Geometrically consistent coupling of beam and continuum models for studying collapse of structures

Structures subject to extreme events such as strong earthquakes, fire, blast and impact are vulnerable to partial or total collapse. In such scenarios, the behavior of structural systems and their components is highly non-linear, usually involving large overall deformations, local material plasticity, damage and failure. Current approaches to study and prevent collapse are based on basic structural models that are sometimes enhanced with plastic hinges. These simplified models are usually unable to capture the response of a structure beyond the initiation of non-linearity and are not readily applicable for studying collapse. Alternatively, one may construct refined finite element models that are capable of simulating highly non-linear response in significant detail. However, due to their large computational cost, these models are often restricted to simulation of individual structural components rather than the entire structure as a whole. This thesis presents a combined approach where conventional structural models can be adaptively refined and coupled with detailed continuum finite element models. The coupling is done in a mathematically consistent manner using Lagrange multipliers to enforce geometric constraints from the structural models onto their interface with the continuum regions of the model. The models include both geometric and material non-linearity. Enhanced solution procedures have also been implemented to capture highly non-linear phenomena that are commonly encountered during collapse of frame structures, such as post-peak softening and snap-through buckling. Several examples are presented for verification and validation of these coupled models. Results from these models are also compared with existing approaches to document its computational efficiency and effectiveness for analysis and evaluation of collapse vulnerability of frame structures. The present approach will enable engineers to analyze and design against collapse with more realistic and computationally efficient models that are mathematically consistent with the underlying structural and continuum theories of mechanics. The present study also lays the foundation for further research and development of these coupled models including a more in-depth study of the consistency and stability properties of different coupling constraints, extension to 3-dimensional structural models and extension to other multi-scale problems in mechanics