INTEGRATED STRUCTURAL-ANALYSIS AND DESIGN USING 3-DIMENSIONAL FINITE-ELEMENTS

A design approach that combines iterative structural analysis with a traditional iterative optimization algorithm is applied to the optimum design of the shape of a hole in a plate in tension. The plate is modeled by three-dimensional finite elements, and an element-by-element preconditioned conjugate gradient iterative algorithm is used for solving the equations of equilibrium. Several parameterizations of the optimum shape are considered, and it is shown that a sine series can describe the optimum shape with only three design variables, whereas other series require seven variables for similar results. The optimum shape compares well with an experimental optimum obtained by A. J. Durelli. An investigation is performed to determine the best way of obtaining finite-difference derivatives of the stresses with respect to design variables. It is shown that a method based on modifying the equations of equilibrium for the perturbed problem performs best. The benefit of the integrated approach is determined by comparing convergence with different initial iterates for the displacement field. It is shown that using the final iterate of the previous solution can reduce the number of analysis iterations by about 40% compared to starting with a zero initial iterate.