| The
Isoparametric Element formulation |
An example derivation for a
simple "bar" element to demonstrate the part
played by shape functions, Jacobians and
strain-displacement matrices in generating a finite
element stiffness matrix |
| The
Local Coordinate System |
An explanation of the local
coordinate system used by element shape functions |
| Shape
Functions |
A description of shape
functions and their effect on the evaluation of element
displacements, the choice of linear versus quadratic
elements, nodal temperature loading with temperature
dependent materials and element thickness interpolation |
| Equivalent
Force Distribution |
A description of how the
applied loads are actually applied to finite elements,
including the effects on multiple element loading,
loading visualisation arrows in reverse directions,
obtaining planar displacement fields, non-constant
reactions along a supported boundary, equivalent nodal
loading for beam/shell/plate elements and joining lower
and higher order elements |
| Numerical
Integration |
Describes the reasons for,
and methods available to implement numerical
integration. Also discusses explicit integration for
beam elements |
| Element
Mechanisms |
Explains what an element
mechanism is and what to do if such behaviour occurs in
an analysis |
| Evaluating
The Mass Matrix |
Describes how to create a
mass matrix for an isoparametric finite element.
Discusses the difference between lumped and consistent
mass formulations |
| Finite
Element Equilibrium |
How is equilibrium achieved
and when are results correct? This section answers such
questions and specifically deals with smoothed and
unsmoothed stress contours, limitations of the averaging
scheme and why the removal of elements affects the
stress contours |
| Element
Quality |
Describes the effect that
poor element quality has on the analysis results,
including aspect ratios, warping, distortion
(translation and angular) and issues with the Jacobian
matrix |
| The
Jacobian Matrix |
Explains what it is, why is
it important and how to eliminate problems arising from
it |
| Element
Aspect Ratio Considerations |
Describes the element
aspect ratio test and considerations should this test be
violated |
| Ill-Conditioned
Matrices |
Explains ill-conditioning
in finite elements and the typical causes |
| Links
to Useful Reference Material |
Links to the NAFEMS website
as well as recommended reference books |
