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, | Formula and Description |
| Force
qfInt_Force |
\[ \mathbf F = \oint (σ·\mathbf n)ds\]
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 |
\[ \mathbf F = \frac{1}{2} \oint \mathbf r × (σ·\mathbf n)ds\]
Total torque of the forces acting on a particular volume, where r is a radius vector of the point of integration.
|
| Lengthen
qfInt_lengthen |
\[ ΔL = \oint (δ·\mathbf t)dl\]
Relative lengthen of the contour. |