SOME UNEXPECTED PROPERTIES OF EXACT LEAST-WEIGHT PLANE TRUSS LAYOUTS WITH DISPLACEMENT CONSTRAINTS FOR SEVERAL ALTERNATE LOADS

Basic geometrical properties of optimal plane truss layouts for multip le displacement constraints and several load conditions are derived. T hese include the feature that at any point, optimal bars may run in at most two directions and that even for two nonsymmetric alternative lo ads at the same point the optimal two-bar layout is always symmetrical for a vertical support. The above general findings are illustrated wi th examples, in which the results are derived by several independent m ethods, including a proof of global optimality of the layout.