Special Issues of Journals

Special issue of Reliable Computing Journal on Reliable Engineering Computing, Vol. 13, No. 2, April 2007 (part III), Muhanna, R. L. and Mullen, R. L, Guest Editors.

Special issue of Reliable Computing Journal on Reliable Engineering Computing, Vol. 13, No. 1, February 2007 (part II), Muhanna, R. L. and Mullen, R. L, Guest Editors.

Special issue of Reliable Computing Journal on Reliable Engineering Computing, Vol. 12, No. 6, December 2006 (part I), Muhanna, R. L. and Mullen, R. L, Guest Editors.

## Publications from REC Sponsored Workshops

NSF International Workshop on Imprecise Probability in Analysis and Design, Savannah GA, February 20-22, 2008

NSF International Workshop on Modeling Errors and Uncertainty in Engineering Computations, Savannah GA, February 22-24, 2006

NSF International Workshop on Reliable Engineering Computing, Savannah GA, September 15-17, 2004

Theses

Nondeterministic Limear Static Finite Element Analysis: An Interval Approach, Ph. D. thesis, Hao Zhang, 2005.

Dynamic Analysis of Structures with Interval Uncertainty , Ph. D. thesis, Mehdi Modares Zadeh, 2005.

Interval Finite Element Analysis for Load Pattern and Load Combination , MS thesis, Veshal Saxena, 2003.

Publications in Journals and Books

Muhanna, R. L., Mullen, R. L., and Zhang, H., "Interval Finite Element as a Basis for Generalized Models of Uncertainty in Engineering Mechanics,” *Reliable Computing Journal,* *Springer Netherlands*, Vol. 13, No. 2, pp. 173-194, April 2007.

Mehdi Modares, Robert Mullen, Paul X. Bellini, and Rafi L. Muhanna, “Buckling Analysis of Structures with Interval Uncertainties”, *SAE Transactions Journal of Passenger Cars –Mechanical Systems*, pp. 284-290, March 2006.

Pereira, S., Mello, U., Nelson, M., and Muhanna R., L. "Uncertainty in Thermal Basin Modeling: An Interval Finite Element Approach, " *Journal of Reliable Computing,* *Springer Netherlands,* Vol. 12, No. 6, pp. 451-470, December 2006.

Modares, M., Mullen, R., L. and Muhanna, R. L. " Natural Frequency of a Structure with Bounded Uncertainty, "*Journal of Engineering Mechanics,* ASCE, Vol. 132, No. 12, pp. 1363-1371, 2006.

Muhanna, R. L. and Mullen, R. L, Editors. Proceedings of the NSF Reliable Engineering Computing Workshop on “Modeling Errors and Uncertainty in Engineering Computations, ” Georgia Tech Savannah, February 2006.

Muhanna, R. L. and Mullen, R. L., *Interval Methods for Reliable Computing*, Chapter in Reliability Design Handbook, CRC Press LLC, ISBN 0-8493-1180-2, edited by Efsratios Nikolaidis and Dan Ghiocel, 2005.

Muhanna, R. L., Mullen, R. L., and Zhang, H., "Penalty-Based Solution for the Interval Finite Element Methods, "*Journal of Engineering Mechanics, *ASCE, Vol. 131, No. 10, pp.1102-1111, 2005.

Muhanna, R. L. and Mullen, R. L, Editors. Proceedings of the NSF Reliable Engineering Computing Workshop on “Reliable Engineering Computing, ” Georgia Tech, Savannah September 2004.

Muhanna, R. L. and Mullen, R. L., "Treatment of Geometric Tolerances in Finite Element Analysis," *International Journal of Advanced Manufacturing Systems, *Vol. 4, No. 1, pp 143-162, 2001.

Muhanna, R. L. and Mullen, R. L., Uncertainty in Mechanics Problems-Interval-Based Approach, "Journal of Engineering Mechanics, ASCE, Vol. 127, No. 6, pp 557-566, 2001.

Mullen, R. L. and Muhanna, R. L. "Bounds of Structural Response for All Possible Loadings, "*Journal of Structural Engineering, ASCE*, Vol. 125, No. 1, pp 98-106, 1999.

Muhanna, R. L. and Mullen, R. L., "Formulation of Fuzzy Finite Element Methods for Mechanics Problems, " *Computer-Aided Civil and Infrastructure Engineering *(*previously Microcomputers in Civil Engineering*), Vol.14, pp 107-117,1999.

Conference Publications

B.F. Zalewski, R.L. Mullen, R.L. Muhanna, “Boundary Element Analysis of Systems UsingInterval Methods”, Proceedings of the NSF Workshop on Modeling Errors and Uncertainty in Engineering Computations, Georgia Tech Savannah, February 2006.

Rafi Muhanna, Vladik Kreinovich, Pavel Solin, Jack Chessa, Roberto Araiza, and Gang Xiang, “Interval Finite Element Methods: New Directions”, Proceedings of the NSF Workshop on Modeling Errors and Uncertainty in Engineering Computations, Georgia Tech Savannah, February 2006.

Rafi L. Muhanna, Ayše Erdolen and Robert Mullen, “Geometric Uncertainty in Truss Systems: An Interval Approach”, Proceedings of the NSF Workshop Modeling Errors and Uncertainty in Engineering Computations, Georgia Tech Savannah, February 2006.

Zhang, H., Muhanna, R. Mullen, R., "Finite Element Analysis for Uncertain Structures: An Interval Approach," Proceedings of the 9th International Conference on Structural Safety and Reliability (ICOSSAR 2005), Rome, Italy, June 19-23, 2005.

Modares, M., Mullen, R., Bellini, P., and Muhanna, R., “Buckling Analysis of Structures with Interval Parameters,” Proceeding of the 2005 SAE World Congress, Reliability and Robust Design in Automotive Engineering, Detroit, Michigan, April 11-14, 2005.

Muhanna, R., Mullen, R. and Zhang, H., “Interval Finite Element as a Basis for Generalized Models of Uncertainty in Engineering Mechanics,” Proceeding of NSF Workshop on Reliable Engineering, Georgia Tech, Savannah, GA, 2004.

Modares, M., Mullen, R., Muhanna, R., and Zhang, H., "Buckling Analysis of Structures with Uncertain Properties and Loads Using an Interval Finite Element Method," Proceeding of NSF Workshop on Reliable Engineering, Georgia Tech, Savannah, GA, 2004.

Zhang, H. and Muhanna, R. “Finite Element Analysis for Structures with Interval Parameters,” proceedings of the 9th ASCE joint Specialty Conference on Probabilistic Mechanics and Structural Reliability, New Mexico, July 26-28, 2004.

Mullen, R. L. and Muhanna, R. L. "Efficient Interval Methods for Finite Element Solution," Proceedings of the High Performance Computing Systems and Applications, IEEE, editors: Almhana J. N. and Bhavsar V. C., 2002.

Mhanna, R. L. and Mullen, R. L., " Critical Issues in the Application of Interval Methods to Finite Element Analysis, " proceedings of SCAN2002, 10th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics, Paris, France, September, 24-27, 2002.

Muhanna, R. L. and Mullen, R. L., " Sharp Rigorous Bounds On Interval Estimates For Finite Solutions With Uncertain Material Properties, " proceedings of the 2000 NSF Design & Manufacturing Research Conference, Vancouver, British Columbia, Canada, January 3-6, 2000.

Muhanna, R. L. and Mullen, R. L., "Sharp Enclosure for Material Uncertainty in Solid and Structural Mechanics-Interval Based Approach, Part I, " proceedings of the Eighth ASCE Joint Specialty Conference on Probabilistic Mechanics and Structural Reliability University of Notre Dame, Notre Dame, Indiana July 24-26, 2000.

Muhanna, R. L. and Mullen, R. L., "Sharp Enclosure for Material Uncertainty in Solid and Structural Mechanics-Interval Based Approach, Part II, " proceedings of the Eighth ASCE Joint Specialty Conference on Probabilistic Mechanics and Structural Reliability University of Notre Dame, Notre Dame, Indiana July 24-26, 2000.

Muhanna, R. L. and Mullen, R. L., "Sharp Enclosure for Material Uncertainty in Solid and Structural Mechanics-Interval Based Approach, Part II, " proceedings of the Eighth ASCE Joint Specialty Conference on Probabilistic Mechanics and Structural Reliability University of Notre Dame, Notre Dame, Indiana July 24-26, 2000.

Muhanna, R. L. and Mullen, R. L., "Sharp Enclosure for Material Uncertainty in Solid and Structural Mechanics-Interval Based Approach, Part II, " proceedings of the Eighth ASCE Joint Specialty Conference on Probabilistic Mechanics and Structural Reliability University of Notre Dame, Notre Dame, Indiana July 24-26, 2000.

Mullen, R. L. and Muhanna, R., L., "Sharp Interval Estimates for Finite Element Solutions with Fuzzy Material Properties, " proceedings of the 14th ASCE Engineering Mechanics Conference, The University of Texas at Austin, May 21-24, 2000.

Muhanna, R. L. and Mullen, R. L., "Interval based Methods for Load and Stiffness Uncertainty in Computer-Aided Analysis, " proceedings of the 1999 NSF Design & Manufacturing Grantees Conference, Queen Mary,LongBeach,CA,January5-8,1999. http://www.usc.edu/dept/ise/NSF/proceedings/.

Mullen, R. L. and Muhanna, R., L., "Interval-Based Geometric and Material Uncertainty for Mechanics Problems," proceedings of the 13th ASCE Engineering Mechanics Division Conference, The Johns Hopkins University, Baltimore, MD, June 13-16, 1999.

Mullen, R. L. and Muhanna, R. L., "Interval Based Finite Element Methods, " Recent Advances in Numerical Methods and Applications, editors: Iliev O. P., Kaschiev M. S., Margenov S. D., Sendov Bl. H., Vassilevski P. S., World Scientific Publishing Co. Pte. Ltd., 1999.

Muhanna, R., Ballarini, R. and R. Mullen, "Calculation of Stress Intensity Factors with Fuzzy Loading, " proceedings of the 4-th International Conference on Stochastic Structural Dynamics, University of Notre Dame, Notre Dame, IN, USA, Aug. 6-8, 1998. http://www.nd.edu/~ssd98/.

Mullen, R. L. and Muhanna, R. L. "Structural Analysis with Fuzzy-Based Load Uncertainty, " proceedings of the 7th ASCE EMD/STD Joint Specialty Conference on Probabilistic Mechanics and Structural Reliability, WP I, MA, pp 310-313, August 7-9, 1996.

Muhanna, R. L. and Mullen, R. L. "Development of Interval Based Methods for Fuzziness in Continuum Mechanics, " proceedings of ISUMA-NAFIPS’95, pp 145-150, September 17-20, 1995.

Presentations

Computing on Sets– Bounds on the Local Error in Numerical Solutions of Partial Differential Equations, Tufts University, November 29, 2007

Interval Finite Elements as a Basis for Generalized Models of Uncertainty in Engineering Analysis, Collaborative Research Center 528, German National Science Foundation (DFG), TU Dresden, Germany, June 19, 2007. (Presentation ppt) or (Presentation pdf)

**Interval Finite Element Methods for Uncertainty Treatment in Structural Engineering Mechanics,**Second Scandinavian Workshop onInterval Methods and Their Applications, August 25-27, 2003,Technical University of Denmark, Copenhagen, Denmark. (Presentation ppt) or (presentation pdf)

**Penalty-Based Solution for the Interval Finite Element Methods**, First Scandinavian Workshop on Interval Methods and Their Applications, August 14-16, 2003,Technical University of Denmark, Copenhagen, Denmark. (Presentation ppt) or (Presentation pdf)