Section 4, classification of fatigue load and life estimation. I will first introduce different types of fatigue loading, then I'll talk about fighting purposes of material as a stress live diagram in different regions. In the following relationships for solving high sycophantic problems on the actual constant amplitude loading and the effects of ministers emphatic life are presented. Finally, several well-known methods for cycle counting for second, third type of loads, namely variable amplitude loading and random loading are discussed. Their ideology is truthfully explained, and one of the most create methods, namely rainflow cycle counting, is taught to using an application software. As I stated earlier, fatigue loads have cyclic or repetitive problems. The two most prominent features of these are frequency and amplitude. Therefore, based on these two parameters, fatigue loads are divided into three main groups. Constant amplitude loading, which is so-called CAL, in this type of loading both amplitude and frequency are constant in terms of time. A sinusoidal function is a simple example of this type of loading that has a constant maximum, and minimum values throughout the history, and is also a fixed time period. For example, consider a sinusoidal function that has a frequency of 10 hertz and the maximum amplitude of 2 millimeters. Now, if you are at the top level, means 2 millimeter, you will be always on the same peak in the 10 hertz interval. It means 10, 10, 10, 10. You are in the top, top and top. For this wave, you can consider the following formula. Y is equal to 2 multiple sine 10 plus T. In this figure, you can see the details for our fatigue point of view, there are many definitions in a loading history like maximum loading, minimum loading, mean loading, loading ratio, loading range, and loading amplitude. You can see the mathematical relationships between these parameters in this slide. Loading ratio; this parameter is defined as the ratio of minimum loading to maximum loading. It should be noted that the loading can be anything. For example, stress ratio, force ratio, strength ratio and so on. Loading range; that is defined as a maximum loading, subtract minimum loading and loading and amplitude, that is the half of loading range. Mean loading is defined as summation of maximum and minimum load divide into two. In this figure, they form of various common functions for the constant amplitude mode is shown. Sine, square, triangle, and sawtooth. Previous mathematical relationships for each of these patterns are also defined. For example, these features for the triangle function are shown in this figure. The second group is variable amplitude loading, which is so-called VAL. In this type of loading on the frequency parameter is constant, and the amplitude changes over time. Let's go back to the previous example, and think of this formula, y is equal to A multiple sine 10 T, in which A is a random number. The shape of this function resembles a sinus which has varying range over time. These domains have no particular pattern and are completely random, however they have a fixed frequency of 10 hertz. That is the intervals between the data are the same. An example of this type of loading is shown in this figure. The third group is random loading, which is so-called RL. This is the mass complex type of loading in which post- amplitude and frequency parameters are variable. In nature mass of laws are inherently random, such as earthquake, wind, [inaudible] roughness, sea waves, and so on. Here is an example of random loading. Of course, it should be noted that the laws of nature have a normal probability distribution function. Please be careful. A very important and challenging question. Suppose you want to estimate the SRS on a mechanical parts of your vehicle as a result of road roughness. To this end, consider the certain paths from your home to the University. Also assume that the entire path is empty and free. There is no cars, no people, and so on, and nothing else that will change your driving behavior during the test. For a test, please use your accelerometer application of your cell phone. Repeat these experiments several times and compare recorded history with each other. Are all histories the same? Now, we are studying in time domain. Surely all of them are different and this expresses the nature of road excitation that are random. Important question. Which history should be used for analysis? Maybe some of you say that we can use each one. All of them are right because they are the results of experiments. Well, now that there are different histories, the corresponding answers are definitely different. Which is the right answer? What should we do? Good, that's right. Use their average. How is their average calculated? Or how many histories do we have to record firstly, and then calculate the average. Now, let's go to the solution. Many of these answers can be obtained by converting time domain into the frequency domain. What does it mean? Like using the Laplace transformation to solve differential equations, do you remember? Here, the frequency domain can be hope to solve the problem. Where we have less data. Look at the shape of sinusoidal function. At least five points containing the x and y components are required to draw it. In other words, at least 10 mathematical data are required, which five of them are x and the rest are y. In order to have a more accurate drawing or a smooth shape, it is better to have more data. But in the frequency domain only two data, including frequency and amplitude, are needed. It means only one point. Look at this diagram. These points represent the behavior of a sinusoidal function. Obviously, it is much better to perform a complex calculation with less data. Of course, some researchers, and especially [inaudible] , believe that frequency domain solutions are far more in line with laboratory results than time domain results. However, in very complex issues, they will have a much lower computational occurs, which is sometimes preferred to investigate in frequency domain. The time to frequency domain conversion is done using Fast Fourier transformation function, which is so-called FFT. Its inverse, namely, IFFT, is used to convert frequency to time domain. In this regard, power spectral density is defined as the best thing is when the statistical parameters including mean, mean squared and variance, have the same values across all recorded histories. In other rules, also the timing storage recorded differ. They have the same statistical parameters and their behavior in the frequency domain are equal. It can be calculated the conversion of time to frequency, there is a unit. But it is not true for inverse of it. The mathematical equation for obtaining these statistical parameters are shown in this slide.