The equilibration of configurational forces in the tendon layout optimisation of pre-stressed concrete beams

The concept of configurational forces has been explored recently as an optimisation tool. Configurational forces are the derivative of the energy with respect to the initial coordinates of the material. Solving for a zero residual of configurational forces implies that no further energy can be released by changing the material positions. Configurational forces are used to optimise tendon layouts in pre-stressed concrete beams. The dual set of equilibrium equations is derived and implemented in a finite element code. Inequality constraints are added in order to ensure that the optimal tendon position is always located within the cross-section.