Weight minimisation of displacement-constrained truss structures using a strain energy criterion Original Research Article

This paper discusses a new method for the solution of the general truss weight-minimisation problem under simultaneous stress and displacement constraints. The method introduces a novel strain-energy-density criterion that refers to the ratio of the virtual strain energy per unit volume in each structural member to its average value on the whole structure. The virtual strain energy comes from the unit-load theorem and it is proportional to the product of the axial member forces due to both the actual loads and a virtual unit load that is applied at the node with the maximum displacement. A simple recursive formula for updating the cross-sectional areas, based on displacement constraints, is presented. A general subsequent algorithm applicable to both single and multiple load cases follows this formula. The results are encouraging since in all test cases the method was found to be robust and generally led to the same weight level as the literature, in both small and large structures.