ESDU TM 119:2002

INTRODUCTION

Stress analysis and rigid body motion are just two of the fields
of mechanics in which area and area moment properties are
frequently required. Such properties.

where distances are measured from some moment axis to the
elemental area and the integration is applied over the whole of the
area of interest (the zero^th moment when n =
0 gives the area).

In the numerous text books that derive the various moments, a
cartesian approach is invariably taken whereby the shape of
interest is decomposed into essentially rectangular elements in
order for the integration to be applied. This approach is perfectly
acceptable for the relatively simple shapes that are normally
considerd but becomes less so when the shape is complex. The
approach becomes particularly messy when shapes with re-entrant
boundaries are to be analysed.

In this note an alternative, pseudo polar, approach is developed
in which a triangular "slice" element is used for the required
integration. It is demonstrated that such an approach leads to
easily implemented computational algorithms that are general and
can cope with shapes of arbitrary complexity. Having obtained the
area and moment properties, the mass-based properties can be easily
calculated for a real shape, or plate, of finite thickness.