THREE-DIMENSIONAL CONSTANT – STRENGTH SINGULARITY ELEMENTS

In the three-dimensional case, as in the two-dimensional case, the discretiza­tion process includes two parts: discretization of the geometry and of the singularity element distribution. If these elements are approximated by polynomials (both geometry and singularity strength) then a first-order approximation to the surface can be defined as a quadrilateral[2] panel, a second-order approximation will be based on parabolic curve-fitting, while a third-order approximation may use a third-order polynomial curve-fitting. Similarly, the strength of the singularity distribution can be approximated (discretized) by constant-strength (zero-order), linearly varying (first-order), or by parabolic (second-order) functions.

The simplest and most basic three-dimensional element will have a quadrilateral geometry and a constant-strength singularity. When the strength of this element (a constant) is unknown a panel code using N panels can be constructed to solve for these N constants. In the following section, such constant-strength elements will be described.

The derivation is again performed in a local frame of reference, and for a global coordinate system a coordinate transformation is required.