The nonlinearities in the wind and wave loadings of compliant off shore structures result in response statistics that deviate from a Gaussian distribution. This study focuses on the analysis of these structures to nonlinear wind and wave loadings.; The first part of this study concerns two approximate analytical methods, the equivalent statistical quadratization method (ESQM) and cubicization method (ESCM), to analyze the nonlinear dynamic systems as extensions of the linearization method. Both of these methods are based on the Volterra theory and represent two types of nonlinearities, symmetrical and asymmetrical nonlinearities. The contributions of the nonlinear structural velocity to the overall loading description are included. A splitting technique is presented to analyze this system with the underlying assumption of small structural velocity. As the first four cumulants are generally necessary to describe a non-Gaussian distribution, the direct integration technique and Kac-Siegert technique are utilized to evaluate these cumulants. An example of tension leg platform is utilized to demonstrate the methodology. Only surge response is analyzed under wind and wave loading. The wave loading is expressed in terms of the Morison equation. The methodology is applicable to other nonlinear loading contributions. The ESQM provides satisfactory results in the presence of current that represent asymmetrical nonlinearity. In the absence of current, the Morison wave drag force presents a symmetrical nonlinearity. In this case, the ESCM provides satisfactory response statistics. The application of ESCM to a Duffing stiffness system is also possible, but the accuracy depends on the level of system damping. Three types of non-Gaussian distribution models are utilized to quantify response statistics based on the computed values of response cumulants. The crossing rate and distribution of the peak response are evaluated, which exhibit departure from Gaussian case, and provide a good comparison with the simulation results. A gust factor based on nonlinear wind loading description is developed.
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