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Stevens Institute of Technology

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Dr. Xi Frank Xu

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Dr. Xi Frank Xu
Assistant Professor
Location:307 Rocoo
CE 681
CE 660
School:  Schaefer School of Engineering & Science
Program:  Nanotechnology
Research & Education

General Interests

  • Multiscale Theory and Modeling – multiscale materials and random media, upscaling techniques, multiscale mechanics, multiscale stochastic numerical methods 
  • Computational Mechanics – Multiscale Stochastic Finite Element Method (MsSFEM), stochastic finite element methods, Fourier Spectral method (Fast Fourier Transform) 
  • Mechanics and Inhomogeneous Materials – nano- and micro-mechanics, composite theory, morphological characterization and modeling, damage and fracture, structural optimization, sandwich structures 
  • Homogenization Methods – Numerical Stochastic Homogenization Method (NSHM), periodic homogenization, non-periodic homogenization, stochastic homogenization  
  • Uncertainty Quantification and Probabilistic Theories – stochastic theory, simulation of random fields, reliability, risk and hazard assessment

New Methods/Models Recently Proposed

  • The Multiscale Stochastic Finite Element Method (MsSFEM): The MsSFEM is proposed to tackle multiscale problems involving uncertainties by using the Variational Multiscale Method (VMM), the stochastic Galerkin method, and the deterministic multiscale finite element method (MsFEM). The applications include two-scale stochastic porous media problems, heterogeneous materials subject to stochastic loads, and functional graded composites.
  • The Numerical Stochastic Homogenization Method (NSHM): Stochastic homogenization has been tackled with purely mathematical formulation without giving a practical numerical recipe. A first attempt is provided by the NSHM that develops a concept of stochastic representative volume element (SRVE), in combination with the Fourier spectral method and the stochastic Galerkin method. The NSHM provides not only a means of global homogenization but also solution for statistical descriptors of the local solutions.
  • The Short-Range-Correlation (SRC) Model for Characterization and Simulation of Random Materials/Media: In the framework of Markov/Gibbs random field theory, the Metropolis spin-flip algorithm is applied to build a robust simulator for multiphase random materials, by which higher-order statistical simulation of random materials becomes computationally feasible. The SRC model can be extended to higher-order high fidelity simulation of wind pressures, ocean waves and earthquake accelerations, etc.
  • Ph.D. ,Civil Engineering, 2005, The Johns Hopkins University, Baltimore, MD
  • M.S. , Civil Engineering, 2001, The University of Akron, Akron, OH
  • B. E. , Hydraulic Structures, 1993, Tsinghua University, Beijing, China.
Achievements & Professional Societies
Honors & Awards
  • Member, Tau Beta Pi Engineering Honor Society

  • Finalist, Melosh Competition for the Best Paper in Finite Element Analysis, 2005

  • Meyerhoff Fellow, The Johns Hopkins University, 2001

  • Richard D. Hickman Travel Award, The Johns Hopkins University, 2001
Professional Societies
  • Member, American Society of Civil Engineers
  • Member, Organizing Committee, NSF Workshop - Probability and Materials: From Nano-to-Macro-Scale, Baltimore, MD, January 5-7, 2005
Selected Publications

  • X.Frank Xu. (2006). "The multiscale stochastic finite element method on elliptic problems involving multiscale uncertainties.".

  • L. Graham-Brady. (2006). "Computational stochastic homogenization of random media elliptic problems using Fourier Galerkin method", Finite Elements in Analysis and Design, The Seventeenth Annual Robert J. Melosh Competition.

  • Lori Graham-Brady. (2005). "A stochastic computation method for evaluation of global and local behavior of random elastic media.", Comput. Methods Appl. Mech. Engrg. . 194 (42-44), 4362-4385.

  • Pizhong Qiao. (2005). "Refined Analysis of Torsion and In-plane Shear of Honeycomb Sandwich Structures", Journal of Sandwich Structures and Materials. 7 (4), 289-305.

  • Sarah C. Baxter and Lori L. Graham-Brady.. (2004). "Modeling the effects of elastic and inelastic contrast ratios in two-phase heterogeneous materials on local fields using moving window micromechanics.", International Journal of Nonlinear Mechanics. . (40), 351-359.

  • Pizhong Qiao. (2002). "Homogenized Elastic Properties of Honeycomb Sandwich with Skin Effect", International Journal of Solids and Structures . (39), 2153-2188.

  • Pizhong Qiao, and Julio F. Davalos.. (2001). "Transverse Shear Stiffness of Composite Honeycomb Core with General Configuration", ASCE Journal of Engineering Mechanics.. 127 (11), 1144-1151.

  • Julio F. Davalos, Pizhong Qiao, Justin Robinson and Karl E. Barth.. (2001). "Modeling and characterization of fiber-reinforced plastic honeycomb sandwich panels for highway bridge applications", Composite Structures . 52 (3-4), 441-452.

  • Lori Graham-Brady.. "Stochastic Morphological Modeling of Random Multiphase Materials".

  •    Conference Proceedings

  • Lori Graham-Brady. (Jul 16-18, 2003). "Nonlinear analysis of heterogeneous materials with GMC technique", Proceedings of the 16th ASCE Engineering Mechanics Conference, ASCE,Seattle, WA, 2003. .

  • Lori Graham-Brady.. (Jul 16-18, 2003). "A FFT based method on mechanics of random media", Proceedings of the 16th ASCE Engineering Mechanics Conference, ASCE, Seattle, WA, 2003.

  • Pizhong Qiao. (Jun 2-5, 2002). "Multi-pass homogenization of honeycomb sandwich plates", Proceedings of the 15th ASCE Engineering Mechanics Conference, ASCE, New York, NY, 2002.

  • Pizhong Qiao and Julio F. Davalos. (Sep 10, 2001). "Evaluation of Transverse Shear Stiffness of Composite Honeycomb Core with General Configuration", 16th Annual Technical Conference, American Society for Composites, Blacksburg, VA, 2001 .

  • Justin Robinson, Julio F. Davalos, Karl E. Barth and Pizhong Qiao.. (Sep 10, 2001). "FRP composite honeycomb sandwich beams under bending", 16th Annual Technical Conference, American Society for Composites, Blacksburg, VA.

  • Jennifer Righman, Karl E. Barth, Julio F. Davalos and Pizhong Qiao.. (Sep 10, 2001). "Development of an economic and efficient connect system for FRP decks to steel bridge girders", 16th Annual Technical Conference, American Society for Composites, Blacksburg, VA.


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