Theoretical description

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QuickField solves 2D boundary value problems for elliptic partial differential equation for either scalar or one-component vector potential. It also solves 2D solid stress analysis problems (plane stress, plane strain, axisymmetric stress). There are three main classes of 2D problems: plane, plane-parallel and axisymmetric.

Plane problems usually arise when describing heat transfer processes in thin plates. They are solved in planar rectangular coordinate system. Plane-parallel problems use right-handed Cartesian coordinate system xyz.
It is assumed that neither geometric shape and properties of material nor field sources vary in z-direction. The problem is described, solved and the results are analyzed in xy-plane, which we will call the plane of model.

Axisymmetric problems are formulated in cylindrical coordinate system zrθ. The order of axes is chosen for conformity with the plane-parallel case. Physical properties and field sources are assumed to not depend on the angle coordinate.
All operations with the model are done in zr-plane (more precise in a half plane r ≥ 0). Z-axis is assumed to be horizontal and directed to the right, r-axis is directed up.

The geometric configuration of the problem is defined as a set of curved polygonal subregions in the plane of model. Each region corresponds to a domain with a particular set of physical properties.
We will use term blocks for polygonal subregions, term edges for line segments and circular arcs that constitute their boundaries and term vertices for ends of edges and for isolated points.
Those edges that separate whole problem region from other part of the plane, where no field is calculated, constitutes the outward boundary of the region. Other edges constitute inner boundaries.

Specific Analyses Description