Integral calculation

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In addition to the local field values QuickField can calculate integral parameters, such as electric charge, mechanical force and electric field energy. Integration region for the volume integrals includes the selected bodies, and for the surface integrals - the selected faces or the planar section of the 3D model.

In the electrostatic problems the following integrals may be calculated:

• The electric charge of the body
  q = _s∮ D·n ds
  is calculated as an integral of the electric displacement vector D flux through the closed surface, surrounding the body.
• Electric field energy
  W = ½_v∫ (E·D) dV
  is calculated as an integral of the field energy density in the body volume.
• Mechanical force acting on the body from the electric field
  F = ½_s∮ (E(D·n) + D(E·n) - n(E·D)) ds
  is calculated as an integral of the Maxwell tensor flux across the closed surface, surrounding the body.

In the DC conduction problems the following integrals may be calculated:

1. Current through the surface
   I = _s∮J·ds
   is calculated as the integral of the current density J through the closed surface, surrounding the body.

In the heat transfer problems the following integrals may be calculated:

1. Thermal flux through the specified surface
   Φ = _s∮λ·gradT·ds
   is calculated as the integral of the thermal flux density through the closed surface, surrounding the body.

Integration area of the surface integrals, calculated over the planar section includes the cross-sections of all the visible bodies which were cut by the plane. Turning their visibility on/off will control the integration area. Integration results are shown in the Integral Calculator tab of the 2D section window.

Integral calculation mode may be turned on by pressing the button on the toolbar, or by selecting the pane Integral Calculator from the field calculator dialog, or by using the command Integral Values from the View menu. This mode is indicated by the cursor shape .

All available by the moment integral values are calculated by integration across the selected bodies (or their external surfaces). All changes in this selection invoke automatic calculation of the new integral values.