Most current-technology elements support linear perturbation analysis.
Because linear perturbation is based on a solution at a particular time from a linear or nonlinear analysis, known as the base (or prior) analysis, the element behaviors are based on the properties and behavior of the base analysis, but are different from the base analysis.
The following elements can be used in a linear perturbation analysis as well as any downstream analyses:
Table 5.6: Elements Supporting Linear Perturbation Analysis
| Category | Element Name(s) |
|---|---|
| Beam | BEAM188, BEAM189 [a] |
| Circuit | CIRCU94, CIRCU124 |
| CMS Superelement (or substructure) | MATRIX50 [b] |
| Contact[c] | TARGE169, TARGE170, CONTA172, CONTA174, CONTA175, CONTA177, CONTA178 |
| Elbow | ELBOW290 |
| Hydrostatic Fluid | HSFLD241, HSFLD242 |
| Interface | INTER192, INTER193, INTER194, INTER195 |
| Pipes | PIPE288, PIPE289 |
| Reinforcing | REINF263, REINF264, REINF265 |
| Shells | SHELL181, SHELL208, SHELL209, SHELL281[a] |
| Solid (2D) | PLANE121, PLANE182, PLANE183, PLANE222, PLANE223, PLANE233, FLUID243, FLUID244 |
| Solid (3D) | FLUID30, SOLID122,SOLID123,SOLID185, SOLID186, SOLID187, SOLID285, SOLID225, SOLID226, SOLID227, SOLID236, SOLID237, FLUID220, FLUID221, SOLID272, SOLID273 |
| Solid-Shell | SOLSH190 |
| Spar | LINK180 |
| Specialty | MASS21, MATRIX27, TRANS126, PRETS179, MPC184, MESH200, FOLLW201 |
| Spring/Damper | COMBIN14, COMBIN39, COMBI214, COMBI250 |
| Surface | SURF153, SURF154, SURF156, SURF159 |
[a] Not supported for nonlinear general beam sections (SECTYPE,GENB) or preintegrated general shell sections (SECTYPE,GENS).
[b] MATRIX50 can be used in a linear perturbation analysis the same way it is used in a typical substructure use pass. However, MATRIX50 is treated as a linear element in the linear perturbation analysis and is not prestressed.
[c] When using contact elements in a linear perturbation analysis, it is generally recommended to include large-deflection effects by issuing NLGEOM,ON to ensure correct results. Otherwise, the algorithms that bond the contact interface use the original undeformed geometry for NLGEOM,OFF, which could lead to an inaccurate solution (or possibly a memory error in the case of linear perturbation eigenvalue buckling) if there is significant deformation in the base analysis.
The base analysis of the linear perturbation can be a nonlinear analysis with
nonlinear materials, geometric nonlinearity, or contact elements included in the
model. In the linear perturbation analysis, the geometric nonlinearity at the
substep where linear perturbation is initiated is completely inherited in
of Equation 15–252 in the
Mechanical APDL Theory Reference. This includes large deformation, large rotation, and contact effects.
The linear perturbation analysis can be understood as an iteration in the nonlinear
base analysis. In the linear perturbation analysis, all of the nonlinear effects are
taken into consideration and “frozen” so that the loading and
deformation is linear. The nonlinear effects are also carried to the stress
expansion pass and the following downstream analysis, if any.
Any nonlinear material must behave linearly in the linear perturbation analysis. For all materials, the same material properties used in the linear perturbation are also used in the stress-expansion pass and in all subsequent downstream analyses, if any.
Linear Materials
For pure linear elastic materials used in the base analysis, the same
properties are used in the linear perturbation. Because the material
constitutive curve is a line, the tangent is the same as the line. The
material-handling key (MatKey) specified via
PERTURB is ignored.
Hyperelastic Materials
For hyperelastic materials used in the base analysis, the material properties
are assumed to be linear elastic. The program obtains the material property data
(material Jacobian) based on the tangent of the hyperelastic material's
constitutive law at the point where restart or linear perturbation occurs. The
material-handling key (MatKey) specified via the
PERTURB command is ignored.
Hyperviscoelastic Materials
For hyperviscoelastic materials used in the base analysis
and then transferred to a perturbed full harmonic analysis, the program uses the
preloaded harmonic hyperviscoelastic material stiffness. The material-handling
key (MatKey) specified via PERTURB
is ignored.
Other Nonlinear Materials
For any other nonlinear materials used in the base
analysis, the material properties are assumed to be linear elastic. The program
determines the material properties based on the material-handling key
(MatKey) specified via
PERTURB, as follows:
If the default automatic material-handling behavior (
MatKey= AUTO) is in effect, the program uses the linear portion of the nonlinear materials (that is, the parts defined via MP) for the linear perturbation.If the tangent option (
MatKey= TANGENT) is in effect, the program uses the consistent tangent on the material constitutive curve for the linear perturbation. The program obtains the consistent tangent at the point where restart or linear perturbation occurs.
For most materials, the tangent option gives different material properties than those given by the automatic option. It is possible, however, that they could be identical or very similar if a.) the material is elastoplastic rate-independent and is unloading (or has neutral loading) at the restart point, or b.) the material is rate-dependent, depending on the material properties and loading conditions.
After a linear perturbation analysis, the reported stress, elastic strain, and thermal strains are the values due to the loads applied in a linear perturbation analysis; for example, for linear perturbation modal analysis, the stress and elastic strain are the values due to the mode shapes. In general, the effects of any nonlinearity are not taken into consideration in the stress expansion. However, some element results can be inherited from the base analysis as detailed below.
Because a linear perturbation analysis can be understood as an extra iteration of a base analysis, all history-dependent results of the base analysis are inherited in the results of the linear perturbation analysis. Therefore, any plastic strains, creep strains, swelling strains, and contact results from the base analysis are available in the results data of the linear perturbation analysis.
The total strain is the sum of all strains (for example, PLNSOL,EPTO). The nonlinear solution quantities such as equivalent stress, stress state ratio, and plastic state variable (for example, PLESOL,NL,...) are also available. The one exception is that hydrostatic pressure is the value from the linear perturbation analysis instead of from the base analysis.
For hyperelastic materials, the strain after the linear perturbation analysis is the elastic strain due to the loads applied in a linear perturbation analysis, and the total strain is the same as the elastic strain. For plane stress cases, the direct strain in the Z direction is calculated with the incompressible condition for hyperelastic materials, and with linear elastic material properties for any material other than hyperelastic materials.
The energy densities (for example, PLESOL,SEND,...) are inherited from the base analysis, except for the elastic energy density which is energy density calculated in the linear perturbation analysis. However, the reported strain energy (for example, PRESOL,SENE) includes the elastic part due to linear perturbation and others inherited from the base analysis (if any).
If the base analysis includes geometric nonlinearity, the Euler angles of the base analysis are also available in the linear perturbation results file. Thus, all the output quantities of the linear perturbation analysis are reported consistently in global, local, and rotated local coordinate systems, as in the base analysis.
Temperatures saved in the linear perturbation results (Jobname.rstp) are the temperatures that have been modified during the second phase of the linear perturbation procedure (that is, as the perturbation load). This is only applicable to linear perturbation eigenvalue buckling analysis.
The following restrictions apply to linear perturbation analysis:
Perturbation loads cannot be non-mechanical loading such as initial conditions (INISTATE) or swelling effects. These loads cannot be modified or deleted during the linear perturbation analysis.
For a linear perturbation static or eigenvalue buckling analysis, a thermal load can be modified by specifying a new temperature in the second phase of the linear perturbation procedure. In a linear perturbation static or buckling analysis, assuming that the base analysis is nonlinear, the reference temperature is the temperature from which the linear perturbation analysis is restarted (and not the reference temperature (TREF) from the base analysis).
If the base analysis is linear, then the reference temperature used in the linear perturbation is the TREF temperature from the base analysis.
Thermal loads from the base analysis are ignored in a linear perturbation modal or full harmonic analysis. In addition, you cannot apply thermal loads in the second phase of a linear perturbation modal or full harmonic analysis.
No element can be activated or deactivated using the birth and death feature during the second phase of a linear perturbation analysis; however, this is allowed in the first phase of linear perturbation.
Linear perturbation analyses do not support user-defined materials (user subroutine
UserMat).