Minimum Weight Design of Beams With Inequality Constraints on Stress and Deflection

Abstract

A nonlinear optimal design problem, with state variable inequality constraints, is solved. The problem is reduced to a Lagrange problem in the Calculus of Variations and necessary conditions are presented. For a certain class of problems, the necessary conditions are reduced to a system of nonlinear algebraic equations which are solved by an iterative procedure. The computational algorithm is efficient and is easily programmed for use on a digital computer.

A Structural Optimization Framework for Multidisciplinary Design

“…Three problems are studied regarding the sizing design of a cantilever beam with different loading conditions. Two problems have analytic solutions and serve as validation of the optimization framework [19,20]. Then, a topology design problem is demonstrated.…”

“…The analytic minimum beam volume reported in [20] is specified for a maximum tip displacement of 0.5 in. (0.0127 m), maximum stress of 30,000 psi (207 MPa), and lower and upper limit on the design variables of 0.3 and 0.5 in., respectively.…”

Practical Optimization of Steel Highway Bridge Beams : Technical Paper

“…The cost of any weld can be determined from Equation 9: weld =^1^^2 (^^^S^^^ (9) In Equation 9, C is the fixed cost of the given weld, C (V) is a variable cost based on the volume of the weld material and C^(L) is a variable cost based on the length of the weld. The equation for the cost of a fillet weld iŝ fillet =^1 " 1/2 t/ L^c^-L^C3 (10) and the equation for the cost of a butt weld is…”

“…The optimization of girders has been extensively approached in the past by using minimum weight as the measure of effectiveness (8,9,11,12). The procedure has been to minimize the cross-sectional area of the girder.…”

On the Masur Paradox∗

“…Extending a pioneering paper by Haug and Kirrnser [3], the general formulation (see Appendix) is based on both stress and displacement constraints, as well as a minimum cross section constraint.…”