Optimal design of frame structures using multivariate spline approximation
The objective of this work is to demonstrate the efficiency and applicability of the optimization algorithm using a multivariate spline approximation. In the present algorithm, based on the function values and first-order derivatives of the constraints available at the intermediate points of optimization, an explicit approximation of constraint functions is created by using the least squares spline algorithm. The nonlinearity of the function is adaptively updated using feedback information from the previous two iterations for finding the order of spline approximation. In addition, constraint deletion and design variable linking concepts are employed in solving the approximate problem by using the quasianalytical sequential quadratic programming and dual methods. The behavior constraints include stresses, displacements, and local buckling in the optimum design of frame structures. To demonstrate the broad applicability of the optimization algorithm, the cross-sectional dimensions are directly selected as the design variables for frame problems having thin-walled rectangular and tube cross-sectional members, and the cross-sectional areas are selected as design variables for an /-section problem.