# Comparison of Stress Concentration Factors Obtained by Different Methods
## 2 Notches as Stress Concentrators  
In practical applications of structural components, especially in the field of engineering and construction, it is often necessary to suddenly change the shape or cross-section of a component from a functional point of view. At the points of any cross-sectional and shape change in the structure (especially in cases of sudden changes), the continuity of the force flow is disturbed, the force lines are locally condensed, resulting in a local increase in the nominal stress. The presence of changes in the form of discontinuities in the structure leads to a modification of the simple stress distribution over the cross-section or over a localized volume of the component so that a local stress concentration is produced. This results in complex uniaxial, biaxial or even triaxial stresses, with the stress peak located at the root of the notch and its value decreasing towards the depth of the body [4, 5, 6]. Sources of increasing stress concentration are referred to as stress concentrators or generally notches. Notches can generally be divided into several basic groups:  
* Structural notches, determined by shape and geometric changes in bodies in the form of offsets, recesses, grooves, threads, holes, etc.;
* Technological notches, determined by the properties of the surface layer of the material after chemical, thermal or mechanical processing, where a special role is played by transitions between the resulting different material structures, traces of chip machining, stamped markings, grooves, etc.;
* Metallurgical notches, associated with heterogeneity and anisotropy of the material resulting from disturbances of the internal structure of the material (dislocations, vacancies, scratches, etc.);
* Notches formed during the operation of the material due to aggressive environment (corrosion) or wear (grooves, scratches) [7].  
Of the types of notches mentioned, only structural notches are desirable from a functional point of view. However, from a design and operational point of view, all stress concentrators are undesirable. To a large extent, they negatively affect the service life of the component and reduce its resistance to fatigue failure [8], because fatigue cracks initiate at the locations of local stress increase [9].  
Stress and strain analysis in the notch region is quite a challenging discipline. Historically, the regularities of stress changes with the notch region began to be more seriously addressed in the 1930 by [PERSON]. However, this problem was addressed only at the level of simple structural elements.  
In this paper, according to Figure 1, 6 shape-discontinuity-dimension-load configurations are considered:  
1. [label=()]
2. Axially symmetric 3-dimensional stepped tension bar of circular cross-section with shoulder fillet.
3. A 2-dimensional stepped flat tension bar with shoulder fillet.  
3. Axially symmetric 3-dimensional tension bar of circular cross-section with a U-shaped groove. 4. A 2-dimensional flat tension bar with opposite U-shaped notches. 5. A 2-dimensional infinitely wide thin flat body with opposite deep hyperbolic notches in tension. 6. A 3-dimensional infinitely wide body with deep hyperbolic groove in tension.