Abstract Summary
In order to reduce the numerical cost of dynamic time history analysis, this research proposes to extend the application of the Proper Orthogonal Decomposition (POD) to reinforced Concrete (RC) structures with material nonlinearities subjected to earthquakes. To achieve this time economy in nonlinear dynamic analysis, the structural model is reduced by projection on the POD modes. Material nonlinearity in reinforced concrete structures is due to steel ductility and concrete damaging. In this work, it is modeled by the fiber section technique for 1D members (beams and columns) and by the layered shell approach for 2D elements (walls). Two reduction techniques are used. The first one is for structures studied for a single base excitation. In this application, a full model nonlinear time history analysis is conducted on an initial small duration portion of the earthquake. The obtained results are statistically analyzed to find the most dominant POD modes. Then, these POD modes are used to reduce the dynamic system. Next, the analysis for the remaining portion of the earthquake is conducted on a reduced model. The second technique is for structures studied for multiple earthquakes. In this approach, a full model nonlinear time history analysis is conducted for one selected earthquake. Based on the obtained results, a principal component analysis is conducted to find the dominant POD modes. Then, these POD modes are used to reduce the dynamic system. Next, the remaining earthquakes are entirely analyzed using the reduced dynamic model. For the conducted tests, reduced models gave very close results to the full models at a fraction of the time cost (time economy up to 96%). Thus, this work demonstrates that the POD method can be used to reduce the numerical cost of dynamic time history analysis for RC structures with material nonlinearities subjected to earthquakes.
