About this course:

  • Course Name: Mesh Reduction Methods and XFEM
  • Course Code: ME 663
  • L-T-P-C : 3-0-0-6
  • Syllabus: NaN
  • Course Type: Core course


    • Mesh Reduction Methods and XFEM

    Description:

    Course Objective: Though FEM is a robust and thoroughly used technique for static and dynamic problems, there are limitations of this popular tool which are becoming increasingly evident. Creation of a good quality mesh requires enormous computational and human effort. When handling large deformation problems, the computation may not be accurate due to element distortions. Further, it is difficult to simulate crack growth with arbitrary paths without remeshing and the crack trajectory coinciding with the nodal lines. The meshfree methods and the eXtended finite element method (XFEM) have shown great potential for overcoming the difficulties associated with the mesh-based methods.

    This course covers topics relating to mesh reduction methods in computational solid mechanics. The objective of this course is to introduce these emerging numerical methods to budding scientists and engineers so that they are equipped to solve various problems of engineering, sciences and industries. Some emphasis is placed on application of the meshfree methods and XFEM towards modelling fracture mechanics problems to elucidate the benefits of the proposed course.

    Pre-requisite: FEM course and a basic background of engineering/applied sciences is required for the understanding of the content covered in the course.

    This course will be opened to ME Computational Mechanics, Machine Design and CE structural engineering students. It will be also opened to the UG students from the ME, CE, and Maths and Computing backgrounds.

    Course Content: Introduction of PDE, Need for numerical methods, Differential scheme – FDM and Integral scheme - finite element method (FEM) review, Meshing issues in FEM, Introduction to boundary element method (BEM), Introduction to meshfree methods, Types of meshfree methods, Element-free Galerkin (EFG) method shape function construction, Weakforms of EFG method, Application of EFG method to 2D solid mechanics and thermal problems, Introduction to Fracture mechanics, Partition-of-Unity approach, Level-set methods, Extended FEM (XFEM) and extended EFG (XEFG) methods, XFEM and XEFG applied to crack problems, XFEM modelling in Abaqus, Coupling of EFG and FEM, Smoothed Particle Hydrodynamics (SPH).

    Course Outcome: The students will learn the application of modern numerical methods to solid mechanics problems.

    This course will involve usage of computer programming to solve basic problems using meshfree methods and XFEM in ABAQUS platform.

    Textbooks/Other Materials

    1. G.R. Liu, Meshfree methods: Moving beyond the finite element method. US: CRC Press, 2010.
    2. Hua Li, Shantanu S. Mulay, Meshless methods and their numerical properties, CRC Press, 2013.
    3. G.R. Liu, M.B. Liu, Smoothed Particle Hydrodynamics: A meshfree particle method, World Scientific, 2003.
    4. Vinh Phu Nguyen, Timon Rabczuk, Stéphane Bordas, Marc Duflot. "Meshless methods: A review and computer implementation aspects," in Mathematica and computers in simulation 2008; 79:763-813.
    5. Belytschko T, Lu YY, Gu L. "Element-Free Galerkin Methods" in International Journal for Numerical Methods in Engineering 1994, 37, 229-256.
    6. Nicolas Moës, John Dolbow, Ted Belytschko. "A finite element for crack growth without remeshing" in International Journal for Numerical Methods in Engineering 1999; 46:131-150.

    References:

    1. U.S. Dixit, Finite Element Methods for Engineers, Cengage Learning Asia; 1st edition,2009.
    2. Gernot Beer, Programming the Boundary Element Method: An Introduction for Engineers, Wiley 1st edition, 2001.
    3. S.K. Maiti, Fracture Mechanics: Fundamental and Applications, Cambridge University Press, 2015.
    4. S. Mohammadi, XFEM fracture analysis of composites, 1st ed. Chichester, West Sussex: John Wiley and Sons, 2012.