Plastic frames: Reduction of the kinematical inequality and optimization

It is well-known that the following inequality plays an essential part in the theory of perfectly plastic frames: for all kinematically admissible mechanisms and for bending moments associated with the hinge rotations by the flow rule, the plastic dissipation power is greater than or equal to the load power. This inequality will be termed as the kinematic inequality. It contains parameters generating the mechanisms. In simple cases, several ingenious authors obtained appreciable results excluding parameters. But, in more complicated cases, for instance when the given quantities are not numerical, the parameters remain in the kinematic inequality, thereby precluding exploitation of the kinematic approach. In the present work we overcome this dificulty: we reduce the kinematic inequality, i.e., we replace it by inequalities containing no variable parameter; we then state a process giving automatically such inequalities; finally, we treat a practical application. (orig.)