## 1 Introduction  
Fatigue analysis is an essential part of the design of machine elements and structures subjected to variable loading [1; 2]. It is carried out at the design stage and during the improvement of the structure using basic fatigue information related to the materials. These are mainly fatigue stress or strain characteristics, so called fatigue curves, which are obtained in the laboratory under simple loading conditions, such as axial push-pull or reverse torsion [3; 4; 5]. In order to use such simple information about materials to predict the fatigue life of complex structures under real loading conditions, an algorithm should be developed that takes into account all aspects affecting the fatigue life of the machine and structure components. Typically, the following elements are considered [6; 7; 8]:  
Load Analysis: The algorithm should take into account the complexity of the loads, including static and dynamic loads. This includes understanding the magnitude, frequency, and distribution of loads to which the machine components or structures will be subjected during their service life. In addition, the load should be represented by appropriate quantities, such as time histories, PSD functions, or other statistical quantities required by the computational algorithm. In many cases, numerical modelling, including the finite element method (FEM), is used to determine the load; therefore, the input quantities should be matched to the tools used in fatigue analysis. Stress and Strain Analysis: The algorithm should account for the stresses and strains generated in the machine elements or structures due to the applied loads. This involves performing stress analysis and calculating the stress and strain amplitudes at critical locations. In this case too, tools such as FEM are helpful, but classical formulas for stress concentration or stresses in cross-sections are also used. It should be remembered that the stress value has a large influence on the calculated life because the SN characteristics are exponential in nature. It is crucial to account for the response of the material to variable loads by employing suitable hypotheses for the accumulation of fatigue damage, such as Miner's rule or other more advanced models based on the specific application. Additionally, the algorithm should address the multiaxial nature of the stress state. Material Properties: It is crucial to consider the material properties, such as yield strength, ultimate tensile strength and fatigue strength limit. These properties determine the response of the material to cyclic loading and are essential for accurate fatigue life prediction. This data is typically represented by an S-N curve, which relates stress amplitudes to the number of cycles to failure. The quality of the material also plays a huge role in determining fatigue life. Usually, the more inclusions and inhomogeneities a material has, the greater the scatter in the experimental results of fatigue life tests. This must be taken into account in the calculations. Environmental Factors: The algorithm should account for environmental factors that can affect fatigue life, such as temperature, corrosive conditions and exposure to other potentially damaging agents. Scale and Stress Concentration Effects: If the machine elements or structures contain notches, fillets, or other stress concentration features, the algorithm should incorporate methods to assess their impact on fatigue life. This may involve applying appropriate stress concentration factors and combining them with FEA to model local stress concentrations. It should be remembered that the concentration of fatigue stresses in a given element causes different fatigue effects depending on the material it is made of--some materials are more or less sensitive to the effect of stress concentration. The scale effect should be considered if the volume of material subjected to fatigue stresses is not comparable with laboratory samples.