truss and frame designs illustrate applications of the formulation.

Optimized Components in Frame Synthesis

The incorporation of optimized thin-walled beam elements into procedures for the minimum-weight design of indeterminate elastic planar frame structures is examined. It is shown that all frame structures composed of beam elements with thin-walled cross sections will be fully stressed in the sense that each element should be proportioned to be on the verge of local instability under at least one independent load condition. This fact leads to a formulation of the design requirements as an inequality-constrained minimization problem with the only variables being moments of inertia of the elements. Solutions are examined numerically by use of a nonlinear programing technique. The formulation also suggests a simple and efficient direct iterative procedure for obtaining designs which are fully-stressed with respect to both local buckling and yielding. For the examples considered, both procedures are shown to produce identical results. Nomenclature A = cross-sectional area D = depth of beam cross section E = Youngs rnodulus / = moment of inertia K = buckling coefficient M = bending moment 9fTl = maximum absolute value of M in element W = weight Z = section modulus kAjki = constants I — length t = thickness p = specific weight ay = yield stress a = Wl/Z

Stability analysis by matrix decomposition

Abstract A method is presented for the stability analysis of structures using a combination of matrix iteration and matrix decomposition. The method is extented to stability analysis of structures in which two critical loads are present whose absolute values are relatively close or identical.