Demo model 1 - Section Bearing Capacity

**iee Finite Elements**

system has the following distinctive features:

-** A****ccessibility**. The entire IEE Finite Elements system is an open source freely available utility; there is no need to pay for its installation or tutorials, as there is no need to acquire an expensive powerful computer. Problems are solved on a specialized computational Cloud-type server, which allows to perform high-speed parallel computations using graphic processors based on Cuda ™ technology. Meanwhile a workstation user may not be any the wiser as to the complex technology of sending and receiving data through the Internet, and simply obtain the solution of the required problem. For the needs of the future project development, paid access will only apply to usage of the computational server in commercial projects. The parametrical problems created on the basis of Iee Finite Elements can be accessible from any Internet-connected device, thus making the finite-element method accessible for tablets and smartphones.

**- Transparency.** IEE Finite Elements is an open source system, in which all models and methods of calculation are transparent for users to analyze. Material models and finite-elements are written in the simple Java ™ programming language applying technologies of IEE Mathematics, which makes the program code accessible not only to programmers, but also for any specialists on material models and finite-element method.

**- Openness. **IEE Finite Elements permits users to realize their scientific ideas on development of new finite-elements and material models. Computational schemes can contain arbitrary sets of degrees of freedom and can be used to model a broad range of physical processes and phenomena (calculation of deformations, temperature fields, filtrations of fluids and many others). The users shall also have an opportunity to sell access to the models created by them.

**Finite-element scheme editor (IEE Editor)**

The Iee Finite Elements system provides the user with a very broad range of opportunities for parametrical creation of computational schemes. All examples featured on the site are created this way. Sometimes this approach is more convenient than editor-drawn geometrical schemes. Conversely, we are not going to force users to program geometry when it easier to draw it. That is why the IEE Editor is an important component of the system. Currently the editor is being actively developed. We aspire to create a simple and convenient toolbox for three-dimensional drawing. To simplify drawing in three-dimensional space we created special tools intuitively clear even to a beginner - a virtual ruler and a virtual protractor. The following figure features an example of these tools being used in the developed IEE Editor.

Finite-element meshes for geometrical figures are created automatically, with automatic conjugation of meshes for contiguous geometrical objects.

The finite-element mesh generation algorithm allows connections between differently sized objects, which disposition is especially often used in structural modelling. In the example given below, one-dimensional rod elements are conjoined with flat ones.

The important feature of IEE Finite Elements architecture is division of model geometry and finite-element mesh geometry. All computational scheme parameters (boundary conditions, load factors, materials, finite-element types) are linked to geometrical objects, such as sides and edges of volumetric bodies, lines and axes. Finite-element mesh generation settings are also linked to geometrical objects.

As a result, users should have no difficulty in performing calculations with different finite-element mesh breakdowns. In future we plan to develop adaptive mesh technologies, in which sizes of finite elements are chosen automatically.

**IEE Finite Elements** **scheme-programming environment **allows to create parametrical models in the modern Java ™ programming language using full capacity of a powerful OpenCASCADE ™ based geometrical modelling library, however, its three-dimensional drawing commands are simplified as much as possible.

Parametrical models are good for problems with similar geometry which are often repeated but use various parameters (for example, calculation of cofferdams in various ground conditions and at different excavation depths). Working in the graphic editor, users automatically create a commands protocol, studying which it becomes easy to start building up a parametrical problem. Programming of models can be performed in IEE Mathematics, which allows to display results of geometrical structuring, finite-element mesh generation and calculations directly in the text of the program. Examples of such calculations can be found on the site. The scheme programming environment in conjunction with IEE Mathematics allows, for example, to plot solution results against a computational scheme parameter according to solution of a series of finite-element problems.

**IEE Finite Elements models library **

IEE Finite Elements is a novelty programming system, which means that in its development the most advanced programming technologies are employed, simplifying both the created models and their analysis by users. However, in the core of the system there is a long-term experience that stems out of creating programs and solving a diverse range of problems using the finite-element method embodied in various previously created software such as Geomechanica (1980-1990), FEM models 1.0 (1999) and FEM models 2.0 (2002). The algorithms realized in these programs and calculation techniques are now being transferred into the library of models. Using the IEE Mathematics technology in writing the program code makes it more readable and clear not only for professional programmers.

The main motto of the developed library is openness of the initial code of all models. Each model can be studied in all its details, should the user so desire. This is very important for the practical use of the program, because it is our strong conviction that *engineers should not be held responsible for the results of using a model whose initial code is completely obscure and whose principles of operation are clear to no one.*

The finite-elements library gives users an opportunity to participate in creation of IEE Finite Elements program. Unlike the majority of programs in which the user is only allowed to create the User Defined Material, IEE Finite Elements gives users an opportunity of complete participation in development of the program. It is even possible to create a completely alternative library of elements and models. Users can develop new models of materials, create new finite-elements with any set of degrees of freedom, create special programs for converting models into other formats, analyzing results, *etc*. Generally speaking, because of the open initial code and simplicity of Java ™ based programming, IEE Finite Elements has unique potential for scientific research.

The closed code of IEE Solver functions as a kind of "key" and allows to keep the code open even for commercially available models. Model developers will be given open source access to the Solver and (at their discretion) the opportunity of opening paid access to solution of problems using the models which they developed themselves.

**Complex nonlinear problems solver (IEE Solver).**

Development of the solver for nonlinear problems had the sole purpose of making solutions as quick as possible. In modern fast-lane life and work regimes long-term solution of nonlinear problems is an inadmissible luxury. This is achieved by means of:

- high-efficiency calculations based on Cuda ™ technology using the customized computational server with the special computational processors by NVidia ™.

- nonlinear problem solution algorithms especially written to be used in parallel calculations.

For solution of problems a special preconditioner was developed, allowing a guaranteed reduction of the definition matrix condition number by a set value. Unlike the frequently applied schemes of incomplete factorization similar to Incomplete Cholesky, the developed preconditioner guarantees solution of any problem by iterative methods, allowing solution with high-efficiency parallel algorithms.

Out of the entire system IEE Finite Elements + IEE Mathematics it is only the IEE Solver which is not an open-source product. The Solver will generally be available on the paid basis. Free-of-charge access to problems solution will be available for the period of testing the service, and additionally to educational establishments and authors of new material models and finite-elements. Naturally, at the present moment, the access to the demo version of problems solution is absolutely free. The principles of access to the service will become clearer in future. However in any case our purpose is to keep the service accessible to the greatest possible number of users.