### Elements 18 and 20: results on the top and bottom layers.

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### Elements 18 and 20: results on the top and bottom layers.#1770

vom finzi
#1770
Hi all,
in respect of the elements 18 and 20, I'd like to obtain the results on the top and bottom layers.
Do you think that is possible?
In case, you have a sample routine?
Or some document describing the procedure?

Thank you all,
Andrea

### Re: Elements 18 and 20: results on the top and bottom layers#1773

#1773
Hello Andrea,

no, this is not possible for plate elements. What you may do is investigating the stresses file Z88O3.TXT: The first two entries XX and YY are the locations of the Gauss Points, thus, you get the stresses inside the plate element, but because a plate element has no Z direction (the height exists only inside the formulas for computation), this stresses apply to the surface (top & bottom are identical!) of the plate element.

If you really want the stresses on top or bottom you may use a hexahedron No.1 or No.10.

See our book (in German) "Finite Elemente Analyse fuer Ingenieure", 4th edition, ISBN 978-3-446-42776-1 for further details - besides, we are working on an English edition of this book.

Regards

Prof. Rieg

### Re: Elements 18 and 20: results on the top and bottom layers#1792

vom finzi
#1792
Thank you Prof. Rieg,
I'm waiting the English version of your book.

I checked the stresses file Z88O3.TXT (and I studied the Mindlin plate theory) and it is reported that Z88r calculate the following:
XX YY MXX MYY MXY QYZ QZX SIGXX SIGYY TAUXY TAUXZ(Z=0) TAUYZ(Z=0) SIGV

So, would it be possible to estimate top and bottom stress (using bending moments information) by the following formulas?

SIGXX_top = SIGXX + 6*MXX/(t*t)
SIGYY_top = SIGYY + 6*MYY/(t*t)
TAUXY_top = TAUXY + 6*MXY/(t*t)
SIGXX_bootom = SIGXX - 6*MXX/(t*t)
SIGYY_bootom = SIGYY - 6*MYY/(t*t)
TAUXY_bootom = TAUXY - 6*MXY/(t*t)

where t=thickness.

Thank you for the support,
Andrea

### Re: Elements 18 and 20: results on the top and bottom layers#1796

#1796
Dear Andrea,

this could work because plate theory states according to Pilkey, W.: Formulas for Stress, Strain and Structural Matrices. Wiley: New York: 1994:

t= thickness
z= Z coordinate

SIGMA XX = 12 * z / t**3 * MXX
SIGMA YY = 12 * z / t**3 * MYY
TAU XY = 12 * z / t**3 * MXY
TAU XZ = 30 * QXX / 2 / t *(1 - (2*z/t)**2)
TAU YZ = 30 * QYY / 2 / t *(1 - (2*z/t)**2)

Regards

Prof. Rieg
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