Yield surface approximation for lower and upper bound yield design of 3D composite frame structures

• Yield surfaces of composite beam sections are numerically computed.
• Computed yield surfaces are approximated by a Minkowski sum of ellipsoids.
• Static and kinematic approaches are formulated using finite elements and SOCP.
• Limit loads estimates on a complex frame structure are obtained within seconds.

The present contribution advocates an up-scaling procedure for computing the limit loads of spatial structures made of composite beams. The resolution of an auxiliary yield design problem leads to the determination of a yield surface in the space of axial force and bending moments. A general method for approximating the numerically computed yield surface by a sum of several ellipsoids is developed. The so-obtained analytical expression of the criterion is then incorporated in the yield design calculations of the whole structure, using second-order cone programming techniques. An illustrative application to a complex spatial frame structure is presented.