Geometrical aspects of optimum truss like structures

The authors obtain graphical rules to construct discrete optimum structures without the use of analytical or numerical optimization processes. Structures investigated are limited to those having a single loaded point and two points of support (three‐point problems). The cost of structures is assumed to be proportional to their theoretical weight and to a performance index. The performance index is derived using the Lagrange multiplier method to minimize deflection of the loaded point with the given total volume of material. Solutions of simple problems, obtained with a gradient‐based minimizing procedure, lead through a series of observations to the generalized solution of optimum discrete structures. The authors determine that optimum discrete structure for three‐point problems can be described using the angles between four truss elements connected in every non‐support node. These four angles are the same for every node of the structure.