Computational Mechanics Australia Pty Ltd
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QUAD-PLATE
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).

Mesh of perforated panel
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.
Loaded fragment of perforated panel
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.
Deformed perforated panel
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:
    Bending moment Mx in perforated panel under uniform load
    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 Mx around top left-hand side opening in perforated panel
    Bending moment My:
    Bending moment My in perforated panel under uniform load
    Twisting moment Mxy:
    Twisting moment Mxy in perforated panel under uniform load
    Reactions in the clamped nodes (forces and moments are coloured magenta and blue, correspondingly):
    Nodal reactions (forces and moments) in perforated panel
    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 also invite you to contact us with any questions, preferably by e-mail on comecau@ozemail.com.au or comecau1@bigpond.net.au.