Model reduction in nonlinear finite element method for engineering structures

The approximate solutions for complex nonlinear mechanical systems by using standard approaches (finite element, finite volume etc) are expensive with respect to storage and CPU costs. Therefore, Reduced-Order Model (ROM) is usually thought as computationally inexpensive mathematical representations that offer potential for near real-time analysis such as systems of nonlinear structural mechanics. Nevertheless, ROM usually lacks robustness with respect to parameter changes and therefore must often be rebuilt for each parameter variation. Together, these two issues underline the need for a fast and robust method for adapting recomputed ROMs to new sets of physical or modeling parameters. ROM is based on eliminating degrees of freedom from the computational problem as appropriate to attain required computational efficiency.