Advanced Methods in Computational Solid Mechanics

This is an advanced course for graduate students . The course is tailored to introduce students to advanced applied numerical methods for solid mechanics simulations. These advanced methods can be viewed as the natural evolution of finite elements during the last years. The course covers the following topics:

    • One-dimensional and two-dimensional finite element method: variational weak formulation, weighted-residual method, numerical integration; applications to 1D bar, 1D Bernoulli beam and 2D Poisson equation.
    • Meshfree methods: element-free Galerkin method, maximum-entropy meshfree method; applications to 2D linear elastostatics.
    • Polygonal finite element method: approximations for polygonal elements, applications to 2D linear elastostatics.
    • Virtual element method: formulation for 2D Poisson problem, formulation for 2D linear elastostatics.
    • Extended finite element method: intrinsic enrichment, extrinsic enrichment, 1D applications, applications in fracture mechanics.
    • Isogeometric analysis: computational geometry, Non-rational B-splines, B-splines basis functions, formulation for 2D Laplace equation, formulation for 2D linear elastostatics.
    • Extended isogeometric analysis: isogeometric enrichment, applications in fracture mechanics.

Software related to this course:

Most of the methods covered in this course are not available in commercial simulation packages. Students are expected to implement their own codes. Regarding the Virtual Element Method, a MATLAB-based software named VEMLab has been developed, which students use for solving homeworks and/or as a base for adding new features to it. VEMLab can be downloaded from here.

Official syllabus can be found here