Finite Element Methods.

At the end of this course, the students should be able to: 1. explain the numerical methods involved in finite element theory; 2. discuss the role and significance of shape functions in finite element formulations and use linear, quadratic, and cubic shape functions for interpolation; 3. apply direct and formal (basic energy and weighted residual) methods for deriving finite element equations; 4. explicate global, local, and natural coordinates; 5. explain the formulation of one-dimensional elements (truss and beam); 6. elucidate the formulation of two-dimensional elements (triangle and quadrilateral continuum and shell elements); 7. discuss the formulation of three-dimensional elements (tetrahedral and brick elements); 8. select appropriate space (planar (plane stress or strain), axisymmetric, or spatial), idealization (type of element), and modelling techniques; and 9. perform and verify finite element analysis (FEA) using commercial FEA software; and 10. recognise sources of errors in FEA.

Direct approach for truss analysis, strong form and weak form, approximation functions for finite element methods, weighted residual methods, Ritz method, variational method, convergence criteria and rate of convergence, natural coordinates and shape functions, iso- parametric finite elements, finite element formulation of multidimensional heat flow and elasticity, numerical integration and approximation properties, finite element formulation of beam.