The 6th IASTED African Conference on
Modelling and Simulation
AfricaMS 2016

September 5 – 7, 2016
Gaborone, Botswana


Meshfree Methods: Strong, Weak and Weakened Weak (W2) Formulations

Prof. Gui-Rong Liu
University of Cincinnati - Department of Aerospace Engineering and Engineering Mechanics, USA


Theory and Formulation for Meshfree methods: This talk introduces various formulations for Meshfree methods for solid and fluid mechanics problems, including Strong, Weak and Weakened Weak (W2) formulations. The focus will on the so-called weakened weak (W2) formulation will be presented that guarantees stable and convergent solutions, in comparison with the strong and weak formulations. We then present a family of W2 models known as S-PIM and S-FEM. Properties of this class of methods important for automations in computation will be discussed including: 1) spatial and temporal stability and convergence; 2) softening effects induced by various types of smoothing domains; 3) upper bound properties leading to certified solutions real-time computational models; 3) insensitivity to the quality of mesh allowing effective uses of triangular/tetrahedral meshes best suited for adaptive analyses.
Applications: Examples will be presented for simulating engineered material behavior at various extreme situations, fluid structural interaction problems (helicopter blades interacting with subsonic airflows), inverse identification of material properties and cracks in engineering aerospace structural systems, crystal plasticity for metallic polycrystalline used in jet engines, and integrity assessment of systems via inverse analysis with real-time computation.

Biography of the Plenary Speaker

Plenary Speaker Portrait

Dr. Liu received PhD from Tohoku University, Japan in 1991. He was a PDF at Northwestern University, USA from 1991-1993. He is currently a Professor and Ohio Eminent Scholar (State Endowed Chair) at the School of Aerospace Systems, University of Cincinnati. He served as the School Faculty Chair the School of Aerospace Systems, University of Cincinnati. He also served as a Deputy Head of the Department of Mechanical Engineering, the Director of the Centre for Advanced Computations in Engineering Science (ACES), National University of Singapore, and the President of the Association for COMPUT MECH, and President of the Asia-Pacific Association for COMPUT MECH. He is currently an Executive Council member of the International Association for COMPUT MECH. He authored a large number of international journal papers and books including two bestsellers: “Mesh Free Method: moving beyond the finite element method” and “Smoothed Particle Hydrodynamics: a Meshfree Particle Methods.” He authored recently a new book on Smoothed Finite Element Methods that are now used for various types of problems. He is the Editor-in-Chief of the IJCM, Associate Editor of the international technical journal Inverse Problems in Science and Engineering (IPSE) and Microfluidics and Nanofluidics (MANO), and served as an editorial member of five other journals including the IJNME. He is the recipient of numerous awards, including the Singapore Defence Technology Prize, NUS Outstanding University Researcher Award and Best Teacher Award, the APACM COMPUT MECH Awards, the ICACM COMPUT MECH Awards, the JSME COMPUT MECH Awards from JSME, and the ASME Ted Belytschko Applied Mechanics Award. He is listed as a world top 1% most influential scientist (Highly Cited Researchers) by Thomson Reuters in both 2014 and 2015, with SCI H-Index: ~57; Google Scholar H-Index: 78.