Structural optimization by simultaneous equilibration of spatial and material forces

In this contribution, a dual equilibrium methodology is applied to the shape optimization of trusses. The spatial co-ordinates as well as the material (i.e. initial) co-ordinates of the joints are taken as unknowns in the potential energy of the structure whereby the connectivity is xed. The conjugated variables, i.e. spatial forces and material forces, are equilibrated. Whereas equilibration of the spatial forces is equivalent to nding the optimal joint displacements, equilibration of the material forces yields the optimal initial joint positions. The two sets of equilibrium equations are derived and solved in a completely coupled manner. With a proper linearization and a Newton–Raphson scheme, shape optimization of the truss can be achieved within a few iterations. This is demonstrated by two numerica