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Subsections


IX.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 IX.C.1 to IX.C.10. The following notations have been adopted:

In the description of Results, one makes the distinction between Real and Complex Results (section IX.C.1 and IX.C.2 respectively).


IX.C.1 Real Results

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


Table IX.C.1: Nodal Results
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


Table IX.C.2: Grid Points Forces.
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


Table IX.C.3: Element General Results.
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


Table IX.C.4: Beam element Results.
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


Table IX.C.5: Bush, Gap and Scalar elements specific Results.
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


Table IX.C.6: Shell elements specific Results.
Result Target Tensor
Name Entities Type
``Curvature Tensor'' E, EN T
``Shell Forces'' E, EN T
``Shell Moments'' E, EN T


Table IX.C.7: Results specific to shear panels.
Result Target Tensor
Name Entities Type
``Shear Panel Strain, Max'' E, EN T
``Shear Panel Strain, Average'' E, EN T
``Shear Panel Stress, Max'' E, EN T
``Shear Panel Stress, Average'' E, EN T


Table: Composite Results, layered failure indices (10).
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


Table: Composite Results, critical ply failure indices (10).
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


Table: Composite Results, critical plies (10).
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


Table IX.C.11: Element Thermal Results.
Result Target Tensor
Name Entities Type
``Temperature Gradient'' E, EN V
``Conductive Heat Flux'' E, EN V
``Specific Heat Energy'' E, EN S
``Applied Heat Flux'' E, EN S

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

  1. ``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:

       $\displaystyle \mbox{\boldmath$F$}$$\displaystyle =\left(
\begin{array}{ccc}
F_{xx} & F_{xy} & F_{xz} \\
F_{xy} & 0 & 0 \\
F_{xz} & 0 & 0
\end{array}
\right)\ ,
\ \ \ \ \ $   $\displaystyle \mbox{\boldmath$M$}$$\displaystyle =\left(
\begin{array}{ccc}
M_{xx} & M_{xy} & M_{xz} \\
M_{xy} & 0 & 0 \\
M_{xz} & 0 & 0
\end{array}
\right)\ .
$

    There is an approximation for the moments above because the torsional component is calculated wrt cross-section shear centre, and bending components are calculated wrt cross-section centre of inertia.

    One assumes that the beam forces are calculated from the Cauchy stress tensor components as follows:

    $\displaystyle \left\{F\right\}
=\left(\begin{array}{c}
F_{xx} \\
F_{xy} ...
...in{array}{c}
\sigma_{xx} \\
\tau_{xy} \\
\tau_{xz}
\end{array}\right)$   d$\displaystyle \Omega\ .
$

    In which $ \Omega$ is the surface defined by a cross-section through the beam orthogonal to beam longitudinal axis. (One presumes here that the beam longitudinal direction corresponds to ``$ x$ '' axis.) Similarly, one assumes that the bending moments tensor is calculated from the Cauchy stress tensor components as follows:

    $\displaystyle \left\{M\right\}
=\left(\begin{array}{c}
M_{xx} \\
M_{xy} ...
...z_0\right)\sigma_{xx} \\
-\left(y-y_0\right)\sigma_{xx}
\end{array}\right)$   d$\displaystyle \Omega\ .
$

    In which $ y$ and $ z$ are the components of coordinates in $ \Omega$ section, $ y_0$ and $ z_0$ correspond to the coordinates of center of gravity of the section, and $ y_C$ and $ z_C$ correspond to the shear center coordinates. Note also that ``Beam Forces'' and ``Beam Moments'' are Results that correspond to most 1D elements. (Bars, beams, rods, bushing elements...). However spring elements do not produce ``Beam Forces'' and ``Beam Moments''.

    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

    $\displaystyle \left\{F\right\}
=\left(\begin{array}{c}
F_{xx} \\
F_{xy} \\
F_{xz}
\end{array}\right)$    and $\displaystyle \left\{M\right\}
=\left(\begin{array}{c}
M_{xx} \\
M_{xy} \\
M_{xz}
\end{array}\right)
$

    correspond to the forces and moments that must be applied on $ +x$ side of the beam. On the $ -x$ side of the beam the components of these vectors must be multiplied by -1.

  2. ``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''.

  3. 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.)

  4. ``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:

       $\displaystyle \mbox{\boldmath$F$}$$\displaystyle =\left(
\begin{array}{ccc}
F_{xx} & F_{xy} & Q_{xz} \\
F_{...
...{yy} & Q_{yz} \\
Q_{xz} & Q_{yz} & 0
\end{array}
\right)\ ,
\ \ \ \ \ $   $\displaystyle \mbox{\boldmath$M$}$$\displaystyle =\left(
\begin{array}{ccc}
M_{xx} & M_{xy} & M_{xz} \\
M_{xy} & 0 & 0 \\
M_{xz} & 0 & 0
\end{array}
\right)\ .
$

    (Symbol $ Q$ has been used for the out-of-plane shear force.)

    One assumes that the shell in-plane forces are calculated from the Cauchy stress tensor components as follows:

    $\displaystyle \left\{N\right\}
=\left(\begin{array}{c}
N_{xx} \\
N_{yy} ...
...{array}{c}
\sigma_{xx} \\
\sigma_{yy} \\
\tau_{xy}
\end{array}\right)$   d$\displaystyle z\ .
$

    Similarly, one assumes that the bending moments tensor is calculated using the distribution through the thickness of the Cauchy stress tensor components as follows:

    $\displaystyle \left\{M\right\}
=\left(\begin{array}{c}
M_{xx} \\
M_{yy} ...
...{array}{c}
\sigma_{xx} \\
\sigma_{yy} \\
\tau_{xy}
\end{array}\right)$   d$\displaystyle z\ .
$

    This is a usual convention for shell elements. For example, this is generally the convention used to present the theory of classical laminate analysis. When a component of the bending tensor is positive, the corresponding component is positive on the upper surface of the shell, and negative on the other face.

  5. The shear components of strain tensors Results stored in FeResPost are the $ \epsilon_{ij}=\gamma_{ij}/2$ .

  6. The shell curvature tensor is defined as follows:

    $\displaystyle \left\{\kappa\right\}
=\left(\begin{array}{c}
\kappa_{xx} \\ ...
...c}
\epsilon_{xx} \\
\epsilon_{yy} \\
\epsilon_{xy}
\end{array}\right)$   d$\displaystyle z
=\left(\begin{array}{c}
w^0_{,xx} \\
w^0_{,yy} \\
w^0_{,xy}
\end{array}\right)\ .
$

    Here again, a positive curvature means that the corresponding component of strain tensor is in tension on the upper face, and in compression on the lower face of the shell.

  7. 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.

  8. Gap elements produce various results. Results are vectorial or tensorial and:

  9. 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.

  10. 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...

  11. 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.


IX.C.2 Complex Results

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


Table IX.C.12: Complex Nodal Results.
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


Table IX.C.13: Element Complex General Results.
Result Target Tensor
Name Entities Type
``Strain Tensor (RI)'' (5) E, EN, EL, ENL T
``Stress Tensor (RI)'' E, EN, EL, ENL T
``Strain Tensor (MP)'' (5) E, EN, EL, ENL T
``Stress Tensor (MP)'' E, EN, EL, ENL T


Table IX.C.14: Beam element Complex Results.
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


Table IX.C.15: Bush, Gap and Scalar elements specific Complex Results.
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


Table IX.C.16: Shell elements specific Complex Results.
Result Target Tensor
Name Entities Type
``Curvature Tensor (RI)'' E, EN T
``Shell Forces (RI)'' E, EN T
``Shell Moments (RI)'' E, EN T
``Curvature Tensor (MP)'' E, EN T
``Shell Forces (MP)'' E, EN T
``Shell Moments (MP)'' E, EN T


next up previous contents index
Next: IX.D Predefined criteria Up: IX. Appendices Previous: IX.B Coordinate system transformations   Contents   Index
FeResPost 2017-05-28