Advanced design optimization of cold-formed steel portal frame buildings

The design optimization of cold-formed steel portal frame buildings is considered in this paper. The objective function is based on the cost of the members for the main frame and secondary members (i.e., purlins, girts, and cladding for walls and roofs) per unit area on the plan of the building. A real-coded niching genetic algorithm is used to minimize the cost of the frame and secondary members that are designed on the basis of ultimate limit state. It iis shown that the proposed algorithm shows effective and robust capacity in generating the optimal solution, owing to the population's diversity being maintained by applying the niching method. In the optimal design, the cost of purlins and side rails are shown to account for 25% of the total cost; the main frame members account for 27% of the total cost, claddings for the walls and roofs accounted for 27% of the total cost.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.