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Integral quantities in stress analysis

For the stress analysis problems, the most interesting integral values are: force, torque and lengthen.
The following notations are used in formulas:

σ – the stress tensor.

Name,
ActiveField constant

Formula and Description

Force

qfInt_Force

F = _s∮ (σ·n)ds

Total force acting on a particular volume. The integral is evaluated over the boundary of the volume, and n denotes the vector of the outward unit normal.

Torque

qfInt_Torque

T = 1/2 ∮r × (σ·n)ds

Total torque of the forces acting on a particular volume, where r is a radius vector of the point of integration.
The torque vector is parallel to z-axis in the planar case, and is identically equal to zero in the axisymmetric one. The torque is considered relative to the origin of the coordinate system. The torque relative to any other arbitrary point can be obtained by adding extra term of [F×r₀], where F is the total force and r₀ is the radius vector of the point.

Lengthen

qfInt_lengthen

ΔL = ∮(δ·t)dl

Relative lengthen of the contour.