Minimum Weight Design of Fillet Welds Using Convex Formulation

This paper presents a discrete formulation of the nonlinear minimum weight design of welded connections, in which global throat stresses along every fillet are approximated by piecewise linear shape functions. With this formulation it is possible to find the set of throat thicknesses of a welded connection that gives the minimum amount of weld metal necessary to support an arbitrary set of external actions and a stress field in equilibrium with these actions and satisfying a strength criterion. The formulation adopted involves a linear form of objective function and equilibrium equations, which, together with the convex character of the nonlinear constraints, gives a full convex set of constraints and consequently a global optimum of the objective function. Moreover, the structure of the set of constraints makes it possible to demonstrate that stress and throat thickness values are unique at the optimum, which allows the optimum stress distributions to be simplified, to establish practical design recommendations. Realistic conditions can be imposed on the stress field. The problem is solved with a very accessible and well-known scientific library, which allows this method to be implemented by anyone involved in welding practice. The method proposed is developed for the case of a planar connection. Two practical applications using the strength criterion of Eurocode 3 are included, discussing the results obtained for two types of common arrangements and showing that numerical results are consistent and CPU times reasonably low.