Note — Load step 2 is left blank if you specify only nodal PSD excitation. Also, if you suppress the dis-placement, velocity, or acceleration solution using the PSDRES command, the corresponding load step is left blank. Also, the superelement displacement file (.DSUB) is not written for load steps 3, 4, or 5 in a PSD analysis.
Table 6.4 Organization of Results Data from a PSD Analysis
Contents Substep
Load Step
Expanded modal solution for 1st mode 1
1
Expanded modal solution for 2nd mode 2
Expanded modal solution for 3rd mode 3
Etc.
Etc.
Unit static solution for PSD table 1 1
2 (Base excit.
only) 2 Unit static solution for PSD table 2 Etc.
Etc.
1 sigma displacement solution 1
3
1 sigma velocity solution (if requested) 1
4
1 sigma acceleration solution (if requested) 1
5
6.7.4.1.1. Read the Desired Set of Results into the Database
For example, to read in the 1 σ displacement solution, issue the command:
SET,3,1
Command(s): SET
GUI: Main Menu> General Postproc> Read Results> First Set
6.7.4.1.2. Display the Results
Use the same options available for the SPRS analysis.
Note — Nodal stress averaging performed by the PLNSOL command may not be appropriate in a random vibration analysis because the "stresses" are not actual stresses but stress statistics.
6.7.4.2. Calculating Response PSDs in POST26
You can calculate and display response PSDs for any results quantity available on the results file (displacements, velocities, and/or accelerations) if the Jobname.RST and Jobname.PSD files are available.
The procedure to calculate the response PSD is as follows:
1. Enter POST26, the time-history postprocessor.
Command(s): /POST26
GUI: Main Menu> TimeHist PostPro
2. Store the frequency vector. NPTS is the number of frequency points to be added on either side of natural frequencies in order to "smooth" the frequency vector (defaults to 5). The frequency vector is stored as variable 1.
Command(s): STORE,PSD,NPTS
GUI: Main Menu> TimeHist Postpro> Store Data
3. Define the variables in which the result items of interest (displacements, stresses, reaction forces, etc.) are to be stored.
Command(s): NSOL, ESOL, and/or RFORCE
GUI: Main Menu> TimeHist Postpro> Define Variables
4. Calculate the response PSD and store it in the desired variable. The PLVAR command can then be used to plot the response PSD.
Command(s): RPSD
GUI: Main Menu> TimeHist Postpro> Calc Resp PSD
6.7.4.3. Calculating Covariance in POST26
You can compute the covariance between two quantities available on the results file (displacements, velocities, and/or accelerations), if the Jobname.RST and Jobname.PSD files are available.
The procedure to calculate the covariance between two quantities is as follows:
1. Enter POST26, the time-history postprocessor.
Command(s): /POST26
GUI: Main Menu> TimeHist PostPro
2. Define the variables in which the result items of interest (displacements, stresses, reaction forces, etc.) are to be stored.
Command(s): NSOL, ESOL, and/or RFORCE
GUI: Main Menu> TimeHist Postpro> Define Variables
3. Calculate the contributions of each response component (relative or absolute response) and store them in the desired variable. The PLVAR command can then be used to plot the modal contributions (relative response) followed by the contributions of pseudo-static and mixed part responses to the total covariance.
Command(s): CVAR
GUI: Main Menu> TimeHist Postpro> Calc Covariance
Section 6.7: How to Do a Random Vibration (PSD) Analysis
4. Obtain the covariance.
Command(s): *GET,NameVARI,n,EXTREM,CVAR GUI: Utility Menu> Parameters> Get Scalar Data
6.7.5. Sample Input
A sample input listing for a random vibration (PSD) analysis is shown below:
! Build the Model
! Obtain the Modal Solution
/SOLU ! Enter SOLUTION
! Obtain the Spectrum Solution /SOLU! Reenter SOLUTION
! Combine modes using PSD method
/SOLU ! Re-enter SOLUTION ANTYPE,SPECTR ! Spectrum analysis
PSDCOM,SIGNIF,COMODE ! PSD mode combinations with significance factor and ! option for selecting a subset of modes for ! combination
SOLVE FINISH
!
! Review the Results
/POST1 ! Enter POST1
SET, ... ! Read results from appropriate load step, substep ...! Postprocess as desired
...! (PLDISP; PLNSOL; NSORT; PRNSOL; etc.) ...
FINISH
!
! Calculate Response PSD
/POST26 ! Enter POST26
STORE,PSD ! Store frequency vector (variable 1) NSOL,2,... ! Define variable 2 (nodal data) RPSD,3,2,,... ! Calculate response PSD (variable 3) PLVAR,3 ! Plot the response PSD
...
! Calculate Covariance
RESET ! Reset all POST26 specifications to initial defaults.
NSOL,2 ! Define variable 2 (nodal data).
NSOL,3 ! Define variable 3 (nodal data).
CVAR,4,2,3,1,1 ! Calculate covariance between displacement ! at nodes 2 and 3.
*GET,CVAR23U,VARI,4,EXREME,CVAR ! Obtain covariance.
FINISH
See the ANSYS Commands Reference for a discussion of the ANTYPE, MODOPT, M, TOTAL, D, EXPASS, MXPAND, SPOPT, PSDUNIT, PSDFRQ, PSDVAL, DMPRAT, PFACT, PSDCOM, SUMTYPE, and PSDRES commands.
6.8. How to Do DDAM Spectrum Analysis
The procedure for a DDAM spectrum analysis is the same as that for a single-point response spectrum (SPRS) analysis (including file requirements), with the following exceptions:
• Use the British system of units [inches (not feet), pounds, etc.] for all input data - model geometry, material properties, element real constants, etc.
• Choose DDAM instead of SPRS as the spectrum type [SPOPT command].
• Use the ADDAM and VDDAM commands instead of SVTYP, SV, and FREQ to specify the spectrum values and types. Specify the global direction of excitation using the SED command. Based on the coefficients specified in the ADDAM and VDDAM commands, the program computes the mode coefficients according to the empirical equations given in the ANSYS, Inc. Theory Reference.
• The most applicable mode combination method is the NRL sum method [NRLSUM]. Mode combinations are done in the same manner as for a single-point response spectrum. Mode combinations require damping.
• No damping needs to be specified for solution because it is implied by the ADDAM and VDDAM com-mands. If damping is specified, it is used for mode combinations but ignored for solution.
Note — As in the Single-point Response Spectrum analysis, DDAM spectrum analysis requires six steps to systematically perform the analysis.
If you are using batch mode, note the following:
• The modal solution and DDAM spectrum solution passes can be combined into a single modal analysis [ANTYPE,MODAL] solution pass with DDAM spectrum loads [ADDAM, VDDAM, SED].
• The mode expansion and mode combination solution passes can be combined into a single modal ana-lysis [ANTYPE,MODAL and EXPASS,ON] solution pass with a mode combination command.
DDAM spectrum analysis is not available in the ANSYS Professional program.
6.9. How to Do Multi-Point Response Spectrum (MPRS) Analysis
The procedure for a multi-point response spectrum analysis is the same as that for random vibration (PSD) ana-lysis (including file requirements), with the following exceptions:
• Choose MPRS instead of PSD as the type of spectrum [SPOPT command].
• The "PSD-versus-frequency" tables now represent spectral values versus frequency.
Section 6.9: How to Do Multi-Point Response Spectrum (MPRS) Analysis
• You cannot specify any degree of correlation between the spectra (i.e., they are assumed to be uncorrel-ated).
• Only relative results (relative to the base excitation) not absolute values, are calculated.
• All mode combination methods are available except PSDCOM.
• Results from a multi-point response spectrum analysis are written to the mode combination file, Job-name.MCOM, in the form of POST1 commands. The commands calculate the overall response of the structure by combining the maximum modal responses in some fashion (specified by the mode combin-ation command in SOLUTION). The overall response consists of the overall displacements and, if placed on the results file during the modal expansion pass, the overall stresses, strains, and reaction forces. If Label = VELO or ACEL on the mode combination command (SRSS, CQC, GRP, DSUM, or NRLSUM) during SOLUTION, the corresponding velocity or acceleration responses are written to the mode combination file.
Multi-point response spectrum analysis is not available in the ANSYS Professional program.
Chapter 7: Buckling Analysis
7.1. Definition of Buckling Analysis
Buckling analysis is a technique used to determine buckling loads - critical loads at which a structure becomes unstable - and buckled mode shapes - the characteristic shape associated with a structure's buckled response.
7.2. Types of Buckling Analyses
Two techniques are available in the ANSYS Multiphysics, ANSYS Mechanical, ANSYS Structural, and ANSYS Pro-fessional programs for predicting the buckling load and buckling mode shape of a structure: nonlinear buckling analysis, and eigenvalue (or linear) buckling analysis. Since these two methods frequently yield quite different results, let's examine the differences between them before discussing the details of their implementation.
7.2.1. Nonlinear Buckling Analysis
Nonlinear buckling analysis is usually the more accurate approach and is therefore recommended for design or evaluation of actual structures. This technique employs a nonlinear static analysis with gradually increasing loads to seek the load level at which your structure becomes unstable, as depicted in Figure 7.1: “Buckling Curves” (a).
Using the nonlinear technique, your model can include features such as initial imperfections, plastic behavior, gaps, and large-deflection response. In addition, using deflection-controlled loading, you can even track the post-buckled performance of your structure (which can be useful in cases where the structure buckles into a stable configuration, such as "snap-through" buckling of a shallow dome).
7.2.2. Eigenvalue Buckling Analysis
Eigenvalue buckling analysis predicts the theoretical buckling strength (the bifurcation point) of an ideal linear elastic structure. (See Figure 7.1: “Buckling Curves” (b).) This method corresponds to the textbook approach to elastic buckling analysis: for instance, an eigenvalue buckling analysis of a column will match the classical Euler solution. However, imperfections and nonlinearities prevent most real-world structures from achieving their theoretical elastic buckling strength. Thus, eigenvalue buckling analysis often yields unconservative results, and should generally not be used in actual day-to-day engineering analyses.