An optimization method for the minimum-weight design of statically indeterminate trusses subject to stress and displacement constraints - Elicano, Raymond Cebrero
A method for determining the optimum design of a truss subject to constraints and under multiple static load conditions is investigated. At the optimum design of the structure, the object to be minimized is the weight of the structure. There are primary and secondary constraints considered: the primary constraints are upper limits on node displacements and member stresses; the secondary constraints are minimum and maximum limits on member sizes, end equal-size constraints (i.e., the requirement that areas of certain members be the same). The method uses the optimally criteria approach to optimization of the objective function. Recursion formulas are derived from the gradients of the stress and displacement constraints. The concept of one most critical constraint is used, allowing for an explicit statement of the Lagrange multipliers for the active constraints. The recursion formulas are then incorporated into the design algorithm.