Computational Mechanics Australia Pty Ltd
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Quadrilateral mesh generator for complex curved and flat surfaces.
One of the most challenging problems in modern engineering is conversion of geometric data produced by CAD systems into finite element meshes acceptable for futher analysis. Thin shells and plates of complex shapes comprise a very large proportion of structures arising in engineering industries, particularly automotive and aeronautical. Analysis - with high degree of precision - of stresses, natural frequencies and other mechanical properties is absolutely vital; this is because if numerical results are "too approximate" then the structure will be either too heavy (if the actual stresses are lower than calculated ones), or not posssesing required strength (in the opposite case).

Quadrilateral finite elements deliver very accurate numerical results. For that reason a quality mesh generator allowing 100% quadrilateral meshing of surfaces in 3D represents a necessary part of any commercial-quality FEA system.

QUAD-SURFACE was developed to directly address that problem; it is the newest addition to the full range of our state-of-the-art quadrilateral mesh generation products. QUAD-SURFACE is a mesh generator capable of delivering exceptionally accurate finite element meshes for a broad range of surfaces in 3D such as: planar, cylindrical, spherical, general 3D, surfaces of revolution, as well as their arbitrarily complex spacial combinations. For complex, real-life surfaces in 3D, QUAD-SURFACE allows generation of 100% quadrilateral meshes of very high quality. In turn, the later will guarantee that the consequent finite element analysis delivers excellent numerical results.

What advantages does QUAD-SURFACE have ?


  • meshing of complex plate and shell structures in 3D space, consisting of flat, cylindrical, spherical components, surfaces of revolution and also general-case 3- and 4-edged patches;
  • meshing of non-homogeneous domains, consisting of multiple plates and shells with different physical and/or geometrical properties;
  • generation of Lagrangian and serendipity meshes on spatial surfaces. In many cases such surfaces are made of composite materials, often consisting of several anisotropic layers. The additional nodes of 8-noded serendipity and 9-noded Lagrangian elements are always placed on the surface, thus preserving as much as possible the original shape of the surface. Whereas 4-noded bilinear finite elements often deliver acceptable results for nodal displacements only, the surface shape preservation is absolutely necessary for obtaining accurate evaluation of the stress tensor components.
  • easily readable and convenient description of geometrical models;
  • fully automatic processing, requiring no interference from the user.

  • QUAD-SURFACE allows generation of refined meshes in user-defined zones inside planar domains, which is very important when the model contains points where large stress tensor gradients are expected (point loads and constrains).

    At the same time, the product input data structures are simple and natural, allowing straightforward incorporation of QUAD-SURFACE into full-scale FEA systems. Processing is fully automatic: no user interference is required during the meshing process, regardless of the actual complexity of particular input data.

    Below we provide a number of difficult geometries to produce meshes that have been successfully generated by QUAD-SURFACE . We invite you to contact us to obtain more examples or additional information; our contact details are placed at the end of this page.
    Example 1. Curved and flat surfaces.
    Example 2. Surface of revolution.
    Among the huge variety of thin-walled shells encountered in the modern engineering, surfaces of revolution occupy a very special place: there are domes, pressure vessels, balloons and many others.
    Example 3. Helicoid.
    Example 4. Tubular joint.
    Tubulat joints represent one of the most common structural components encountered in the offshore engineering models. Being a general-case surface mesh generator, QUAD-SURFACE creates quality, 100% quadrilateral meshes on tubular joints; at the same time, it allows other parts of complex shell constructions to be attached to one or several joints.
    QUAD-SURFACE is available with complete source codes and full commercial lisence, readily allowing incorporation into your own applications. All our codes are written in ANSI C and will compile and run on any UNIX and Windows platform without change. They are also fully commented, allowing easy modification at user's discretion.

    QUAD-SURFACE is available on no-royalties and no annual renewals basis: there is a on-off price for the unlimited commercial lisence.

    QUAD-SURFACE standard distribution kit includes:

    - fully-commented source codes of the program in ANSI C,

    - the product's User Manual containing detailed description of input and output data structures and an example driver program;

    - a smple graphical application that allows displaying domains that are to be meshed, as well as generated quadrilateral meshes.

    QUAD-SURFACE is completely developed by our company and contains no third party code.

    Finally, our "try-before-you-buy" policy. If you send us several examples of your domains, we will run QUAD-SURFACE and send you the generated meshes. If you are satisfied with results, you can then buy QUAD-SURFACE.

    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 or