Release 11.0 Documentation for ANSYS
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| Matrix or Vector | Shape Functions | Integration Points |
|---|---|---|
| Stiffness and Mass Matrices; and Thermal and Pressure Load Vector | (Equation 12–4) and (Equation 12–5) | None |
| Stress Stiffness Matrix | (Equation 12–5) | None |
| Load Type | Distribution |
|---|---|
| Element Temperature | Linear thru thickness and along length |
| Nodal Temperature | Constant thru thickness, linear along length |
| Pressure | Linear along length |
The element stiffness matrix in element coordinates is (Przemieniecki(28)):
| (14–1) |
where:
| A = cross-section area (input as AREA on R command) |
| E = Young's modulus (input as EX on MP command) |
| L = element length |
| I = moment of inertia (input as IZZ on R command) |
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| G = shear modulus (input as GXY on MP command) |
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| Fs = shear deflection constant (input as SHEARZ on R command) |
The consistent element mass matrix (LUMPM,OFF) in element coordinates is (Yokoyama(167)):
| (14–2) |
where:
| ρ = density (input as DENS on MP command) |
| m = added mass per unit length (input as ADDMAS on R command) |
| εin = prestrain (input as ISTRN on R command) |
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The lumped element mass matrix (LUMPM,ON) in element coordinates is:
| (14–3) |
The element pressure load vector in element coordinates is:
| (14–4) |
For uniform lateral pressure,
| (14–5) |
| (14–6) |
| (14–7) |
where:
| P = uniform applied pressure (units = force/length) (input on SFE command) |
Other standard formulas (Roark(48)) for P1 through P6 are used for linearly varying loads, partially loaded elements, and point loads.
The centroidal stress at end i is:
| (14–8) |
where:
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| Fx,i = axial force (output as FORCE) |
The bending stress is
| (14–9) |
where:
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| Mi = moment at end i |
| t = thickness of beam in element y direction (input as HEIGHT on R command) |
The presumption has been made that the cross-section is symmetric.
