Model-order reduction for nonlinear dynamics including nonlinearities induced by damage

Abstract

Fragility curves are one of the main tools used to characterize the resistance to seismic hazard ofcivil engineering structures, such as nuclear facilities. These curves describe the probability thatthe response of a structure exceeds a given criterion, called failure criterion, as a function of theexpected seismic loading level. The numerical construction of these curves leads to many queriesto CPU intensive nonlinear computations. Indeed, a large number of loading scenarios must betreated, but also the uncertainties inherent to the structure must be taken into account through areliability study.The objective of this work is to implement a strategy based on model-order reduction for a calcu-lation generally enabling very important computational time savings. Among the diffeerent possible approaches, the Proper Generalized Decomposition (PGD) coupled with the LATIN method [1] is particularly well suited for solving parametrized problems in nonlinear mechanics in order to buildnumerical charts [2]. The LATIN-PGD method is an iterative approach that seeks the solution of a given problem by building in a greedy way a dedicated reduced-order basis. This basis can bereused and enriched to solve parametrized problems, allowing a very good numerical effciency. It has been applied to solve a wide range of problems in mechanics and more recently for earthquake-engineering applications [3] and provides a particularly good framework for the computation ofnumerical charts.In this contribution, a strategy will be proposed to evaluate the damage state of piping components,characteristic of the primary circuits of pressurized water reactors, subjected to seismic loading consecutive to a preliminary design thermal loading. The developed methodology, using a damageableelasto-plastic material, integrates the initial state of damage prior to the seismic event, which isone of the uncertain parameters of the problem.REFERENCES[1] P. Ladevèze. Nonlinear computational structural mechanics: new approaches and non-incremental methods of calculation. Mechanical engineering series. Springer, New York, 1999.[2] D. Néron, P.-A. Boucard, and N. Relun. Timespace PGD for the rapid solution of 3d nonlinearparametrized problems in the manyquery context. International Journal for Numerical Methodsin Engineering, 103(4):275{292, 2015.[3] S. Rodriguez, D. Néron, P.-E. Charbonnel, P. Ladevéze, and G. Nahas. Non incremental LATIN-PGD solver for nonlinear vibratoric dynamics problems. In 14ème Colloque National en Calculdes Structures, CSMA 2019, Presqu'^Ile de Giens, France, May 2019.