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New shear lock free finite elements with arbitrary higher order derivative

A set of highly efficient and shear lock free finite elements based on Timoshenko  beam and Reissner-Mindlin plate theories has been developed for the analysis of thin and thick structures. These elements have arbitrary higher order derivatives and do not require any spcial integration scheme. All are isoparametric elements.


Ji Wang's picture

Sharing a book draft on the vibration analysis of quartz crystal resonators

In collaborations with industrial engineers on the design and analysis of quartz crystal plate resonators, which involves the high frequency vibrations of piezoelectric plates with Mindlin plate equations, we have to go through the details of plate equations for every stages in the analysis.  In addition, complications and bias fields are also considered.  We have put together our papers and written a draft of a book detailing essential equations and methods.  We now share this draft with you if you would like to read some documents to know insights on this particular subject.

Abaqus results

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i try to simulate a 3 points bending of a glass plate with abaqus.

force 1kN !

young modulus = 7e10 Pa

Poisson's ratio = 0.22

- the plate is square (30 cm) , thickness 8.72 mm

- i use 3D extruded solid

- for the load i can't create a line load so i replace this load by pressure in a thin surface (2mm*30cm) applied in the center of the plate

- C3D8R element type

 but the results are strange:

the maximum displacement is 0.672 mm !

is that realistic ? 1kN and just 0.672 mm of central displacement  ?

Kirchhoff–Love plate using COMSOL


Is it possible to solve with COMSOL a frequency domain problem for a plate using Kirchhoff–Love kinematic assumptions ?

Thank you,

a question about vibration of plates having variable thickness

Hi everybody!

for plates with constant thickness and two opposite sides simply-supported B.Cs, we can write w(x,y)=f(y)*sin(m.Pi.x) and solving the problem from this viewpoin.

I wonder whether this approach is true for plates with (linearly) variable thickness?

many thanks

Rui Huang's picture

von Karman plate equations

Many of us (including myself) have used the nonlinear equations for elastic plates, originally proposed by von Karman (1910). I recently came across a book with some interesting comments about the plate equations, which may be of interest to share with others on imechanica. The book's title is "Plates and Junctions in Elastic Multi-Structures", authored by Philippe G. Ciarlet and published by Springer-Verlag in 1990.

Time depended modeling of plate

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i'm working on the modeling of thin plate under transverse load. The basic function used for approximation of field variable is RBF function. There are a lot of publications, how the static model of the plate can be created, but no information about dynamic modeling. The following questions are not clear for me:

MichelleLOyen's picture

S. Germain, "Memoir on the Vibrations of Elastic Plates"

I have not read the above-mentioned paper, as I have never been able to find it. However it is said to be "a brilliantly insightful paper which was to lay the foundations of modern elasticity." However, I believe it is also noteworthy for being one of the major contributions by a female mechanician prior to the modern era. For a great biography of Sophie Germain, including a fantastic quote from a letter from Carl Gauss on discovering that she was female--and not "Monsieur Le Blanc"--visit this site (from which the above quote, on the impact of her paper, came).

There are no female mechanicians listed on but I believe it could be argued that Germain deserves a mention!

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