Optimal design of plane trusses using material forces

The shape optimization of a plane truss is attained through a simultaneous equilibration of physical and material forces. For this reason, the potential energy of the structure is regarded as an explicit function of the joint displacements of the truss in current configuration (physical space) as well as the joint positions in reference configuration (design space). The equilibrium of physical forces leads to finding the optimal joint displacements in the “physical space” and the equilibrium of the material forces leads to finding the optimal initial joint positions of the truss in the “design space”. The two sets of equilibrium equations are derived and solved in a completely coupled manner.