X.C Results characteristics

One presents in this Appendix the different Results that are pre-defined in FeResPost. All these Results can be read from Results files produced by different finite element solvers described in Part III. The characteristics of the different Results are described in Tables X.C.1 to X.C.10. The following notations have been adopted:

- The entities (Result keys) to which values are attached are noted:
- ``E'' if Result values are attached to element centers,
- ``N'' if Result values are attached to nodes,
- ``EL'' if Result values are attached to element centers and are layered,
- ``EN'' if Result values are attached to element corners,
- ``ENL'' if Result values are attached to element corners and are layered.

- The tensoriality of Results is noted as follows:
- ``S'' means that the Result has scalar values,
- ``V'' means that the Result has vectorial values,
- ``T'' means that the Result has tensorial values.

X.C.1 Real Results

A summary of the Results that can be read is given in TableX.C.1 to X.C.10.

Result | Target | Tensor |

Name | Entities | Type |

``Coordinates'' | N | V |

``Displacements, Translational'' | N | V |

``Displacements, Rotational'' | N | V |

``Displacements, Scalar'' | N | S |

``Velocities, Translational'' | N | V |

``Velocities, Rotational'' | N | V |

``Velocities, Scalar'' | N | S |

``Accelerations, Translational'' | N | V |

``Accelerations, Rotational'' | N | V |

``Accelerations, Scalar'' | N | S |

``Applied Loads, Forces'' | N | V |

``Applied Loads, Moments'' | N | V |

``MPC Forces, Forces'' | N | V |

``MPC Forces, Moments'' | N | V |

``MPC Forces, Scalar'' | N | S |

``SPC Forces, Forces'' | N | V |

``SPC Forces, Moments'' | N | V |

``SPC Forces, Scalar'' | N | S |

``Reaction Forces, Forces'' | N | V |

``Reaction Forces, Moments'' | N | V |

``Reaction Forces, Scalar'' | N | S |

``Contact, Contact Pressure'' | N | S |

``Contact, Friction Stress'' | N | S |

``Contact, Nodal Distance'' | N | S |

``Contact, Normal Distance'' | N | S |

``Temperature'' | N | S |

``Temperature Variation Rate'' | N | S |

Result | Target | Tensor |

Name | Entities | Type |

``Grid Point Forces, Internal Forces'' | EN | V |

``Grid Point Forces, Internal Moments'' | EN | V |

``Grid Point Forces, MPC Forces'' | EN | V |

``Grid Point Forces, MPC Moments'' | EN | V |

``Grid Point Forces, SPC Forces'' | EN | V |

``Grid Point Forces, SPC Moments'' | EN | V |

``Grid Point Forces, Applied Forces'' | EN | V |

``Grid Point Forces, Applied Moments'' | EN | V |

``Grid Point Forces, Reaction Forces'' | EN | V |

``Grid Point Forces, Reaction Moments'' | EN | V |

``Grid Point Forces, Total Forces'' | EN | V |

``Grid Point Forces, Total Moments'' | EN | V |

Result | Target | Tensor |

Name | Entities | Type |

``Mechanical Strain Tensor'' (5) | E, EN, EL, ENL | T |

``Strain Tensor'' (5) | E, EN, EL, ENL | T |

``Stress Tensor'' | E, EN, EL, ENL | T |

``Effective Plastic Strain'' (10) | E, EN, EL, ENL | S |

``Effective Creep Strain'' (10) | E, EN, EL, ENL | S |

``Element Strain Energy'' | E | S |

``Element Strain Energy (Density)'' | E | S |

``Element Strain Energy (Percent of Total)'' | E | S |

``Element Kinetic Energy'' | E | S |

``Element Kinetic Energy (Density)'' | E | S |

``Element Kinetic Energy (Percent of Total)'' | E | S |

``Element Energy Loss'' | E | S |

``Element Energy Loss (Density)'' | E | S |

``Element Energy Loss (Percent of Total)'' | E | S |

Result | Target | Tensor |

Name | Entities | Type |

``Beam Axial Strain for Axial Loads'' (7) | E, EN | S |

``Beam Axial Strain for Bending Loads'' (7) | E, EN | S |

``Beam Axial Strain for Total Loads'' (7) | E, EN | S |

``Beam Shear Strain for Torsion Loads'' (7) | E, EN | S |

``Beam Shear Strain for Total Loads'' (7) | E, EN | S |

``Beam Axial Stress for Axial Loads'' (7) | E, EN | S |

``Beam Axial Stress for Bending Loads'' (7) | E, EN | S |

``Beam Axial Stress for Total Loads'' (7) | E, EN | S |

``Beam Shear Stress for Torsion Loads'' (7) | E, EN | S |

``Beam Shear Stress for Total Loads'' (7) | E, EN | S |

``Beam Forces'' (1) | E, EN | T |

``Beam Moments'' (1) | E, EN | T |

``Beam Warping Torque'' | E, EN | T |

``Beam Deformations'' (2) | E, EN | T |

``Beam Velocities'' (2) | E, EN | T |

Result | Target | Tensor |

Name | Entities | Type |

``Gap Slips'' (8) | E, EN | T |

``Bush Forces Stress Tensor'' (9) | E | T |

``Bush Forces Strain Tensor'' (9) | E | T |

``Bush Moments Stress Tensor'' (9) | E | T |

``Bush Moments Strain Tensor'' (9) | E | T |

``Bush Plastic Strain'' | E, EN | S |

``Spring Scalar Strain'' | E, EN | S |

``Spring Scalar Stress'' | E, EN | S |

``Spring Scalar Forces'' (3) | E, EN | S |

Result | Target | Tensor |

Name | Entities | Type |

``Composite Failure Index, Tsai-Hill Version 1'' | EL, ENL | S |

``Composite Failure Index, Tsai-Hill Version 2'' | EL, ENL | S |

``Composite Failure Index, Tsai-Hill Version 3'' | EL, ENL | S |

``Composite Failure Index, Tsai-Wu'' | EL, ENL | S |

``Composite Failure Index, Hoffman'' | EL, ENL | S |

``Composite Failure Index, Hashin Version 1'' | EL, ENL | S |

``Composite Failure Index, Hashin Version 2'' | EL, ENL | S |

``Composite Failure Index, Hashin Version 3'' | EL, ENL | S |

``Composite Failure Index, Maximum Strain'' | EL, ENL | T (11) |

``Composite Failure Index, Maximum Strain, CompMax'' | EL, ENL | S (11) |

``Composite Failure Index, Maximum Stress'' | EL, ENL | T (11) |

``Composite Failure Index, Maximum Stress, CompMax'' | EL, ENL | S (11) |

``Composite Failure Index, Stress Ratio'' | EL, ENL | S |

``Composite Failure Index, Strain Ratio'' | EL, ENL | S |

``Composite Failure Index, Rice and Tracey'' | EL, ENL | S |

``Composite Failure Index, Interlaminar Shear Stress'' | EL, ENL | S |

Result | Target | Tensor |

Name | Entities | Type |

``Composite Critical Ply Failure Index, Tsai-Hill Version 1'' | E, EN | S |

``Composite Critical Ply Failure Index, Tsai-Hill Version 2'' | E, EN | S |

``Composite Critical Ply Failure Index, Tsai-Hill Version 3'' | E, EN | S |

``Composite Critical Ply Failure Index, Tsai-Wu'' | E, EN | S |

``Composite Critical Ply Failure Index, Hoffman'' | E, EN | S |

``Composite Critical Ply Failure Index, Hashin Version 1'' | E, EN | S |

``Composite Critical Ply Failure Index, Hashin Version 2'' | E, EN | S |

``Composite Critical Ply Failure Index, Hashin Version 3'' | E, EN | S |

``Composite Critical Ply Failure Index, Maximum Strain, CompMax'' | E, EN | S (11) |

``Composite Critical Ply Failure Index, Maximum Stress, CompMax'' | E, EN | S (11) |

``Composite Critical Ply Failure Index, Stress Ratio'' | E, EN | S |

``Composite Critical Ply Failure Index, Strain Ratio'' | E, EN | S |

``Composite Critical Ply Failure Index, Rice and Tracey'' | E, EN | S |

``Composite Critical Ply Failure Index, Interlaminar Shear Stress'' | E, EN | S |

Result | Target | Tensor |

Name | Entities | Type |

``Composite Critical Ply, Tsai-Hill Version 1'' | E, EN | S |

``Composite Critical Ply, Tsai-Hill Version 2'' | E, EN | S |

``Composite Critical Ply, Tsai-Hill Version 3'' | E, EN | S |

``Composite Critical Ply, Tsai-Wu'' | E, EN | S |

``Composite Critical Ply, Hoffman'' | E, EN | S |

``Composite Critical Ply, Hashin Version 1'' | E, EN | S |

``Composite Critical Ply, Hashin Version 2'' | E, EN | S |

``Composite Critical Ply, Hashin Version 3'' | E, EN | S |

``Composite Critical Ply, Maximum Strain, CompMax'' | E, EN | S (11) |

``Composite Critical Ply, Maximum Stress, CompMax'' | E, EN | S (11) |

``Composite Critical Ply, Stress Ratio'' | E, EN | S |

``Composite Critical Ply, Strain Ratio'' | E, EN | S |

``Composite Critical Ply, Rice and Tracey'' | E, EN | S |

``Composite Critical Ply, Interlaminar Shear Stress'' | E, EN | S |

In the following remarks about the information given in Tables X.C.1 to X.C.10, one assumes that the international unit system is used.

- ``Beam Forces'' and ``Beam Moments'' are assumed in FeResPost
to be tensorial Results expressed in N or Nm respectively. However
several components of the tensor are systematically nil.
The non-zero components are:
One assumes that the beam forces are calculated from the Cauchy stress tensor components as follows:

**d****d**These conventions ensure that beam forces and moments behave like real order 2 tensors when transformation of coordinates systems are performed. The vectorial forces and moments at the two extremities are easily obtained. Vectors

**and** - ``Beam Deformations'' is a tensorial Result corresponding to the
difference of displacements of grids B and A of the beam element. The
tensor is expressed in element axes. The ``Beam Velocities'' Result
is the time derivative of the ``Beam Deformations''.
- Spring forces are scalar. The units depend on the connected
components: one has N for displacements and Nm for rotations.
(Of course, it is also possible to define springs connecting
translational and rotational degrees of freedom, but it is generally
an error.)
- ``Shell Forces'' and ``Shell Moments'' are tensorial Results
expressed in N/m or N respectively. These Results contain all
the force and moment tensors produced by 2D elements. The non-zero
components are:
One assumes that the shell in-plane forces are calculated from the Cauchy stress tensor components as follows:

**d****d** - The shear components of strain tensors Results stored in FeResPost
are the
.
- The shell curvature tensor is defined as follows:
**d** - Beam stresses and strains are always scalar Results corresponding
either to the axial component, or to the norm of the shear components.
Depending on the type of element, the axial stress may be calculated from
the axial or bending loads, or to involve both contributions.
- Gap elements produce various results. Results are vectorial
or tensorial and:
- Gap forces results are stored in ``Beam Forces'' tensorial Result as indicated in remark 1. The value of the axial component is multiplied by ``-1.0'', because it is a compression component.
- ``Beam Deformations'' and ``Beam Velocities'' are tensorial Results containing the relative displacements or velocities of end nodes B and A in element coordinate system.
- ``Gap Slips'' is identical to ``Beam Deformations'' except that the axial component is set to ``0.0''.

- Bushing elements produce Stress and Strain tensors obtained by
multiplying the Beam Forces and Beam Moments by specified constants. These
constants are by default set to 1. Therefore, stresses and strains have
often values identical to the forces and moments. Note that the meaning
of modifications of coordinate systems for bush stresses and strains have
may be discussed. This is particularly so for stresses and strains
corresponding to moments.
- Composite Results have non-linear dependence on the primary unknowns
(displacements). Therefore, composite Results obtained by linear
combination of elementary Results are false. This remark applies to all
non-linear Results, plastification Results...
- Actually ``Maximum Strain'' and ``Maximum Stress'' composite Results
are not tensorial because each component is a separate scalar Result. So
no modification of coordinate system can be done for these Results.
The corresponding ``CompMax'' scalar Results are obtained by selecting the maximum failure index value among the six components.

X.C.2 Complex Results

The Complex Result types are summarized in Tables X.C.12 to X.C.16.

Result | Target | Tensor |

Name | Entities | Type |

``Displacements (RI), Translational'' | N | V |

``Displacements (RI), Rotational'' | N | V |

``Displacements (MP), Translational'' | N | V |

``Displacements (MP), Rotational'' | N | V |

``Velocities (RI), Translational'' | N | V |

``Velocities (RI), Rotational'' | N | V |

``Velocities (MP), Translational'' | N | V |

``Velocities (MP), Rotational'' | N | V |

``Accelerations (RI), Translational'' | N | V |

``Accelerations (RI), Rotational'' | N | V |

``Accelerations (MP), Translational'' | N | V |

``Accelerations (MP), Rotational'' | N | V |

``Applied Loads (RI), Forces'' | N | V |

``Applied Loads (RI), Moments'' | N | V |

``Applied Loads (MP), Forces'' | N | V |

``Applied Loads (MP), Moments'' | N | V |

``MPC Forces (RI), Forces'' | N | V |

``MPC Forces (RI), Scalar'' | N | S |

``MPC Forces (MP), Forces'' | N | V |

``MPC Forces (MP), Scalar'' | N | S |

``SPC Forces (RI), Forces'' | N | V |

``SPC Forces (RI), Moments'' | N | V |

``SPC Forces (MP), Forces'' | N | V |

``SPC Forces (MP), Moments'' | N | V |

Result | Target | Tensor |

Name | Entities | Type |

``Beam Axial Strain for Axial Loads (RI)'' (7) | E, EN | S |

``Beam Axial Strain for Bending Loads (RI)'' (7) | E, EN | S |

``Beam Axial Strain for Total Loads (RI)'' (7) | E, EN | S |

``Beam Shear Strain for Torsion Loads (RI)'' (7) | E, EN | S |

``Beam Axial Strain for Axial Loads (MP)'' (7) | E, EN | S |

``Beam Axial Strain for Bending Loads (MP)'' (7) | E, EN | S |

``Beam Axial Strain for Total Loads (MP)'' (7) | E, EN | S |

``Beam Shear Strain for Torsion Loads (MP)'' (7) | E, EN | S |

``Beam Axial Stress for Axial Loads (RI)'' (7) | E, EN | S |

``Beam Axial Stress for Bending Loads (RI)'' (7) | E, EN | S |

``Beam Axial Stress for Total Loads (RI)'' (7) | E, EN | S |

``Beam Shear Stress for Torsion Loads (RI)'' (7) | E, EN | S |

``Beam Axial Stress for Axial Loads (MP)'' (7) | E, EN | S |

``Beam Axial Stress for Bending Loads (MP)'' (7) | E, EN | S |

``Beam Axial Stress for Total Loads (MP)'' (7) | E, EN | S |

``Beam Shear Stress for Torsion Loads (MP)'' (7) | E, EN | S |

``Beam Forces (RI)'' (1) | E, EN | T |

``Beam Moments (RI)'' (1) | E, EN | T |

``Beam Warping Torque (RI)'' | E, EN | T |

``Beam Forces (MP)'' (1) | E, EN | T |

``Beam Moments (MP)'' (1) | E, EN | T |

``Beam Warping Torque (MP)'' | E, EN | T |

Result | Target | Tensor |

Name | Entities | Type |

``Bush Forces Stress Tensor (RI)'' (9) | E | T |

``Bush Forces Strain Tensor (RI)'' (9) | E | T |

``Bush Moments Stress Tensor (RI)'' (9) | E | T |

``Bush Moments Strain Tensor (RI)'' (9) | E | T |

``Bush Forces Stress Tensor (MP)'' (9) | E | T |

``Bush Forces Strain Tensor (MP)'' (9) | E | T |

``Bush Moments Stress Tensor (MP)'' (9) | E | T |

``Bush Moments Strain Tensor (MP)'' (9) | E | T |

``Spring Scalar Strain (RI)'' | E, EN | S |

``Spring Scalar Stress (RI)'' | E, EN | S |

``Spring Scalar Forces (RI)'' (3) | E, EN | S |

``Spring Scalar Strain (MP)'' | E, EN | S |

``Spring Scalar Stress (MP)'' | E, EN | S |

``Spring Scalar Forces (MP)'' (3) | E, EN | S |