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Unexpected discrepancy when solving a plate bending problem using weak form PDE module
Posted 14 gen 2025, 21:39 GMT-5 Equation-Based Modeling, Modeling Workflow 2 Replies
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Hi there,
I am trying to solve the deformation of a boundary clamped thin circular plate bearing uniform pressure. This problem possesses axisymmetry, but I also tried to solve it in 2D space (model 2D) besides in the 1D axisymmetric space (model 1D) for validation. Please note that only the Kirchhoff-Love plate model is employed in model 2D, model 1D, and the analytical solution.
The value of bending stiffness 
is assigned directly, instead of calculated through Young's modulus, so and Poisson ratio 
in this case are considered independent.
It seems there is something wrong with model 2D: i) the model is hard to converge; ii) even if it converged, the deflection would be larger than theoretical prediction and show dependence on Poisson ratio. To be specific, the center deflection predicted by model 2D monotonically decreases toward the analytical solution as Poisson ratio decreases from 0.5 to -1.
By comparison, model 1D works well. It agrees with the analytical solution regardless the value of Poisson ratio.
I would appreciate if you could give me a hint.
Best,
HC L
If we take a=2, q=1, D=1000, and an arbitrary nu, the center deflection is theoretically 2.5e-4.
details about model 2D (the picture is also attached below):
details about model 1D (the picture is also attached below):
The .m files of the two models are attached
Post was updated on 2025.01.16 to provide more details.
Updated on 2025.01.22 to attach the .m files of the two models.
Attachments:
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Hello,
I suspect what you are experiencing is a numerical phenomenon called shear locking. If that is the case, you will notice that the discrepancy between the analytical solution and the numerical solution worsens when the relative thickness of the plate decreases. There is abundant literature on the subject and the link above includes a description of some common remedies. To avoid this phenomenon, the shell elements implemented in COMSOL software are based on the MITC (Mixed Interpolation of Tensorial Components) formulation.
Best,
Jeff
-------------------Jeff Hiller
Please login with a confirmed email address before reporting spam
Hello,
I suspect what you are experiencing is a numerical phenomenon called shear locking. If that is the case, you will notice that the discrepancy between the analytical solution and the numerical solution worsens when the relative thickness of the plate decreases. There is abundant literature on the subject and the link above includes a description of some common remedies. To avoid this phenomenon, the shell elements implemented in COMSOL software are based on the MITC (Mixed Interpolation of Tensorial Components) formulation.
Best,
Jeff
Hi Jeff,
Thanks for your reply.
I looked into the concept of 'shear locking'. This numerical phenomenon happens in the FEA of beams and plates when elements used to analyze deep beams or thick plates are utilized to analyze slender beams or thin plates. It is great that COMSOL provides solutions to this notorious issue in the shell elements.
It is regrettable to me that classical shell models are not appliable to my cases. So, I have to seek more flexibility through the 'weak-form-pde'.
I apologize for not clarifying my question. In the case I post, only the Kirchhoff-Love plate model is employed in model 2D, model 1D, and the analytical solution. Both model 2D and model 1D are implemented through the weak-form-pde module. So, 'shear locking' doesn't seem to be an issue.
Despite this, thank you again for your reply.
Best,
HC L