Mixed Dimensional Hierarchic Partitioned Analysis of Nonlinear Structural Systems

Abstract

The use of most accurate 3D modelling in Finite Element analysis is too computationally expensive to be practical. The alternate simplification of 1D elements may sometimes compromise the accuracy of results. However, the detailed modelling of the critical parts and approximate modelling of the non-critical parts of the structure is often sufficient. A novel hierarchic domain partitioning approach has been developed in this study, which is being presented. The thesis begins with an introduction followed by a literature review. The domain partitioning approach is described next in which, parts of a structural system are removed and replaced by partition super elements. The removed parts are modelled separately with their partitioned boundary wrapped around by dual partition super elements. These partitions are analysed simultaneously using parallel computations. This domain partitioning approach increases the computational efficiency and allows the possibility of the use of differently dimensioned partitions. Using the domain partitioning approach, the complex non-linear structural systems can be subjected to static time-history, proportional loading, and dynamic loading. For dynamic analysis, eigenvalue analysis is required. The eigenvalue problem for large matrices is itself computationally expensive; however, a new parallel implementation of eigenvalue analysis is developed here using the partition super elements. In order to be able to use differently dimensioned partitions, a new dimensional coupling method has been developed. This is implemented with the help of a new master-slave element which has a single node as the master and all the nodes at the partitioned boundary as its slave nodes. This allows the possibility of using 3D brick elements inside a partition, whereas the other partitions at higher levels can use simplified 1D element models. The domain partitioning approach has been further enhanced by making it hierarchical, where, the partitions are further subdivided by replacing their parts with partition super elements and the removed parts modelled at further lower levels of partitioning. The hierarchical modelling is followed by a couple of case studies that demonstrate the applicability of the developed methods. The thesis ends with discussion and with the conclusion that the mixed dimensional hierarchic partitioning methods have greatly increased the computational efficiency of the finite element analysis. Some directions for the future research related to this work have been suggested.