Nonlinear Structural Analysis Towards Collapse Simulations: A Dynamical Systems Approach

Keywords: Nonlinear analysis.  Structural response.  Hazardous loads.  Displacement method.  State space approach.  Lagrangian approach.  Differential algebraic equations (DAE).  Hamilton's principle.  Phenomenological models.

Abstract: In this report, two new approaches, both the state space approach and the Lagrangian approach, are developed to consider the structure as a dynamical system.  These are mixed methods, wherein besides displacements, the stress-resultants and other variable of state are primary unknowns.  These methods can potentially be used for the analysis of structures to collapse as demonstrated by numerical examples.  Attention is focused on skeletal structures, although the extension of the methods to other systems is discussed.  The methods suggested, can be coupled with suitable pre- and post-processors to develop a unified computational platform for analysis of collapsing structures.  Several appendices are included along with numerous equations and diagrams.