The general process for performing a single-point response spectrum analysis consists of four primary steps:
The process for running multiple spectrum analyses can be found in:
If you wish to perform mode selection that includes and expands only the significant modes in a single-point response spectrum analysis, refer to Mode Selection Based on the Mode Coefficients and Mode Selection Based on the DDAM Method.
See Building the Model in the Basic Analysis Guide. For further details, see the Modeling and Meshing Guide.
Only linear behavior is valid in a spectrum analysis. Nonlinear elements, if any, are treated as linear. If you include contact elements, for example, their stiffnesses are calculated based on their initial status and are never changed.
Both Young's modulus (EX) (or stiffness in some form) and density (DENS) (or mass in some form) must be defined. Material properties can be linear, isotropic or orthotropic, and constant or temperature-dependent. Nonlinear properties, if any, are ignored.
You can define damping using damping ratio, material damping and/or proportional damping. For more details about damping definition, see Damping.
The modal solution is required because the structure's mode shapes and frequencies must be available to calculate the spectrum solution.
The procedure for obtaining the modal solution is described in Modal Analysis, but the following additional recommendations apply:
Use the Block Lanczos, PCG Lanczos, Supernode, Subspace method, or Unsymmetric (with
Cpxmod= REAL andModType= BOTH on the MODOPT command) to extract the modes. Other methods are not valid for subsequent spectrum analysis.Extract a sufficient number of modes to characterize the structure's response in the frequency range of interest. The ratio of the effective mass (used in the subsequent spectrum analysis) to the total mass is printed out along with the participation factors at the end of the modal analysis. A ratio greater than 0.9 (more than 90% of the mass is included) is generally considered acceptable.
If groups of repeated frequencies are present, make sure you extract all the solutions in each group. For more information, see Repeated Eigenvalues in the Mechanical APDL Theory Reference.
To include the contribution of higher modes, you can either request the calculation of the residual vectors in the modal analysis (RESVEC) and use them in the spectrum analysis, or you can include the effect of the missing mass directly in the spectrum analysis (MMASS command).
Expand all the modes (MXPAND,
ALL). This is required if you eventually want to calculate summed forces and moments in postprocessing (for example, obtaining the forces across a cut in the model using FSUM).You can also expand the modes after the spectrum solution if the size of the results file Jobname.rst is an issue (see the use of the
SIGNIFargument in the MXPAND command documentation). In this case, use MXPAND,-1 to suppress the expansion during the modal analysis. Expanding modes after a spectrum solution will only expand significant modes based on the excitation direction specified in spectrum analysis. If you included missing-mass effect (MMASS), then the calculation will be done only for these expanded modes. Note that you can limit the expanded mode set using the procedure in Using Mode Selection. If modes are expanded after the spectrum solution (EXPASS,ON), the element results calculation based on element modal results (Elcalcon the SPOPT command) is not supported.To include material-dependent damping in the spectrum analysis, specify it in the modal analysis.
Constrain those degrees of freedom where you want to apply a base excitation spectrum.
At the end of the solution, exit the Solution processor.
If you intend to perform multiple independent spectrum analyses, keep a copy of the Jobname.mode file from the modal analysis. For more information, see Running Multiple Spectrum Analyses.
In this step, the program uses mode shapes extracted by the modal solution to calculate the SPRS solution. The following requirements and limitations apply:
The mode shape file (Jobname.mode) must be available. The left mode shape file (Jobname.lmode) must also be available when the modal solution is obtained with the unsymmetric eigensolver.
The database must contain the same model from which the modal solution was obtained.
The Jobname.esav file must be available.
The Jobname.full file must be available for the participation factors calculation.
The Jobname.rst file from the modal solution must be available for LCOPER calculation.
If the missing mass calculation is activated (MMASS), the element matrices file (Jobname.emat) from the modal analysis must also be available.
Note: If the SPRS analysis is not performed in the same directory as the modal
analysis, remote modal files usage must be activated
(MODDIR). In this case, the SPRS information is stored in the
Jobname.prs file and the modal analysis files in the
modal analysis directory are not modified. Also, if element results calculation
based on element modal results is activated (Elcalc =
YES on SPOPT), the SPRS results file only contains SPRS
results.
Enter SOLUTION (/SOLU).
Define the analysis type and analysis options. The program offers the following analysis options for a spectrum analysis. Not all modal analysis options and not all eigenvalue extraction techniques work with all spectrum analysis options.
Table 6.1: Commands to Define a Single-point Response Spectrum Analysis
Description / Notes Command Select Spectrum (SPRS) as the analysis type. ANTYPE, SPECTR Select Single-point Response Spectrum (SPRS) as the analysis type, and specify the number of modes (enter a value for NMODE).[a]SPOPT,SPRS, NMODE[a] Select enough modes to cover the frequency range spanned by the spectrum and to characterize the structure's response. The accuracy of the solution depends on the number of modes used: the larger the number, the higher the accuracy.
Select one of the mode combination methods.
Mechanical APDL offers six different mode combination methods for the single-point response spectrum analysis, which are invoked by issuing the commands listed below.
Table 6.2: Mode Combination Method Commands
These commands allow computation of three different types of responses that you specify via their
Labelargument as listed in the table below.Table 6.3: Responses Specified by
Labelon the Mode Combination Method CommandsResponse Type LabelDisplacement (displacements, stresses, forces, etc.)
DISP Velocity (velocities, "stress velocities," "force velocities," etc. )
VELO Acceleration (accelerations, "stress accelerations," "force accelerations," etc.)
ACEL These commands also enable you to specify the type of modal forces used in the combination.
ForceType= STATIC (default) combines the modal static forces (that is, stiffness multiplied by mode shape forces, both of which are stress-causing forces) whileForceType= TOTAL combines the summed modal static forces and inertia forces (that is, stiffness and mass forces, both of which forces are seen by the supports).The DSUM method also accommodates time-duration input for earthquake or shock spectrum.
When the missing mass effect is activated (MMASS,ON), the displacements calculated are relative while the accelerations are absolute.
The missing mass effect is ignored (MMASS) for velocity results (
Label= VELO).If the effect of the rigid responses is included (RIGRESP), the mode combination methods supported are SRSS, CQC and ROSE.
Specify load step options. The table below details the available options for single-point response spectrum analysis.
Table 6.4: Load Step Options
Option Command Description / Comments Spectrum Options Type of Response Spectrum SVTYP The spectrum type can be displacement, velocity, acceleration, force, or PSD. All except the force spectrum represent seismic spectra; that is, they are assumed to be specified at the base. The force spectrum is specified at non-base nodes with the F or FK command, and the direction is implied by labels FX, FY, FZ. Excitation Direction SED In addition, the ROCK command enables you to specify a rocking spectrum. Spectral-value-vs-frequency Curve FREQ, SV SV and FREQ commands are used to define the spectral curve with a maximum of 100 points. You can define a family of spectral curves, each curve for a different damping ratio. Use the SPTOPT command followed by the STAT command to list current spectrum curve values, and the SVPLOT command to display the spectrum curves. Missing Mass Effect MMASS The missing mass effect reduces the error caused when the higher modes are neglected in the analysis. Rigid Responses Effect RIGRESP If rigid responses are included, the combination of modal responses with frequencies in the higher end of the spectrum frequency range will be more accurate. Residual Vector RESVEC Just like the missing mass response, the residual vectors reduce the error caused when the higher modes are neglected in the analysis. Unlike the missing mass response, the residual vector is calculated in the modal analysis and is considered as an additional mode. Hence, it is combined as such, and coupling may exist between the residual vector and the modes depending on the mode combination method.
A frequency is associated with the residual vector. The input spectrum for this frequency should correspond to the Zero Period Acceleration value. The frequency is also used for the calculation of the velocity and acceleration solutions.
Damping (Dynamics Options)[a] Beta (Stiffness) Damping BETAD This option results in a frequency-dependent damping ratio. Alpha (Mass) Damping ALPHAD This option results in a frequency-dependent damping ratio. Damping Ratio DMPRAT This option specifies a damping ratio to be used at all frequencies. Modal Damping MDAMP This option results in a frequency-dependent damping ratio. Material-dependent damping ratio MP,DMPR Available only if specified in the modal analysis where an effective damping ratio is calculated based on the elements' strain energies. You must request that element results be calculated in the modal expansion ( Elcalc= YES on the MXPAND command).[a] If you specify more than one form of damping, the program calculates an effective damping ratio at each frequency. The spectral value at this effective damping ratio is then calculated by log-log interpolation of the spectral curves. If no damping is specified, the spectral curve with the lowest damping is used. For more information about different forms of damping, see Damping in Transient Dynamic Analysis.
Start solution calculations (SOLVE).
The output from the solution includes the Response Spectrum Calculation Summary. This table, which is part of the printed output, lists the participation factors, mode coefficients (based on lowest damping ratio), and the mass distribution for each mode. To obtain the response of each mode (modal response), multiply the mode shape by the mode coefficient (based on lowest damping ratio). You do this by retrieving the mode coefficient with the *GET command (Entity = MODE) and using it as a scale factor in the SET command.
The mode coefficients based on the actual damping are listed in the Significant Mode Coefficients (Including Damping) table.
Repeat steps 4 and 5 for additional response spectra, if any. Note that solutions are not written to the Jobname.rst at this time.
Postprocessing can be done in one of two ways:
Directly from the Jobname.rst (
Elcalc= YES on SPOPT command). See Example 6.2: Calculating the Velocity Solution in Addition to the Displacement Solution withElcalc= YES on SPOPT command.Using the mode combination file, Jobname.mcom (
Elcalc= NO on SPOPT command).
For large models, direct postprocessing significantly reduces the total computation and postprocessing time of spectrum analysis, and even greater gains are achieved using remote read-only modal analysis files (MODDIR) and distributed-memory parallel processing (see Running Multiple Spectrum Analyses). The required conditions and settings that determine what is calculated and written during solution to Jobname.mcom and Jobname.rst are described below.
Setup for postprocessing via Jobname.mcom — By default (
Elcalc= NO on the SPOPT command), the mode combination phase writes a file of POST1 commands (Jobname.mcom) that combine the maximum modal responses by the specified mode combination method to calculate the overall response of the structure. Read in Jobname.mcom in POST1 to do the mode combinations, using the results file (Jobname.rst) from the modal expansion pass.Setup for direct postprocessing — If element results calculation based on element modal results is activated (
Elcalc= YES on the SPOPT command), the file Jobname.mcom is written but not used during postprocessing. Modal responses are combined and stored in the Jobname.rst file during solution according to the mode combination method command issued (SRSS, CQC,…). Element results and reaction forces are calculated only if they were also requested during the modal expansion pass (see OUTRES). Note that you must setMSUPkey= YES on the MXPAND command during the modal analysis to write elemental results to the Jobname.mode file. For available element results, see Option: Number of Modes to Expand (MXPAND).The response type you selected on the mode combination method command determines how the structure's modal responses are combined, as detailed in the table below.
Response Type LabelHow modal responses are combined: Displacement (displacements, stresses, forces, etc.)
DISP Displacements and stresses are combined for each mode on the mode combination command. Velocity (velocities, "stress velocities," "force velocities," etc. )
VELO Velocities and stress velocities are combined for each mode on the mode combination command. Acceleration (accelerations, "stress accelerations," "force accelerations," etc.)
ACEL Accelerations and stress accelerations are combined for each mode on the mode combination command. For an example input, see Single-Point Response Spectrum Analysis on a Piping Structure with Excitation Along X, Y, and Z Directions.
Leave the SOLUTION processor (FINISH).
If needed, you can retrieve the frequencies, participation factors, mode coefficients and effective damping ratios with the *GET command (
Entity= MODE).
You can use POST1, the general postprocessor, to review the results from a single-point response spectrum analysis by either of the following methods:
Results from a single-point response spectrum analysis are written to the mode combination file, Jobname.mcom, in the form of POST1 load case combination commands. These commands calculate the overall response of the structure by combining the maximum modal responses in some fashion (specified by one of the mode combination methods). The overall response consists of the overall displacements (or velocities or accelerations) and, if placed on the results file during the expansion pass, the overall stresses (or stress velocities or stress accelerations), strains (or strain velocities or strain accelerations), and reaction forces (or reaction force velocities or reaction force accelerations). Because load case combinations are used, any existing load cases in POST1 will be redefined.
Note: If you want a direct combination of the derived stresses (S1, S2, S3, SEQV, SI) from the results file, issue the SUMTYPE,PRIN command before reading in the Jobname.mcom file. With the PRIN option, component stresses are not available.
The command default (SUMTYPE,COMP) is used to directly operate only on the unaveraged element component stresses and calculate the derived quantities from these. Refer to Creating and Combining Load Cases in the Basic Analysis Guide. Also, see the Command Reference for a description of the SUMTYPE command.
To read the commands on Jobname.mcom, issue the /INPUT command as shown in the example below.
/INPUT,FILE,MCOM !Assumes the default jobname FILE
If you have issued SPOPT with
Elcalc = YES, the spectrum analysis results are
written to the Jobname.rst file. If the missing mass response calculation has been activated
(MMASS,ON), missing mass response sets are stored as loadstep
2. Issue SET,LAST to read the last combined
solution.
Note: The first combined solution is stored at different loadsteps depending
on the response type selected for Label on
the mode combination method command
as detailed in the table below.
| Loadstep of the First Combined Solution | ||
| Response Type | Label | First combined solution is stored at loadstep: |
| Displacement | DISP | 4 |
| Velocity | VELO | 5 |
| Acceleration | ACEL | 6 |
To display deformation, use the PLDISP command.
Use PLNSOL or PLESOL to contour almost any result item, such as stresses (SX, SY, SZ ...), strains (EPELX, EPELY, EPELZ ...), and displacements (UX, UY, UZ ...). When using the .mcom file, if you previously issued the SUMTYPE command, the results of the PLNSOL or PLESOL command are affected by the particular SUMTYPE command option (SUMTYPE,COMP or SUMTYPE,PRIN) that you selected. Instead, with direct postprocessing, the SUMTYPE command is ignored, and derived stresses are calculated from the combination of unaveraged element component stresses.
Use the PLETAB command to contour element table data and PLLS to contour line element data. To display various solution results as vectors, issue the PLVECT command.
Displacements, stresses, and strains are always in the solution coordinate system (RSYS,SOLU).
Derived data, such as stresses and strains, are averaged at the nodes by the PLNSOL command. This averaging results in "smeared" values at nodes where elements of different materials, different shell thicknesses, or other discontinuities meet. To avoid the smearing effect, use selecting (described in Selecting and Components in the Basic Analysis Guide) to select elements of the same material, same shell thickness, etc. before issuing PLNSOL.
You can view correct membrane results for shells (SHELL, MID) by using KEYOPT(8) = 2 (for SHELL181, SHELL208, SHELL209, SHELL281, and ELBOW290). These KEYOPTS write the mid-surface node results directly to the results file, and allow the membrane results to be directly operated on during squaring operations. The default method of averaging the TOP and BOT squared values to obtain a MID value can possibly yield incorrect MID values.
List Results
Use any of the following commands to list various results: PRNSOL (nodal results), PRESOL (element-by-element results), PRRFOR (reaction data), FSUM, NFORCE, PRNLD (nodal element forces sum).
The element forces (PRESOL) and reaction forces
(PRRFOR) are based on the type of force (static or total)
requested using ForceType on the combination commands
(SRSS, CQC, etc.). The same applies to the
values retrieved using
*GET,Par,ELEM,N,EFOR
and
*GET,Par,NODE,N,RF.
The combination always leads to positive forces. Therefore, the summation of
element nodal forces (requested via the FSUM,
PRNLD, or NFORCE command) is performed
prior to the combination, and the output header reads Spectrum Analysis summation is
used. The type of the summed nodal forces is based on the
last spectrum analysis performed. To achieve accurate force calculations, be
sure to use a displacement solution (Label = Disp on
SRSS, CQC, etc.). Also make sure the
.mode and .rst files from the modal
analysis are available when summing the forces.
If element results calculation based on element modal results is activated
(Elcalc = YES on the SPOPT
command), after a SPRS analysis with multiple response spectra and missing mass
effect activated (MMASS,ON), results listed after issuing
PRRFOR, FSUM, PRNLD or
NFORCE are correct only if missing mass responses are
consecutive sets on the .rst file. This is the case if SpecCum = NO
on the SPOPT command, which is the default setting (see 6.4.4: Single-Point Response Spectrum Analysis on a Piping Structure with Excitation
Along X, Y, and Z Directions, missing mass effect, Elcalc
= YES and SpecCum = NO on
SPOPT command). If
SpecCum = YES, this can be achieved by one of the
following methods:
- method 1
Delete intermediate solution sets before entering the postprocessor (see 6.4.5: Single-Point Response Spectrum Analysis on a Piping Structure with Excitation Along X, Y, and Z Directions, missing mass effect, Elcalc = YES and
SpecCum= YES on SPOPT command: method 1).
- method 2
Issue the mode combination method command in a separate solution (see 6.4.6: Single-Point Response Spectrum Analysis on a Piping Structure with Excitation Along X, Y, and Z Directions, missing mass effect,
Elcalc= YES on SPOPT command: method 2).
Other Postprocessing Capabilities
Many other postprocessing functions, such as mapping results onto a path, transforming results to different coordinate systems, and load case combinations, are available in POST1. See The General Postprocessor (POST1) in the Basic Analysis Guide for details.
When running multiple spectrum analyses, it is possible calculate the effects of multiple spectra independently, or to calculate a velocity and/or an acceleration response in addition to a displacement response.
To calculate the effects of multiple spectra independently (for example, for three orthogonal directions which you combine in a separate step to calculate the velocity and acceleration solutions with a missing mass response calculation in addition to the displacement solution), repeat Step 3: Obtain the Spectrum Solution.
After the first spectrum analysis and for each subsequent analysis:
If remote modal files usage is not activated (MODDIR), you must activate the
modeReuseKeyon the SPOPT command so that the database and the needed files are ready for the new spectrum analysis.If remote modal files usage is activated (MODDIR), Jobname.prs file should be previously deleted. Otherwise, SPRS information is appended in Jobname.prs.
Reminder: The existing Jobname.mcom file is appended with the additional spectrum analyses.
To calculate a velocity and/or an acceleration response in addition to a displacement response with no missing mass response calculations (MMASS), the mode combination can be performed in a separate solution phase. In this case, you must save a copy (/COPY) of the Jobname.mode file from the modal analysis step and use it to calculate the velocity and/or acceleration response in addition to the displacement response.
Additionally, you must save a copy (/COPY) of the Jobname.mcom file from the spectrum analysis step. This ensures that the Jobname.mcom file used for generating the downstream mode combinations includes only the mode coefficients from that independent spectra input. If a copy is not saved, the mode combination will be based on the entire set of spectra rather than each independent set, as intended. For an example input, see Example 6.1: Calculating the Velocity Solution in Addition to the Displacement Solution.
Reminder: The existing Jobname.mcom file is also overwritten by the additional mode-combination step(s).
If the SPOPT command has been issued with
Elcalc= YES, the Jobname.mcom file and copy procedure are not required (see direct postprocessing). If remote modal files usage has not been activated (MODDIR), combined responses calculated in the separate solution phase are appended in the Jobname.rst file. If remote modal files usage has been activated (MODDIR), combined responses calculated in the separate solution phase overwrite those of the previous solution phase in Jobname.rst . For an example input, see Example 6.2: Calculating the Velocity Solution in Addition to the Displacement Solution withElcalc= YES on SPOPT command.
The procedure to run multiple spectrum analyses is summarized in the table below.
| Step | Description | Commands |
| 1. | Enter SOLUTION. | /SOLU |
| 2. | Define analysis type. | ANTYPE |
| 3. | Select one of the mode combination methods | mode combination method commands: |
| 4. | Start solution. | SOLVE |
Example 6.1: Calculating the Velocity Solution in Addition to the Displacement Solution
/prep7 /com, Build the Model finish /solution antype,modal modopt,lanb,10 ! Use the Block-Lanczos solver mxpand,10,,,yes solve ! Modal solve finish /copy,jobname,mode,,original,mode ! Copy the Jobname.mode from modal solve /solution antype,spectrum spopt,sprs ! Solve the single-point response spectrum srss,,disp ! Calculate displacement solution svtyp,2 ! Acceleration response spectrum sed,1,0,0 freq,1,50,100 sv,,1,1,1 solve finish /post1 /input,,mcom ! Postprocess the displacement solution prnsol finish /copy,jobname,mcom,,disp,mcom ! Save a copy of MCOM file /delete,jobname,mcom /copy,original,mode,,jobname,mode ! Rename the copied MODE file and Jobname.mode /solution antype,spectrum srss,,velo ! Calculate the velocity solution solve finish /post1 /input,,mcom ! Postprocess the velocity solution prnsol finish
Example 6.2: Calculating the Velocity Solution in Addition to the Displacement Solution
with Elcalc = YES on SPOPT
command
/prep7 /com, Build the Model finish /solution antype,modal modopt,lanb,10 ! Use the Block-Lanczos solver mxpand,10,,,yes solve ! Modal solve finish /solution antype,spectrum spopt,sprs,,yes ! Solve the single-point response spectrum; request element result calculations srss,,disp ! Calculate displacement solution svtyp,2 ! Acceleration response spectrum sed,1,0,0 freq,1,50,100 sv,,1,1,1 solve finish /post1 set,last ! Postprocess the displacement solution !set,4,1 ! Alternative command prnsol finish /solution antype,spectrum srss,,velo ! Calculate the velocity solution solve finish /post1 set,last ! Postprocess the velocity solution !set,5,1 ! Alternative command prnsol finish