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

Verfasst: **Mi 27. Feb 2013, 12:34**

von **finzi**

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

Verfasst: **Sa 2. Mär 2013, 12:14**

von **ccad**

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

Verfasst: **Fr 8. Mär 2013, 18:37**

von **finzi**

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

Verfasst: **So 10. Mär 2013, 12:05**

von **ccad**

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