## 1 Introduction
Typically, the Goodman method (Equation (2)) and Gerber method (Equation (3)) [9] are used to correct non-uniform loading conditions. The Gerber method is less conservative when compared with the Goodman method. Additionally, in case of brittle materials, both methods tend to be similar to the Goodman method [9]. However, actual test data tend to exist between the Goodman and Gerber lines. \[\frac{\sigma_{a}}{\sigma_{ar}}+\frac{\sigma_{m}}{\sigma_{u}}=1 \tag{2}\]  
\[\frac{\sigma_{a}}{\sigma_{ar}}+\left(\frac{\sigma_{m}}{\sigma_{u}}\right)^{2}=1 \tag{3}\]  
where \(\sigma_{ar}\) is the equivalent fully reversed stress amplitude resulting in the same fatigue life, \(\sigma_{a}\) is the amplitude stress, \(\sigma_{m}\) is the mean stress and \(\sigma_{u}\) is the ultimate stress. However, the methods tend to be inaccurate in severe loading conditions wherein plastic deformation can occur in the structure. The strain-life (\(\varepsilon\)-N) curve should be considered to solve the problem [11]. The method is advantageous because it can depict the Bauschinger effect of a material. By highlighting the Bauschinger effect, the method can consider the plastic deformation of the material between loading and unloading regions. The method is given in Equation (4) as follows; [11]. \[\frac{\varepsilon_{a}}{2}=\frac{\sigma_{f}^{\prime}}{E}\times\left(2N\right)^ {b}+\varepsilon_{f}^{\prime}(2N)^{c} \tag{4}\]  
where \(\varepsilon_{a}\) is the strain amplitude, \(\sigma_{f}^{\prime}\) is the fatigue strength coefficient, \(N\) is life cycle, \(E\) is young's Modulus, \(b\) is the fatigue strength exponent, \(\varepsilon_{f}^{\prime}\) is the fatigue ductility coefficient and \(c\) is the fatigue ductility exponent. With respect to the strain(\(\varepsilon\))-life(N) curve, there are two mean stress effect correction models, the Morrow (Equation (5)) [12] and Smith Watson Topper (SWT) (Equation (6)) models [13]. [PERSON] et al. [14] indicated that the SWT model can apply changes in the load by calculating the energy that is multiplied with \(\sigma_{max}\). This method is rather flexible, especially in high loading conditions. \[\frac{\varepsilon_{a}}{2}=\frac{\sigma_{f}^{\prime}-\sigma_{m}}{E}(2N)^{b}+ \varepsilon_{f}^{\prime}\!\!\left(\frac{\sigma_{f}^{\prime}-\sigma_{m}}{ \sigma_{f}^{\prime}}\right)^{\frac{\varepsilon}{b}}(2N)^{c} \tag{5}\]  
\[\sigma_{max}\varepsilon_{a}=\frac{\left(\sigma_{f}^{\prime}\right)^{2}}{E}(2N )^{b}+\varepsilon_{f}^{\prime}\sigma_{f}^{\prime}(2N)^{b+c} \tag{6}\]  
where \(\sigma_{max}\) is the max stress during the cycle. Based on these mean stress effects, many researchers developed models. [PERSON] [15] suggested a multiaxial fatigue damage model based on strain energy. By considering strain shear energy, multi axial fatigue life can be considered. This method can also be adopted in distortion [16]. The form of energy was similar with that of SWT, which can be calculated by multiplying the strain and force of each type. There is little research applying Optistruct in the scroll compressor. However, there are another cases using Optistruct in fatigue simulation. [PERSON] [17] calculated the fatigue life of the skate frame using FEM. In this study, he studied the surface effect and size effect, which can modify the fatigue limit. [PERSON] [18] compared the stress-life and strain-life curve in calculating the fatigue life of the joint prosthesis using FEM. He suggested that, for composite structures which receive excessive force, the strain-life curve is a proper parameter rather than the stress-life curve. The fatigue lifetime of a structure can be divided into three mechanisms, i.e., crack initiation, crack propagation and dynamic instability. Among them, the time for dynamic instability is extremely short compared with the other two mechanisms. However, the contribution of crack propagation on the entire lifetime of a structure should be considered, unless the material fabricating a structure is brittle enough.