Computational Mechanics Australia Pty Ltd
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A new quadrilateral finite element for modeling of shells based on the Kirchhoff-Love theory.

Available with source codes and intended for scientific and engineering research.
We at Computational Mechanics Australia Pty.Ltd. have always considered the development of high quality and precision algorithms for the finite element analysis as our primary mission. One of the aspects of our efforts has been the development of commercial software for quadrilateral meshing of spatial plate-and-shell constructions.

Quadrilateral elements have been long known as the best choice from the precision point of view. The theoretical fundamentals of such quality finite element analysis are quite complex. There are many reasons for that, one of them being that such elements are prone to a phenomenon known as "locking". Also, the global stiffness matrices of finite element models representing thing-walled structures can be rather ill-conditioned.

Those were just a few reasons to mention for which we embarked several years ago on a new project named QUAD-SHELL . It has resulted in a completely new approach to the problem and a new finite element that demonstrated excellent numerical properties for all quadrilateral meshes on shells, regular and irregular .

We decided to publish and distribute the results of our work as a book supplied with codes in C/C++ implementing the newly developed shell element. The book is devoted to two subjects representing some of the most challenging areas of computational mathematics and mechanics of shell structures.
  • We introduce a new method that allows construction of the lines of principal curvature on arbitrarily complex curved surfaces.
  • We also explain in detail the corresponding algorithms and their implementation.
  • We describe an application of the abovementioned algorithms to the finite element analysis of thin shells, with the goal to develop finite elements that would deliver high-quality numerical results, especially for displacements and for the components of the stress tensor.

  • The book provides
  • theoretical introduction in differential geometry, as well as
  • mathematical fundamentals of the theory of thin shells.

  • As a result the readers can study and/or use the book without a necessity to refer to other books or information sources, i.e. just a general mathematical and mechanical engineering background is required.

    As mentioned above, the principal value of the book is a completely new numerical method that allows constructing the lines of principal curvature on any type of curved surface.

    That was a challenging work, and the authors invested a lot of effort to ensure that the developed algorithms are solid and reliable. As an application of the developed method, we chose to create a new 9-node finite element and to test it on several models for which analytical solutions are known. The obtained numerical results have proven that the new approach delivers high quality numerical solutions. Importantly, we provide the complete source codes in C++, which can be immediately compiled and run.

    The book is intended to address the needs of broad community of
  • mathematicians
  • mechanical engineers
  • developers of finite element analysis software
  • academics
  • students.

  • To order your copy of the book and the source codes now , please contact us by e-mail on or
    Example from the book.
    Purchase and Delivery
    The book is available on Amazon as paperback or hardcover.

    You can also order the book by contacting Computational Mechanics Australia Pty. Ltd. As mentioned above, when you purchase the book we shall provide you with the complete, commented source codes of QUAD-SHELL, which you can use for scientific and engineering research purposes. The book will be delivered to you by Air Mail or by a courier service(FedEx delivery available).

    We invite you to contact us, preferably by e-mail on or We can also help you with other
  • mesh generation
  • computational geometry, and
  • general finite element analysis needs.

  • To learn more about full range of our products please follow this link.