A WELL-POSED NONSELF-ADJOINT LAYOUT PROBLEM - LEAST-WEIGHT PLANE TRUSS FOR ONE LOAD CONDITION AND 2 DISPLACEMENT CONSTRAINTS

Exact optimal plane truss layouts are derived for a vertical support a nd a concentrated load with two displacement constraints. The latter a re imposed at the point of application of the load, in the direction o f the load and in another direction. It is shown that for the above cl ass of problems the optimal solution always consists of two symmetrica lly positioned bars. These solutions are derived analytically by two i ndependent methods: (i) in the first one a two-bar topology is assumed and then the orientations and cross-sectional areas of the bars are o ptimized; (ii) in the second one, the same optimal solutions are deriv ed from general optimality criteria, which show that the optimum is va lid even when we consider all possible topologies. The paper demonstra tes the power and versality of continuum-type optimality criteria and also shows that for two displacement constraints at a loaded point the problem is non-selfadjoint but always well-posed, having a stationary optimum with a finite structural weight. The exact layout solutions g iven in this paper can be used as test examples for numerical methods in topology optimization.