You are here
geometrically nonlinear
Thu, 2011-10-06 18:17 - sadeghbeigi
Hi,
I have a quastion about criteria for geometry nonlinear analysis.
I modeled a piezoelectric bimorph cantilever beam as the attached file linearly. I calculated the end free point of the beam displacement through this model.
I would like to know that is there any criteria for recognition the correct type of analysis. In the other hand, how can I chek that the behaviour of this structure is linear or geometrically nonlinear without nonlinear analisis?( for example by calculating the ratio of end point displacement to total length of beam). If there is any reffrenece please let me have thid.
Thank you
Mohsen
»
- sadeghbeigi's blog
- Log in or register to post comments
- 2262 reads
Comments
Approximate deflection curve
For pure bending the exact solution may be obtained.
In case the four point bending we can obtain the following resutls.
f is the exact deflection in center of beam. It is obtained from equation 1/? = M/EJ.
fap - is the approximate deflection. It is obtained from equation y'' = M/EJ.
c is the relative error. c = abs(fap - f)/f * 100%.
Then we have
fap/l = 8.66 sqrt(c) %.
For example, if the maximal deflection is less than 15% beam length then the relative error is less 3%. If the maximal deflection is less than 40% beam length then the relative error is less 22%.