Gradient Methods in Optimum Structural Design

The paper presents two new gradient-based methods for the optimum design of skeletal structures. Both methods can accommodate stress, member size, and displacement constraints and can converge to an optimum that is either a vertex or a nonvertex of the feasible region. The Method of Incomplete Gradients uses the dominant terms of the active constraint gradients and converges rapidly for normal acting structures. The Method of Auxiliary Gradients augments active constraints with auxiliary constraints when necessary, uses the full gradients, and converges rapidily for structures with normal or hybrid action. The two methods, together with the Stress Ratio Method, are arranged into an efficient automatic design technique that can start at any initial design. The technique is applied to the design of two rigid frames having displacement constraints and multiple loadings.