Static Analysis of Structures Subjected to Interval Displacements
Publication: Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management
Abstract
Static analysis is an essential procedure to design a structure. Using static analysis, the structure's response to the applied external forces is obtained. Moreover, the static analysis is performed when the structure is subjected to external displacements, such as differential support settlements. The structure's response includes internal forces/moments and internal stresses that are used in the design process. In general, using a finite-element-based structural analysis scheme, first, the unknown displacements are obtained from equilibrium equations of an active system and then, the external and internal forces and stresses are calculated from structure's global equilibrium equations. However, for a structure subjected to external displacements, the prescribed displacements possess uncertainties because of limited information or measurement errors which alter the structure's response. One method to quantify the presence of these uncertainties is interval or unknown-but-bounded variables. Nevertheless, naïve implementation of intervals in a conventional finite-element scheme for this type of problem may cause errors and overestimations due to existing interval functional dependencies. In this work, a new method is developed that obtains the exact bounds on structure's static response of a structure subjected to interval displacements. This method combines the two steps of conventional analysis aforementioned into a single step, along with application of interval displacements, leading to direct determination of bounds of internal forces/moments and internal stresses. This approach removes the interval functional dependencies in calculations in order to attain exact results. A numerical example that shows the behavior of the developed method along with comparison to Monte-Carlo simulation results is presented. Using this method, it has shown that obtained bounds on static response of a structure subjected to interval displacements do not require an iterative procedure such as Monte-Carlo simulations.
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© 2014 American Society of Civil Engineers.
History
Published online: Jul 7, 2014
ASCE Technical Topics:
- Continuum mechanics
- Displacement (mechanics)
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Equilibrium
- Finite element method
- Methodology (by type)
- Motion (dynamics)
- Numerical methods
- Solid mechanics
- Static structural analysis
- Statics (mechanics)
- Stress (by type)
- Stress analysis
- Structural analysis
- Structural dynamics
- Structural engineering
- Structural mechanics
- Structural response
- Uncertainty principles
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