SHAKEDOWN ANALYSIS OF 3D FRAMES UNDER MULTIPLE LOAD COMBINATIONS USING MIXED FIBER BEAM ELEMENTS

This work presents an efficient shakedown analysis of 3D frames under multiple load combinations. Mixed fiber beam FEs are employed for an accurate discretization. The stress admissible domain is defined at fiber level as a function of the load factor using the maximum and minimum effect due to all loads. An incremental-iterative method is used at structural level. It evaluates a fictitious path made of a sequence of safe states with a load factor converging to the safety limit. Each point is obtained by finding kinematic variables corresponding to self-equilibrated stresses satisfying Melan's condition for the current load factor to be safe. An iterative FE state determination provides stress DOFs corresponding to assigned kinematic DOFs and load factor. Important features of the method are: i) a direct application of the Newton method, ii) a computational cost unaffected by dimension and complexity of the load domain, iii) an accurate safety factor using a small number of fibers and iv) an efficient solution for large buildings.