Seminar - Hao Zhang - Nondeterministic Linear Static Finite Element Analysis: An Interval Approach

Hao Zhang
Department of Civil and Environmental Engineering
Georgia Institute of Technology


Friday 8 February 2008, 1.00 - 2.00 pm
Civil Engineering Lecture Theatre 3

Abstract:
This research presents a nontraditional treatment for uncertainties in the material, geometry, and load parameters in linear static finite element analysis for mechanics problems. Uncertainties are introduced as bounded possible values (intervals). The major difficulty associated with interval computation is the dependence problem, which results in severe overestimation in the system response ranges. Particular attention in the development of the present method is given to control the dependence problem. The developed method is based on an Element-By-Element technique. The penalty method is used to impose the necessary constraints for compatibility and equilibrium. The standard fixed point iteration is modified, enhanced, and used to solve the interval system equations accurately and efficiently. Special algorithms have been developed to calculate accurate results for stress and element nodal force. The present method is generally applicable to linear static interval FEA, regardless of element type. Numerical examples are presented to demonstrate the capabilities of the developed method. In addition to its accuracy, rigorousness and scalability, the efficiency of the present method is also significantly superior to previous methods such as the sensitivity analysis and the Monte Carlo sampling method.