Shock Response Spectrum - Is there a workaround?

1

Hi all,
I would like to conduct a Shock Response Spectrum using Calculix, although I realise that there are no equivalent commands to the Abaqus *SPECTRUM and *RESPONSE SPECTRUM.
Do you know of a procedure using a number of linear dynamic base motion analyses that may be used in combination as a workaround, to achieve the same resulting displacement and stress result for a given SRS curve?
The initial normal modes analyse requires all natural frequencies across the frequency range of the SRS.
I anticipate some scripting to process multiple result sets, if there is a mathematically legitimate procedure.
Would the procedure require running a *BASE MOTION *MODAL DYNAMIC step for each natural frequency, using a prior *frequency step to recover only that single normal mode?
I appreciate any pointer towards a known procedure, workflow or a description of how to achieve the end state.

Tim

1 Like
2

For linear analysis is just a postprocessing of the normal modes output
using the given spectrum, consider this reference Response Spectrum Analysis Definition

Captura de pantalla 2024-11-01 a las 1.43.31
Captura de pantalla 2024-11-01 a las 1.43.31678×1023 88.6 KB

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3

Maybe you could consider using Code Aster, it supports response spectrum analyses. OpenSees also seems to have it.

I know a method to obtain the input spectrum for a known base motion excitation. The rest is more tricky though. You need to estimate the peak values of modal responses and combine them using directional summation methods (to obtain one overall response for all directions) and modal summation methods (to get peak physical responses from peak modal responses) described in literature.

1 Like
4

JuanP74,
Thank you for the reference material, I’m still reading and rereading.
Is it inferred that in Abaqus, the *RESPONSE SPECTRUM command is instigating a post-processing routine of the normal modes results (participation factors), with the SRS defined in the *SPECTRUM?
My question here is to raise the potential for the Shock Response Spectrum analysis to be carried out in a CGX routine rather than a CCX routine?

Calc_em,
Thank you for the workaround of using either Code Aster or OpenSees, and for the further calculation insight.
A little later after reading your kind replies, I recalled that CGX can write mesh and set input for Code Aster, and due to the quite simple base motion nodal BCs, this route to a C-A input file does not seem insurmountable.

Thank you both for your help; my short term plan for a SRS analysis is to try Code Aster and my long term plan is to better understand a potential post-processing algorithm required for Calculix, perhaps a proposal for a CGX enhancement.

Best regards, Tim

1 Like
5

Apparently, the results from code aster are aligned with those from ansys:

6

If you have external access to matrix operations libraries then could be feasible otherwise I’d recommend considering octave, you have to read the modal matrix and the mass matrix from ccx then perform the operations as described in the reference. Try first with a very simple model with a few springs and masses.

7

Code Aster is used by EDF to certify their nuclear reactors, so good to know is reliable :sweat_smile: :rofl:

8

response spectrum method’s has many limitations, i.e elastic material and sign conventions even response curve can modify to adapt ductility and inelasicity. These methods used by early seismic design to predict peak response from sdof’s spectral acceleration. OpenSees basically not supported these analysis type due to problem and limitation, recommended nonlinear dynamic time history analysis instead, but later is available fo complementary purpose. To be implemented and possible in CalculiX, firstly a linear beam user element (U1) and triangular shell (US3) need to support mass attached to nodes, rigid floor diaphragm constraint and modal analysis. Later is required to combine each mode, problem are in all positive results, reverse or negative are strictly by simple add sign for its values.

btw, i’m not sure EDF doing final design of critical project such as nuclear facilities by response spectrum analysis :slight_smile:

9

jbr,
Thank you for the CA / Ansys comparison, it gives good confidence. I am looking at the add-in for Paraview for the post-processing of CA SRS results.

1 Like
10

Juan,
Thank you for the Octave matrix pointer, much appreciated; it would be good to use Calculix in the long term.

11

xyont,
Thank you for your insight into the limitations of of the response spectrum method. There are design codes that provide an SRS for assessing impact performance. I appreciate that the method has its draw backs, although I’m comfortable with it as a first-pass concept structural design code; if I can adopt a suitable workflow using will be ideal although Code Aster and Paraview look like the immediate route.

1 Like
12

That’s a good advice.

There is the clasical aproach in which result is assumed to be a linear combination of single modes individual responses + an apropiate load combination (SSRS). The aim is to translate the dinamic problem to the equivalent static.Check this tutorial.

Not really. A few modes such that Modal Mass Ratio >90% should be enough according to regulation. ccx modal analysis provide those values.

You could try the method with ccx to see if there is any unexpected drawback. I recall trying once but equations did’, t work in dynamic, imposed displacements in beams were not reliable and reaction forces on fixed bases where incorrect at that time so I gave up. There is an applied example in the video but not all the parameters are provided (Stiffness and dimensions ). I will give it a second try.

13

indeed, i’m designing uncounted of building structure by response spectrum, it still widely in use even have a problem and limitation. Regular building structure may not have an issue due to symmetric in plan, but complex and irregular building or any structure can have, support reaction, shell or solid model also can lead to incorrect results. In that situation, time history analysis need to conduct to clarify force or stress results in specific areas due to sign lost in response spectrum analysis.

1 Like
14

The description of the Abaqus implementation can be found here: http://62.108.178.35:2080/v6.14/books/usb/default.htm?startat=pt03ch06s03at15.html

It operates on modes from *FREQUENCY analysis but it’s a step type (like the modal superposition procedures available also in CalculiX) and it would be best to implement it as such in CalculiX as well. You can add a feature request here: Issues · Dhondtguido/CalculiX · GitHub

1 Like
15

I have tried again the method and found some weird things.

The headings (titles) for the eigenvalues are offset and it’is difficult to see what is what.

Participation factors doesn’t agree with hand calculation (scale factor of 1/3) and modes 4,5,6 shows values in the x direction which has no sense to me.

Effective modal masses and total effective masses show again values in the x direction for modes 4,5,6. Looking at the shapes for those modes it seems to me there is no mobilized mass in X direction.

By other hand, reaction forces on the bases are still wrong unless section print is used to extract them.

IMAGE EDITED: Hopefully the discrepancy (1/3) is more clear now. Comparision between total effective modal mass and total effective mass wasn’t right. Not it is corrected.

imagen
imagen1153×783 77.8 KB

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119,S1
119,S2
119,S3
119,S5
120,S1
120,S2
120,S3
120,S5
*SURFACE,NAME=FLOORS1
130,S4
132,S4
134,S4
*SURFACE,NAME=FLOORS2
135,S6
3,S6
56,S6
*SURFACE,NAME=REACTION1
127,S6
11,S6
*MATERIAL,NAME=W3
*ELASTIC,TYPE=ISOTROPIC
2.1E+13,0
*DENSITY
6116207.951
*MATERIAL,NAME=COLUMNS
*ELASTIC,TYPE=ISOTROPIC
33500000000,0
*DENSITY
1E-10
*MATERIAL,NAME=W2
*ELASTIC,TYPE=ISOTROPIC
2.1E+13,0
*DENSITY
7339449.541
*MATERIAL,NAME=W1
*ELASTIC,TYPE=ISOTROPIC
2.1E+13,0
*DENSITY
5504587.156
*BEAM SECTION,ELSET=W3,MATERIAL=W3,SECTION=RECT
0.1,0.1
1,0,0
*BEAM SECTION,ELSET=COLUMNS,MATERIAL=COLUMNS,SECTION=RECT
0.1,0.1
1,0,0
*BEAM SECTION,ELSET=W2,MATERIAL=W2,SECTION=RECT
0.1,0.1
1,0,0
*BEAM SECTION,ELSET=W1,MATERIAL=W1,SECTION=RECT
0.1,0.1
1,0,0
*BOUNDARY
1,1,,0
1,2,,0
1,3,,0
1,4,,0
1,5,,0
1,6,,0
2,1,,0
2,4,,0
2,5,,0
2,6,,0
3,1,,0
3,4,,0
3,5,,0
3,6,,0
4,1,,0
4,4,,0
4,5,,0
4,6,,0
5,1,,0
5,4,,0
5,5,,0
5,6,,0
6,1,,0
6,4,,0
6,5,,0
6,6,,0
7,1,,0
7,4,,0
7,5,,0
7,6,,0
8,1,,0
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8,6,,0
9,1,,0
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10,1,,0
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10,3,,0
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22,1,,0
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56,1,,0
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70,1,,0
70,4,,0
70,5,,0
70,6,,0
71,1,,0
71,4,,0
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71,6,,0
72,1,,0
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72,5,,0
72,6,,0
73,1,,0
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74,1,,0
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74,5,,0
74,6,,0
75,1,,0
75,4,,0
75,5,,0
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76,1,,0
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76,5,,0
76,6,,0
77,1,,0
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79,1,,0
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80,1,,0
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80,6,,0
81,1,,0
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82,6,,0
83,1,,0
83,4,,0
83,5,,0
83,6,,0
84,1,,0
84,4,,0
84,5,,0
84,6,,0
85,1,,0
85,4,,0
85,5,,0
85,6,,0
86,1,,0
86,4,,0
86,5,,0
86,6,,0
87,1,,0
87,4,,0
87,5,,0
87,6,,0
88,1,,0
88,4,,0
88,5,,0
88,6,,0
89,1,,0
89,4,,0
89,5,,0
89,6,,0
134,1,,0
134,4,,0
134,5,,0
134,6,,0
143,1,,0
143,4,,0
143,5,,0
143,6,,0
*EQUATION
2
6,3,1,2,3,-1
*EQUATION
2
7,3,1,3,3,-1
*EQUATION
2
8,3,1,4,3,-1
*EQUATION
2
6,2,1,2,2,-1
*EQUATION
2
7,2,1,3,2,-1
*EQUATION
2
8,2,1,4,2,-1
*STEP,PERTURBATION
*FREQUENCY
6
*NODE FILE,GLOBAL=YES
U
*EL FILE
S,NOE,ENER
*END STEP
1 Like
16

OpenSees implementation with an example: 3.2.11. responseSpectrumAnalysis Command — OpenSees Documentation documentation

1 Like
17

Searching for the normalization criteria for participation factors I realized Don Guido is working on something related.

“Add output for fraction of total effective modal mass and total effective mass.”

ADDED: It seems to me the participation factors are not computed using the displacements values obtained for each mode shape. In my example above, the participation factor has been computed using mode shape displacements reduced by 1/3.
As a result of that , the user can’t directly make the product of the Sai * Participation factor * mode shape because the connection is broken.

Wouldn’t the actual displacement results combined with the actual Participation factors lead to incorrect Shear forces on each Stori?

imagen
imagen1833×462 130 KB

IMAGE EDITED: Hopefully the discrepancy (1/3) is more clear now. Comparision between total effective modal mass and total effective mass wasn’t right. Not it is corrected.
screenshot.31
screenshot.311153×783 189 KB

1 Like
18

in chapter 10 of this book you have a complete worked example with masses and springs, that can be used for a more complete understanding and development of the algorithms and for checking as well. Strongly recommended.
Mechanical Vibrations in Spacecraft Design | SpringerLink

19

Thank you all.
I will start with Fig. 10.6. Four mass-spring-system. Looks easy and directly computable.
Book provides Mode shapes, natural frequencies, and modal participation factors to use as reference.
Let’s see if I can find where that strange 1/3 comes from.

20

For the simplest unidimensional problem of Four puntual mass-spring-system the result is as expected.

imagen
imagen1137×778 61.6 KB

Participation factors and mode shapes in ccx need to be scaled by an overal factor of 1/2.236 and 2.236 respectively to agree with the book solution.
I understand that is not a problem. Displacements and Stresses can be arbitrary scaled in a frequency analisys if it is done globally and if Participation factor is done acordingly too.
In Ccx, modes are mass-normalized. Once scaled, they perfectly agree with the book reference.

The problem is that, for the previous case (2D Building), the mass is distributed acoss the floor and roof. The TOTAL EFFECTIVE MASS do not coincide with the input masses as it happens in this simplified problem. By other hand, the three Strori building shows EFFECTIVE MODAL MASSES into directions that are constrained. No mass can be movilized into those directions (x). I think that is a bug.
This do not happen in the 1D springs model where EFFECTIVE MODAL MASS in constrained directions are exactly zero.