Course Details

1. Illustrate the various steps in the Displacement Finite Element Method from assumed displacement polynomial to determination of stresses.
2. Evaluate degree of approximation.
3. Employ an analysis system for the determination of stresses and strains in small displacement, linear elastic problems.
4. Develop an analysis strategy that enables the relative significance of individual model parameters and their interactions to be evaluated.
5. Formulate a series of smaller studies, benchmarks or experimental tests in support of a FEA modelling strategy.
6. Select appropriate idealisation(s) for components / structures, which are consistent with the objectives of the analyses.

General

·        Finite element concepts; modeling; discretization; element selection; testing; model validation

·        Matrix operations, numeric integration (Gauss-quadrature), and Mathcad

Line elements (1-D)

·        Axial line element (bar); C0 shape functions (interpolation functions); element matrix formulation; integration; loads; assembly of global matrices; solution; force recovery; coordinate transformations

·        Element matrix formulation techniques: virtual work; method of weighted residuals; variational methods; strong form; weak form; essential and natural boundary conditions; Galerkin method; Rayleigh-Ritz method

·        Flexural line element (beam); C1 shape functions (interpolation functions); element matrix formulation; integration; loads; assembly of global matrices; solution; force recovery; coordinate transformations

Surface (area) elements (2-D)

·        Shape functions; strain-displacement relationships; constitutive relationships (stress-strain relationships, material models)

·        Plane-stress, plane-strain, and axi-symmetric analysis using rectangular elements; locking; full vs. reduced integration; spurious modes; incompatible modes; stress recovery; interpretation of analysis results (principal stress, effective stress)

·        Isoparametric surface element formulations; shape functions; consistent loads; effects of element distortion; stress recovery, extrapolation, and smoothing

·        Plate bending elements; Kirchoff vs. Mindlin formulations; constitutive relationships; interpretation of analysis results (principal moments and shears)

·        Flat shell elements; superposition of membrane and plate bending; drilling DOF

·        Axisymmetric elements

Volume (solid) elements (3-D)

Isoparametric volume (solid brick) elements; shape functions; constitutive relationships

• “A First Course In The Finite Element Method” by Daryl L. Logan
• “How to Model with Finite Elements”, Baguley D and Hose D R, NAFEMS, 1997

• “The Finite Element Method, Volume 1 Basic Formulation and Linear Problems, Zienkiewicz O C, Taylor R L, 4th Edition, Published by McGraw-Hill.