Joint Materials/Solid Mechanics Seminar Series with Prof. Gui-Rong Liu

BROWN UNIVERSITY
Joint Materials/Solid Mechanics Seminar Series

“Computational methods for certified solutions, adaptive analysis, real-time computation, and inverse analysis of engineering systems”

Friday, April 30, 2010 4:00-5:00 pm B&H Room 751

Prof. Gui-Rong Liu
Deputy Head of Mechanical Engineering
National University of Singapore

Abstract:

Rationale: Engineering systems become more and more sophisticated. Computer modelling for such systems is a must for optimal design, healthy monitoring, NDE, existing strength assessments, and service life prediction. The necessary requirements for an effective computational method have now become stability, convergence, automation, solution certification, adaptation, and real-time computation.
Theory: This talk introduces first the basic theory for a unified formulation of a wide class of compatible and incompatible methods based on FEM and meshfree settings. Important properties and inequalities for G spaces are proven, leading to the so-called weakened weak (W2) formulation that guarantees stable and convergent solutions. We then present some possible W2 models that meet all these challenges: 1) linear conformability ensuring the stability and convergence; 2) softening effects leading to certified solutions and real-time computational models; 3) insensitivity to the quality of mesh allowing effective uses of triangular/tetrahedral meshes best suited for automatic adaptive analyses.
Applications: A large number of benchmarking examples and practical examples will be presented to examine the theory and various numerical models, including material behavior at various extreme situations, dynamic behavior and interactions of red blood cells, inverse identification of material properties and cracks in engineering structural systems, and integrity assessment of dental implant systems via inverse analysis with real-time computation.