A global secant relaxation (GSR)-based accelerated iteration scheme can be used to carry out the incremental/iterative solution of various nonlinear finite element systems of offshore structural mechanics problems. This computation procedure can overcome the possible deficiency of numerical instability caused by local failure existing in the iterative computation. Moreover, this method can efficiently accelerate the convergency of the iterative computation. This incremental/iterative analysis can consistently be carried out to update the response history up to a near ultimate load stage, which is important for investigating the global failure behaviour of a structure under certain external cause, if the constant stiffness is used. Consequently, this method can widely be used to solve general nonlinear problems. Mathematical procedures of Newton-Raphson techniques in finite element methods for nonlinear finite element problems are summarized. These techniques are the Newton-Raphson method, quasi-Newton methods, modified Newton-Raphson methods and accelerated modified Newton-Raphson methods. Numerical results obtained by using various accelerated modified Newton-Raphson methods are used to study the convergency performances of these techniques for material nonlinearity problems and deformation nonlinearity problems, separately.

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