Static Analysis of Rotating Solid Disc of Constant Thickness (surface)

Static Analysis of Rotating Solid Disc of Constant Thickness

Let us consider a disc of radius R and thickness h (see figure).

Rotating Solid Disc of Constant Thickness

In analysis we consider only 1/4 th part of the disc with application of symmetry conditions at the corresponding edges (restraint of displacements in the direction of normal to plane of an edge & restraint of rotations that are not around the normal).
The disc is subjected to the centrifugal force F = ρω2R, where ρ - is the mass of the unit volume of the disc's material, ω - angular velocity of rotation.

Rotating Solid Disc of Constant Thickness, the finite element model with applied loads and restraints

The finite element model with applied loads and restraints

Input data and analytical solution can be viewed here.

After carrying out calculation with the help of AutoFEM, the following results are obtained:

Table 1.Parameters of finite element mesh

Finite Element Type	Number of nodes	Number of finite elements
linear triangle	829	1546

Table 2. Result "Displacement, magnitude"*

Numerical Solution Displacement w*, m	Analytical Solution Displacement w, m	Error δ = 100%* \|w* - w\| / \|w\|
5.8028E-005	5.7430E-005	1.04

Result "Displacement, magnitude" of finite element modelling of rotating disk

Table 3. Result "Equivalent Stress"*

Numerical Solution Stress σ*, Pa	Analytical Solution Stress σ, Pa	Error δ = 100% * \|σ* - σ\| / \|σ\|
6.0078E+007	6.0111E+007	0.05

Result "Equivalent Stress" of finite element modelling of rotating disk

*The results of numerical tests depend on the finite element mesh and may differ slightly from those given in the tables.