You can display the results for solids graphically using the Solids navigator category. You find the numerical results of solids in the Results by Solid table category.
Deformations
The Results by Solid in Table image shows the table with deformations of the boundary surfaces. Displacements and rotations are displayed in the surface grid points (see Surfaces chapter).
The deformations have the following meaning:
|u| | Absolute value of total displacement |
uX | Displacement in direction of global axis X |
uY | Displacement in direction of global axis Y |
uZ | Displacement in direction of global axis Z |
φX | Rotation about global axis X |
φY | Rotation about global axis Y |
φZ | Rotation about global axis Z |
Stresses
In the navigator, define the stresses to be displayed on the boundary surfaces of solids. The table lists the stresses of these surfaces according to the specifications set in the Result Table Manager .
The solid stresses are divided into the following categories:
- Basic Stresses
- Principal Stresses
- Equivalent Stresses
Unlike surface stresses, solid stresses cannot be described by simple equations. The basic stresses σx, σy, and σz including the shear stresses τyz, τxz, and τxy are determined directly by the computation kernel.
If a cube with the edge lengths dx, dy, and dz is cut out of a multiaxial stressed object, the stresses available in each cube surface can be decomposed into normal and shear stresses. If neither the spatial force nor stress differences on parallel surfaces are considered, the stress condition in the cube's local coordinate system can be described by nine stress components.
The matrix of the stress tensor is the following:
The principal stresses σ1, σ2, and σ3 result from the eigenvalues of the tensor as follows:
E | 3x3 unit matrix |
The maximum shear stress τmax is determined according to Mohr's circle:
The equivalent stresses σeqv according to von Mises can be determined by two equivalent formulas.
To determine the equivalent stress σeqv according to Tresca , the differences from the principal stresses are examined in order to determine the maximum value.
The equivalent stress σeqv according to Rankine is determined from the greatest absolute values of the principal stresses.
To determine the equivalent stress σeqv according to Bach , the principal stress differences are examined, taking into account the Poisson's ratio ν, in order to determine the maximum value.
Strains
In the navigator, define the strains to be displayed on the boundary surfaces of solids. The table lists the strains of these surfaces according to the specifications set in the Result Table Manager .
The solid strains are divided into the following categories:
- Basic Total Strains
- Principal Total Strains
- Equivalent Total Strains
The basic total strains including shear strains are determined directly by the computation kernel. The general definition of the tensor for the spatial strain state is as follows:
The elements of the tensor are defined as follows:
The principal total strains ε1, ε2, and ε3 are determined from the basic strains.
The equivalent total strains εeqv are determined according to four different stress hypotheses as follows.
R | Matrix (see below) |
R | Matrix (see below) |
R | Matrix (see below) |