Simulation Strategies for FE Systems Under Uncertainties

The prodigious development in computer technology strongly supports the developments of Finite Element method. Finite Element method is based on discretization of the structures to be analyzed into finite elements, a procedure to solve partial differential equations with any required accuracy. This method revolutionized structural analysis and it is today the prevailing method used exclusively for non-trivial structural analyses. As it is widely accepted nowadays, in order to rationally and realistically model the behavior of structural systems, one must take into account all the uncertainties in the material properties, the loading conditions, the geometrical imperfections, the environmental phenomena that affect the integrity of the structure etc. The combination of the two most powerful methods in probabilistic and deterministic analysis, that is Monte Carlo simulation and Finite Element-analysis, respectively, allow the quantification of uncertainties of the response for larger engineering structures. However, the total computational costs of this analysis is governed by the number of Finite Element-analyses that have to be carried out. Hence, in most practical cases the propagation of the uncertainties was limited to a few parameters due to the excessive computational cost of the full analysis. In this context the advanced simulation methods for reliability estimation of structural systems represent a great promise for an efficient solution of larger types of problems. This is of great importance for the acceptance of rational uncertainty analysis by the engineering practice. Despite the remarkable achievement made during the first term of this research project for reliability estimation of structural systems in high dimensions under uncertainties, the further development of advanced methods is still urgently needed to extend their applicability in a robust manner and improve their efficiency even further whenever possible. The engineering practice requires highly efficient procedures which are applicable to high dimensional problems. This represents the main reason why the development of advanced simulation methods have been and are even more so in center of interest. Only with these methods at hand structures of the engineering practice can be analyzed.

The prodigious development in computer technology strongly supports the developments of Finite Element method. Finite Element method is based on discretization of the structures to be analyzed into finite elements, a procedure to solve partial differential equations with any required accuracy. This method revolutionized structural analysis and it is today the prevailing method used exclusively for non-trivial structural analyses. As it is widely accepted nowadays, in order to rationally and realistically model the behavior of structural systems, one must take into account all the uncertainties in the material properties, the loading conditions, the geometrical imperfections, the environmental phenomena that affect the integrity of the structure etc. The combination of the two most powerful methods in probabilistic and deterministic analysis, that is Monte Carlo simulation and Finite Element-analysis, respectively, allow the quantification of uncertainties of the response for larger engineering structures. However, the total computational costs of this analysis is governed by the number of Finite Element- analyses that have to be carried out. Hence, in most practical cases the propagation of the uncertainties was limited to a few parameters due to the excessive computational cost of the full analysis. In this context the advanced simulation methods for reliability estimation of structural systems represent a great promise for an efficient solution of larger types of problems. This is of great importance for the acceptance of rational uncertainty analysis by the engineering practice. Despite the remarkable achievement made during the first term of this research project for reliability estimation of structural systems in high dimensions under uncertainties, the further development of advanced methods is still urgently needed to extend their applicability in a robust manner and improve their efficiency even further whenever possible. The engineering practice requires highly efficient procedures which are applicable to high dimensional problems. This represents the main reason why the development of advanced simulation methods have been and are even more so in center of interest. Only with these methods at hand structures of the engineering practice can be analyzed.