1. Reference problem

1.1. Geometry

All three bars have the same length \(L=\mathrm{1m}\), and are \(l\mathrm{=}\mathrm{1m}\) apart.

1.2. Material properties

Standard perfect thermo-elastoplastic behavior law, with VonMises criterion. The plastic deformations are zero in the initial state.

1.3. Boundary conditions and loads

The three bars have a blocked movement following \(\mathit{Oy}\) at the upper end points, where they are articulated, and they are clamped at the lower points \({P}_{\mathrm{1,}}{P}_{\mathrm{2,}}{P}_{3}\), which can be represented by a rigid frame forced to move vertically, of length \(\mathrm{4l}\), on which the three bars are articulated. The bars are free of mechanical force.

The loading path is described by the evolution of the temperature, uniform in each bar (\({T}^{\mathit{max}}\mathrm{=}330°C\)):