## Geometrical modelling of the stress state on the basis of the functional voxel method.

### Reporter: Pushkarev S.A.

In the context of the ambiguity of various approaches to the study of the stress state of a solid body, the search for new algorithms and methods for solving this class of engineering problems is relevant. One of such directions is the functional-voxel modeling. The methodology of this method is aimed at building a voxel computer representation of a functional area of any dimension and complexity of description.

The advantage of the functional voxel model is that it is differentiated and carries information about the local geometric characteristics at each point. It allows to use it for obtaining integrated characteristics, including simulation of the stress state. On the other hand, the color coding of such models allows a person to make their visual assessment.

This approach allows us to talk about the following advantages of the functional-voxel modeling in relation to problems of tension:
• Potentially increases the accuracy of the data.
• Reduces the probability of blind spots in the structure of the object.
• It is possible to transmit information about the complex properties of the object, such as the internal structure of the material, etc.

The described method is based on the decomposition of the process of external force on a number of physical phenomenon. After that, the graphic images of these processes are obtained and combined into a total graphic image of the stress state at a point called the single image of stress state. Single images of stress state can be united in fields of tension depending on geometry of the considered bodies.

At the moment, the authors have examined in detail the issues of mathematical substantiation of the proposed methodology, problems of accuracy and conversion of the received models. Comparison of the obtained results with the results obtained using CAD based on the finite element method (FEM) were given.
The described method allows to approach the modeling of the stress state from the new side. According to the authors, this approach is closer to classical theories of stress than modern numerical simulation methods, since, unlike operations on a minimum volume (finite element), it relies on the solution of the problem of finding tension at each point of the body. This opens up broad prospects in the field of solving problems of modeling not only stress, but also more complex problems of modeling deformation and fracture.

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