Ключевое слово: «numerical modeling.»

The elasticity problem is widely used in various fields of engineering and construction, as well as in materials science and mechanics. This work examines the application of elasticity problems for analyzing the behavior of materials under various loads and influences, as well as for calculating deformations and stresses in structures and elements[3]. Numerical modeling of elasticity problems is a relevant and important area in engineering practice. This method makes it possible to predict the behavior of materials under different loads and conditions, which is essential for the design and analysis of various structures. Perforated domains play a key role in engineering applications; however, the presence of holes can significantly affect the mechanical behavior of the material[1]. This article focuses on presenting mathematical models and numerical methods for analyzing the behavior of materials with perforations. Such models make it possible to account for the influence of hole geometry, their sizes, and arrangement on the distribution of stresses and deformations. Numerical modeling is carried out using the finite element method, the FEniCS library, the gmsh program, and visualization in Paraview.

This paper presents the development and research of a compact digital holographic microscope model based on Gabor's in-line holography scheme. The model is implemented on the Raspberry Pi Zero 2W platform, ensuring portability and low system cost. The capability to record holograms of diffraction gratings and biological samples has been experimentally confirmed. A comprehensive numerical approach has been developed to analyze the system's limitations, evaluating the influence of five key factors on resolution: object-to-sensor distance, temporal and spatial coherence of the source, pixel size, and field of view. The method was validated using the USAF-1951 test target. It has been established that the most significant limitations are associated with pixel size and the geometry of the optical setup. The proposed tool allows for optimizing microscope parameters at the design stage without conducting physical experiments.