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Injury domain method does not let the cracks close to the critical level to start growing and lead to the critical length before the time of periodic visits. Until now, calculation method of the tension in a perforated plate has been assessed in two- or three-dimensional mode by considering the special opening (holes with different geometry). But, the tension calculation in a plate included opening with edge crack presence in three-dimensional mode has not been studied. So, in this study, in addition to the assessment of this mode, calculation method of the tension in the plates including different opening will be assessed. Generally, when the object endures the tensions for a long time, the geometric deformation will be occurred. Used plates in this study are made of isotropic materials. In these materials, when the force is applied, they show the same function in any direction and the direction of applying force has any on effect their treatment. For analyzing the data, the Abaqus software is used. The results of the research show that the kind of the boundary conditions has effect on the value of critical load in the tension and kind of created tension. In the joint-joint boundary conditions, tension critical load increases with length-to-width ratio increase, and local tension occurred in the higher penetration ratio. However, in the joint-open boundary conditions, by increasing the length-to-width ratio, the tension critical load is decreased and in often cases, the tensions are kind of general. According to this, the plates including cavity with bigger dimensions are subjected to local tension in smaller ratios of yielding dimension.

The forced Korteweg-de Vries (fKdV) equations are solved using Homotopy Analysis Method (HAM). HAM is an approximate analytical technique which provides a novel way to obtain series solutions of such nonlinear problems. It has the auxiliary parameter ℏ, where it is easy to adjust and control the convergence region of the series solution. Some examples of forcing terms are employed to analyse the behaviours of the HAM solutions for the different fKdV equations. Finally, this form of HAM solution is compared with the analytical soliton-type solution of fKdV equation as derived by Zhao and Guo. The results is found to be in good agreement with Zhao and Guo.

The homotopy analysis method (HAM) is applied to obtain the approximate analytic solution of the Korteweg-de Vries (KdV) and Burgers equations. The homotopy analysis method (HAM) is an analytic technique which provides us with a new way to obtain series solutions of such nonlinear problems. HAM contains the auxiliary parameter ħ, which provides us with a straightforward way to adjust and control the convergence region of the series solution. The resulted HAM solution at 8th-order and 14th-order approximation is then compared with that of the exact soliton solutions of KdV and Burgers equations, respectively, and shown to be in excellent agreement.