Least weight design of truss structures with buckling constraints

Design of least weight truss structures is formulated as the combinations of the nonlinear truss optimization problems. The aim of this work is to obtain the optimum solution of the nonlinear truss optimization problem for a given truss member combination. Then the real optimum of the truss structure can be obtained by searching the least weight amongst the optimum solutions of all the valid combinations.For a given truss member combination, the nonlinear truss optimization problem is linearized at a feasible point. By this way the member stresses and the nodal displacements can be expressed linearly in terms of member cross-sectional areas. As a result of this the linearized truss optimization problem can be expressed as an original linear optimization problem in member cross-sectional area space. Within the predetermined move limits the optimum of the above linearized truss optimization problem is calculated. This completes one of the iterations of the sequential linear programming. The above iterations are repeated until the difference between the calculated consecutive optimum solutions vanishes.The expression of member buckling stresses and member slenderness ratios, are originally formulated in terms of member cross-sectional areas, which are then linearized and included among the constraints of the above sequential linear programming problem. By means of these buckling constraints the true optimum solutions of the truss structures are obtained. In this work several example problems are solved by using the developed computer program and the results are compared with the results found in the literature. When buckling constraints are active then, as opposed to approximate solutions found in literature, the optimum solutions found in this work are the true solutions. For other cases similar optimum solutions are found as in literature.