|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Finite Element Analysis of perforated panel: deflections, bending moments, shear forces.
|
|
|
|
|
Over several years our company devoted its efforts to developement of a very accurate and time-efficent software
for modeling of bending of plates using quadrilateral elements based on the Mindlin theory.
The result of our efforts has been
a release of QUAD-PLATE -
a very advanced program for Finite Element Analysis of stresses, strains and deflections arising in complex structures
comprised of plates and beams.
QUAD-PLATE is offered
with complete source codes written in standard C/C++.
It is available without any royalties or additional fees.
This page is devoted to an example commonly encountered in modern civil engineering: bending of perforated panels under lateral loads.
Perforated panels are very popular, for a variety of reasons. Perforated
sunshades and sunscreens provide
privacy for building occupants
without blocking the view. And they
offer a comfortable level of natural
lighting during daylight hours while
deflecting heat.
At the same time, perforated panels must be able to withstand, without excessive deformation or total failure,
certain loads, for example: strong winds. An example of FEA analysis of one such panel is provided below.
Consider analysis of a thin, square-shaped perforated panel with "diamond"-shaped
openings under the action of uniform lateral load (for example: a strong wind).
Two opposite edges of the panel are jammed (no displacements of rotations are permitted);
the other two edges are free.
A 100%-quadrilateral finite element model was generated by
QUAD-GEN 3.5 - our advanced 2D product intended
for meshing of complex domains with numerous, variously shaped openings.
Calculations were performed for a plate made of material with the following properties: the Young modulus of 200 GPa,
the Poisson ratio of 0.3.
The shape of the panel is square, with the edges' length of 0.5 m; the panel thickness is 3 mm. The applied load (surface pressure) equals 1.2 kN(m*m).
|
|
|
|
|
|
|
|
|
|
As mentioned above, the panel is laterally loaded with evenly distributed forces. A zoomed fragment
of a part of model (indicated by green-edged rectangle on the image above) is presented below, with
the applied loads represented by pink-coloured arrows.
|
|
|
|
|
|
|
|
|
|
The model contains 37076 quadrilateral finite elements based on the Mindlin theory. The corresponding
global stiffness matrix has the size corresponding to 116277 degrees of freedom; it is fully assembled and solved in about
90 seconds on a PC with Intel i5 Dual Core processor (solution is obtained much faster for thicker plates,
due to better spectral properties of the global stiffness matrix). On the image below, the panel is shown in its deformed state
under the abovementioned lateral load.
|
|
|
|
|
|
|
|
|
|
That model was sufficiently accurate to evaluate deformations of the panel. However, it also
turned out that the finite elements in the vicinity of round corners of the panel were too large
to adequately evaluate the bending and twisting moments, due to their large gradients, which
is a well-known phenomenon arising where significant geometrical irregularities are present.
In order to evaluate the moments (and the shear forces, although they are not important in this case due to the
low thickness of the panel) in the vicinity of round corners,
another mesh was created, this time containing 145625 quadrilateral elements, and the
number of degrees of freedom in the whole model was 445305, i.e. almost half-million. (The
bending and twisting moments are calculated in kN*m per meter length.)
|
|
|
|
|
We present the following results for:
bending moments
twisting moment
reactions (forces and moments) in the nodes of the clamped edges of the panel
|
|
|
|
|
Bending moment Mx:
|
|
|
|
|
|
|
|
|
|
From the image above it can be seen that the moment values
experience maximum gradients
in the vicinities of round corners of the openings.
In a zoomed image below, illustrating the moment distribution around
the second from the top lent-hand corner opening, that fact can be readily observed.
|
|
|
|
|
|
|
|
|
|
Bending moment My:
|
|
|
|
|
|
|
|
|
|
Twisting moment Mxy:
|
|
|
|
|
|
|
|
|
|
Reactions in the clamped nodes (forces and moments are coloured magenta and blue, correspondingly):
|
|
|
|
|
|
|
|
|
|
|
|
QUAD-PLATE is available with complete source codes
and the full commercial lisence allowing easy incorporation into your own
applications.
All our codes are written in standard C/C++ and will compile and run on all UNIX
and Windows platforms without changes. They are also
fully commented, allowing easy modification at user's discretion.
QUAD-PLATE is available on no-royalties and
no-annual-renewals basis: there is a one-off price for an
unlimited commercial lisence.
QUAD-PLATE standard distribution kit includes:
- fully-commented source codes of the program in C and C++.
- the product's User Manual containing detailed description of input and output
data structures;
- a graphical application that allows the user to visualize input and output data of QUAD-PLATE for each particular
example created by the user.
QUAD-PLATE has been completely developed by our company and contains
no third party code.
To learn more about the full range of our products please follow this
link.
We invite you to contact us, preferably by e-mail on
comecauinfo@gmail.com
Alternatively, please send us SMS message on +61-411-278-528 or call us on the same number.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
