Wave leads to the orbital motion of the water. The orbital motion in a closed cycle, but slightly drive forward due to surface wind effect. Current flow is generated by the wave. The current flow in a wave tends to drag wavelength. The induced current flow force on the cylindrical structure is defined as follows [12] :

In this equation, F_D, C_d, ρ, A, and U, are the drag force in Kilo Newton, drag coefficient, sea water density per ton per cubic meter, cross section depicted in terms of square meter and current flow rate in meters per second, respectively. The flow rate is usually between 0.1 and 2.3 meters per second. Profiles of sea currents in the Gulf of Mexico are shown according to the API [13] in Figure 1.

The regular wave theories are used to calculate the forces on fixed offshore structures, illustrated in Figure 2, and based on the three parameters of water depth (d), wave height (H) and wave period (T), respectively. Hydrodynamic force vector is calculated in all degrees of freedom. The intensity of the wave force on each meter of the structure is calculated based on Morison formula shown in Equation (2), [13] .

where, F, C_m, u, du/dt, and V are total force exerted on an object, the coefficient of inertia, current flow rate, current flow acceleration and object size, respectively.

When a structure is placed in the path of the moving air so that wind is stopped or is deflected from its path all or part of the kinetic energy is transformed into the potential energy pressure. Therefore wind forces on any structure result from the differential pressure caused by the obstruction to the free flow of the wind. These forces are functions of the wind velocity, orientation, area, and shape of the structural elements. Wind forces on a structure are a dynamic problem, but for design purposes, it is sufficient to consider these forces as an equivalent static pressure. The force of the wind according to the API is shown in Equation (3).

In this equation, F, C_s, A_p and U₁₀ are the wind force in Kilo Newton, shape structure factor, cross section depicted in terms of square meter and wind speed in kilometers per hours, respectively.

The finite element method is for the approximate solution of differential equations governing on the continuous areas. This method was initially proposed as a method of stress analysis and is widely used for this purpose. For a non-persistent problem, finite element approximation is defined as follows [14] :

By transforming this equation into the integral one, and by using the weighted residual function (W_(x)), we have:

Finite element is defined as follows:

Using the relations (5) and (6), this equation will change as follows:

In the above equation, M_IJ and K_IJ, represent the mass matrix and stiffness matrix respectively.

The finite element method uses the integral shapes of equations; it means that integration have to be carried out on governing equations of the scope of problem; Therefore, finite element is only used for discretization the local terms of the equations and for discretization of the time terms the finite difference method is used consequently [14] .

In the theory of nonlinear waves, the sinusoidal shapes of wave profile and rotation of the particles in a circular path in the profile does not exist simultaneously. One of the nonlinear wave’s theory in 1880 was presented by Stokes; it was based on adding unlimited number of successive approximation and adding it to a series of equations. In this research, the 5^th order Stokes nonlinear wave theory is used to estimate the water particle kinematics. In this theory, by using the two characteristics amplitude and period of the wave, water particle kinematics is determined using the following equations. One of the ways by which the higher order Stokes theory can be estimated is Fenton method [15] . The wave profile can be written as:

Horizontal and vertical velocities are calculated as follows:

In these equations k is wave number, ω is angular velocity, f is velocity potential function, C_E is average of steady flow, α_i, A_ij and β_ij are affiliate factor related to k_d that d is the depth of the water. The coefficients are available in reference number [15] .

In order to understand the behavior of fixed offshore platform, the analysis of these platforms in water to a depth of 54.5 meters under the sea waves, winds and sea currents were studied. Maximum deformations under mentioned loads have been precisely calculated. Deformations responses of U₁, U₂ and U_abs (which represents the absolute horizontal displacement is equal to the square root of the sum of squares U₁ and U₂) and are depicted in the following figures in line with platform height under the action of waves loads and sea currents with return period of 1-year (operating conditions) and 100-year (extreme conditions/ storm). U₁, U₂ deformation are in X and Y directions, respectively.

For operating conditions of platform, based on Figure 4, Figure 5 and Figure 6, with increasing angle of the sea current attack, angle from zero to 180, platform displacements are reduced, so that the angle of zero degrees shows the maximum displacement and 180 degrees exhibits the minimum displacement in the X direction. This condition is contrary for the Y direction, attacks with angle of 90 degree showing the maximum displacement and the minimum displacement are with zero and 180 degrees angle. Furthermore, the average value of absolute displacement difference for the 1-year sea current for combined number 4 (maximum absolute displacement) and combined number 6 (minimum absolute displacement) is about 11 percent. For operating conditions of platform, based on Figure 7, Figure 8 and Figure 9, with increasing angle of the wave, wind and sea current attack, angle from zero to 180, platform displacements is reduced, so that the angle of zero degrees shows the maximum displacement and 135 degrees exhibits the minimum displacement in the X direction. This condition is contrary for the Y direction, attacks with angle of 90 degree showing the maximum displacement and the minimum displacement is with 180 degree angle. Also the average value of absolute displacement difference for the 1-year wave, wind and sea current for combined number 8 (maximum absolute displacement) and combined number 10 (minimum absolute displacement) is about 16 percent. For storm conditions, as Figure 10, Figure 11 and Figure 12 illustrates, hits with 90 degree angle create the maximum displacement, while hits with 180 degree angle create the minimum displacement. The average value displacement difference for a 1-year wave of combination number 4 (maximum absolute displacement) and combination number 6 (minimum absolute displacement) is at about 8 percent. With increasing angle of the sea current attack, angle from zero to 180, platform displacements is reduced, so that the angle of zero degrees shows the maximum displacement and 180 degrees exhibits the minimum displacement in the X direction. This condition is contrary for the Y direction, attacks with angle of 90 degree showing the maximum displacement and the minimum displacement is with 180 degree angle. Also the average value of absolute displacement difference for the 100-year sea current for combined number 14 (maximum absolute displacement) and combined number 15 (minimum absolute displacement) is about 15 percent. In Figure 13, Figure 14 and Figure 15, with increasing angle of the sea current attack, angle from zero to 180, platform displacements is reduced, so that the angle of zero degrees shows the maximum

displacement and 135 degrees exhibits the minimum displacement in the X direction. This condition is contrary for the Y direction, attacks with angle of 90 degree showing the maximum displacement and the minimum displacement is with zero degree angle. Also the average value of absolute displacement difference for the 100-year sea current for combined number 17 (maximum absolute displacement) and combined number 19 (minimum absolute displacement) is about 37 percent.

Figure 16 and Figure 17, indicates that the maximum displacement at a₁ (still water level) and a₄ (junction between deck and jacket) are under the combined effect of all the loads. As the figure suggests, by changing the operating mode to a storm condition, column 1 displacement becomes more. The average displacement value for the node a₁ in two modes of one and 100-years with the same wave, wind and sea current hit, angles is about 7 percent and for the node a₄ this difference is about 13 percent.

Figure 18, Figure 19 and Figure 20 show the bending moment M_2-2, M_3-3 and absolute for levels of a₀ to a₃. The values for the bending moments of a₁ to a₃ levels are almost uniformly and changes in hit angles of the wave, wind and sea currents have little effect on the bending. The average bending moment value of one and 100-years with the same wave, wind and sea current hit, angles is about 54 percent. In Figure 21, the maximum amount of bending moment at the base of columns of jacket is shown. According to this figure, in both operating and storm condition, with increase angle of attack of the wave, wind and sea current, the bending moment decrease.

Figure 22 shows the maximum axial force at critical levels in line with the height of the jacket platform structure. It is important in the design of a platform bases that the maximum axial force be considered, because the thickness of the base platform can be reduced with respect to the maximum stresses.

In order to compare the behavior of fixed offshore platform, three different wave theories (Stokes IV, Cnoidal I & Cnoidal II) were developed. In Figure 23 and Figure 24 displacements of (Node a₁) and moment of (Node a₀) under these three different wave theories with all load combinations were shown respectively. As was shown in Figure 23, the average of absolute displacement in column 1 (Node a₁) by using Cnoidal I wave theory is 3.4 percent more than Stokes IV wave theory and 12.6 percent more than Cnoidal II wave theory. In Figure 24, the average amount of absolute moment in column 1 (Node a₀) by using Cnoidal I wave theory is 11.8 percent more than Stokes IV wave theory and 24.5 psercent more than Cnoidal II wave theory.

As respects, load combination 2 shows the maximum displacement and moment with return period of 1-year (operating conditions) and load combination 11 shows the maximum displacement and moment with 100-year (extreme conditions/storm), the parametric comparison on (Node a₁) shows that by increasing wave height, the moment and displacement of jacket increases exponentially. These results are shown in Figure 25 and Figure 26 respectively. In Figure 27, the normalized comparison of wave height on (Node a₁) shows that by increasing (H/d) in which (H) is wave height and (d) is constant water level, the amount of (D/d) in which (D) is displacement of jacket is increases exponentially and can performs by Y = me^nX equation, that m is (0.0002) and b is between (3.38 - 4.2).