Optimization of truss topology using boundary cycle : Derivation of design variables to avoid inexpedient structure

This paper deals with optimization of truss topology using boundary cycle in algebraic topology. Elimination of unnecessary members from the ground structure, one of the popular means to optimize truss topology, is employed. The elimination has a disadvantage that unstable structures possibly appear in the process of the optimization. Boundary operator, which has the ability to represent equilibrium of internal force in members, is used to generate the boundary cycle from chain. Design variables derived by the boundary cycle can always satisfy this equilibrium and avoid a category of unstable structures without imposing any constraint. An attempt is made through numerical examples to minimize the total weight of a plane truss, which is fixed to a rigid wall and supports a vertical load acting at a point distant from the wall, under the condition that the distribution of strain energy density is uniform and equal to a certain value. The validity of this formulation is verified by the numerical examples concerned with the weight minimization of the truss.