New adaptative static condensation method for the simulation of large dimensions prestressed reinforced concrete structures
Résumé
In order to evaluate the cracking process in large reinforced and prestressed concrete structures, a predictive model of concrete damage with refined mesh and a nonlinear law can be required. Because of the computational load, such modelling is not applicable directly on large-scale structures whose characteristic dimensions are over several meters. To solve this problem, a method based on the static condensation, which concentrates the computational effort on the damaged area has been proposed. The so-called “zones of interest” are evolutionary to be adapted to the cracking process.
The method has been developed, improved and implemented in the finite element code Cast3m. It follows different steps including an initial cutting of the mesh into sub-zones, a condensation of these zones on their borders and the definition of the first “zone of interest” by a preliminary linear computation. The borders of « non-risky » zones are then condensed at the interface of this initial zone of interest (“double condensation”). The nonlinear computation is finally applied only on the zone(s) of interest, consequently reducing the computational load. At the end of each calculation time, a potential evolution of the zones of interest is considered through either criteria of “propagation” or “apparition” (evolving method). In this contribution, the “adaptive condensation method” is presented and the influence of the input parameters is discussed. Among them, the initial decomposition of the mesh into sub-zones plays a key role in the efficiency of the method. In order to improve the initial method, an automatic division procedure is proposed to enhance the initial mesh cutting. It is especially shown how this procedure, based on a limited number of parameters, can significantly decrease both the user effort and the computational time.
The method is finally applied on test cases of different complexity: a 2D three-point bending beam, a simplified reinforced concrete containment and a prestressed beam. Both global and local results are compared to “reference” simulation using classical finite element methods. Similar results are obtained, even for very local quantities (damage), with a variable calculation time saving factor ranging from 4 to 15 for the case of the prestressed beam.