OPTUMG2/Results

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1 GENERAL INFORMATION

The results of the analyses can be visualized using the tools under Results ribbon. Plots of both variables associated with solid domains (stresses, displacements, etc) and variables associated with structural elements (bending moments, displacements, etc) may be plotted. Detailed point information about either category of variables can be obtained by mouse click anywhere in the domain (see figure below).

resultsclick.png
Figure 1.1: Results associated with solid domains (top) and with structural elements (bottom). The white circles indicated the position (determined by mouse click) corresponding to the results shown in the property window on the right.

2 SOLIDS

2.1 Stresses

In OptumG2, stress sets are available: Initial Stresses and Final Stresses. The former set are the initial stresses at the beginning of the analysis while the latter are the stresses that follow as a result of the analysis. Depending on the settings of a given analysis, the initial stresses may be calculated automatically or they may be transferred from a previous stage. In the latter case, the stresses are mapped from one mesh to another which may induce some slight artifacts. For example, the mere process of mapping stresses from one mesh to another may induce artificial deformations. However, in far most cases these are several orders of magnitude less than the actual deformations resulting from the application of load, removal of material, etc.
Following Terzhagi’s principle for fluid saturated media, the total stress is the sum of the effective stress, and the pressure of the pore fluid:

where

  • in plane strain.

Depending on the type of analysis, both these types of stresses may be available in the Initial and Final Stresses results sets. The quantities in the two sets are:

Total Stresses

Variable Unit Description
, , kPa Total normal stresses in the , , and directions
kPa Total shear stress on - planes
kPa Principal total stresses ordered so that . Hence, for problems
where both principal stresses are compressive, we have
kPa Mohr-Coulomb measure of mean total stress
kPa Mohr-Coulomb measure of deviatoric total stress
kPa Hydrostatic total pressure and Drucker-Prager measure of total
mean stress .
kPa Drucker-Prager measure of deviatoric stress,
vectors Vector plot showing direction and magnitude of principal total
stresses, red and in blue

Effective Stresses

Variable Unit Description
, , kPa Effective normal stresses in the , , and directions
kPa Effective shear stress on - planes. Equal to the total shear stress,
kPa Principal effective stresses ordered so that . Hence, for
problems where both principal stresses are compressive, we have
kPa Mohr-Coulomb measure of mean effective stress
kPa Mohr-Coulomb measure of deviatoric effective stress
kPa Hydrostatic total pressure and Drucker-Prager measure of mean total stress,
.
kPa Drucker-Prager measure of deviatoric stress,
vectors Vector plot showing direction and magnitude of principal effective stresses,
red and in blue

Undrained Shear

Variable Unit Description
kPa Undrained shear strength according to the Tresca criterion .
Available under Initial Stresses for stages with Time Scope = Short Term.

Note: for Limit Analysis and Strength Reduction only Total Stresses are available in the Results ribbon even though both steady state and excess pore pressures may be part of the calculation.

2.2 Strains

Strains derive from displacements assuming infinitesimal deformations. In plane strain we have

where are the strains and are the displacements.
In general, a distinction must be made between elastic and plastic strains. These add up to the total strains:

where

In OptumG2, the following quantities related to total and plastic strains are available in the Results ribbon:

Total Strains

Variable Unit Description
, , Total normal strains in the , , and directions
Total shear strains on - planes
Principal total strains ordered so that . Hence, for problems where
both principal strains are compressive, we have
Volumetric total strain,
Deviatoric total strain
vectors Vector plot showing direction and magnitude of principal total strain,
in red and in blue

Plastic Strains

Variable Unit Description
, , Plastic normal strains in the , , and directions
Plastic shear strains on - planes
Principal plastic strains ordered so that . Hence, for problems
where both principal strains are compressive, we have
Volumetric plastic strain,
Deviatoric plastic strain
vectors Vector plot showing direction and magnitude of principal total strain,
in red and in blue

Note: for Limit Analysis and Strength Reduction, the difference between total and plastic strains is immaterial. In such cases, only Total Strains are available in the Results ribbon.  

2.3 Displacements

OptumG2 operates with two types of displacements: Stage Displacements and Total Displacements. The former are the displacements incurred in the given stage while the latter are the accumulation of former. It should be noted that the small deformation assumption is used throughout. As such, all operations involving the removal of material, addition of structural elements, etc. are referenced to the original geometry, i.e. neglecting the effects of the displacements on the geometry. As an example, if an anchor is added to a sheet pile wall that has already undergone displacements, the anchor should be added with reference to the original geometry, disregarding the fact that this has changed slightly as a result of the deformations.
The following displacement quantities are available in the Results ribbon:

Stage Displacements

Variable Unit Description
m Stage displacements in the -direction
m Stage displacements in the -direction
vector Stage displacement vectors

Total Displacements

Variable Unit Description
m Total displacements in the -direction
m Total displacements in the -direction
vector Total displacement vectors

Note: for Limit Analysis and Strength Reduction, the difference between total and stage displacements is immaterial. In such cases, only Total Displacements are available in the Results ribbon.

2.4 Plasticity

This results set contains various quantities related to plasticity and plastic deformations.
Recall that the stress are limited by the yield function:

where is the yield function, are the effective stresses and is a set of stress-like hardening variables.
Further recall that the plastic strain rates follow from the flow rule:

where are the plastic strain increments, is the plastic potential (which may or may not be equal to the yield function ), and is the plastic multiplier. Assuming that the magnitude of is independent of, or insensitive to, the magnitude of (which is usually the case), the plastic multiplier is a direct measure of the magnitude of the plastic strain increment.
Another central quantity to plastic deformation is the dissipation:

Again, this quantity is a direct measure of the intensity of the plastic straining over a volume .
While the dissipation often is a good indicator of the intensity of plastic deformation, it does occasionally fail in this regard. In particular, for purely frictional materials with an associated flow rule, it may be shown that . In such cases, the shear dissipation provides a more useful indicator of plasticity. This quantity is defined as:

where

are the deviatoric stress and strain respectively ( and being the hydrostatic pressure and volumetric plastic strain respectively).
The following quantities related to plasticity are available in the Results ribbon:

Plasticity  

Variable Unit Description
Yield Function kPa See discussion above
Plastic Multiplier See discussion above
Total Dissipation kJ See discussion above
Shear Dissipation kJ See discussion above

Note: in Limit Analysis and Strength Reduction, the total strains are equal to the incremental plastic strains which are used in place of in the above.

2.5 Pore Pressures

Two types of pore pressures are accounted for in OptumG2 those resulting from seepage and those generated as a result of mechanical deformation under undrained conditions (for analyses with Time Scope = Short Term and Drained/Undrained materials).
The following quantities are available in the Results ribbon:

Seepage Pressures

Variable Unit Description
kPa Seepage pressure
m Seepage pressure head, with being the vertical
coordinate and m/s
Degree of saturation in accordance with the hydraulic model used

Effective Unit Weights

Variable Unit Description
kN/m Horizontal effective unit weight,
kN/m Vertical effective unit weight,

Excess Pressures

Variable Unit Description
kPa Excess pore pressure
m Excess pore pressure head

Fluxes

Variable Unit Description
m/day Fluid velocity in the -direction
m/day Fluid velocity in the -direction
vector Fluid velocity vector
m/day/m Nodal flux (only relevant on boundaries, otherwise equal to zero)

 

3 STRUCTS

For problems involving structural elements, a separate category, Structs, appears in the Results ribbon.
Structural elements also involve a distinction between the left and right sides. These are defined as shown in Figure 3.1. Note that the interface and symbols indicate the left and right sides respectively. Following conventional sign notations, bending moments are positive when they generate tension on the right side of the beam.

beamorient.png
Figure 3.1: Orientation of structural elements.

 

3.1 Forces

In analogy with stresses in solids, both Initial Forces and Final Forces are available (when relevant) in the Results ribbon. These result sets contain the following variables:

Sectional Forces

Variable Unit Description
Normal Force kN/m Positive in tension
Shear Force kN/m Derivative of bending moment with respect to local -coordinate
Bending Moment kNm/m Positive corresponding to tension on the right side of the beam

Earth Pressures

Variable Unit Description
Tangential Left kN/m Sign consistent with solid shear stress
Normal Left kN/m Sign consistent with solid normal stress (positive in tension)
Tangential Right kN/m Sign consistent with solid shear stress
Normal Right kN/m Sign consistent with solid normal stress (positive in tension)

3.2 Displacements

In analogy with solids, both Stage Displacements and Total Displacements are available. The following displacement quantities are available in the Results ribbon:

Stage Displacements

Variable Unit Description
m Stage displacements in the -direction
m Stage displacements in the -direction

Total Displacements

Variable Unit Description
m Total displacements in the -direction
m Total displacements in the -direction

Note: for Limit Analysis and Strength Reduction, the difference between total and stage displacements is immaterial. In such cases, only Total Displacements are available in the Results ribbon.



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