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A COMPARISON OF NUMERICAL INTEGRATION METHODS FOR DYNAMIC ANALYSIS OF OFFSHORE STRUCTURES SUPPORTED ON PILE FOUNDATIONS

Luiz Landau, N F Ebegken

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Abstract

The mode superposition technique for approximately solving nonlinear equations arising from the dynamic analysis of soil-structure interaction problems is discussed. Three algorithms are presented. The first treats the nonlinearities as pseudo-forces and uses exact integration to solve the modal system of equations. The second is based on a modified Newton-Raphson approach and on the Newmark operator. The third is derived by the pure incremental formulation and also uses exact integration continuously up dating the frequency spectrum. The results of these numerical integration methods for the case of a typical offshore problem are compared to those obtained with the Newmark implicit direct integration method.

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The mode superposition technique for approximately solving nonlinear equations arising from the dynamic analysis of soil-structure interaction problems is discussed. Three algorithms are presented. The first treats the nonlinearities as pseudo-forces and uses exact integration to solve the modal system of equations. The second is based on a modified Newton-Raphson approach and on the Newmark operator. The third is derived by the pure incremental formulation and also uses exact integration continuously up dating the frequency spectrum. The results of these numerical integration methods for the case of a typical offshore problem are compared to those obtained with the Newmark implicit direct integration method.

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Available abstract

The mode superposition technique for approximately solving nonlinear equations arising from the dynamic analysis of soil-structure interaction problems is discussed. Three algorithms are presented. The first treats the nonlinearities as pseudo-forces and uses exact integration to solve the modal system of equations. The second is based on a modified Newton-Raphson approach and on the Newmark operator. The third is derived by the pure incremental formulation and also uses exact integration continuously up dating the frequency spectrum. The results of these numerical integration methods for the case of a typical offshore problem are compared to those obtained with the Newmark implicit direct integration method.

Key concepts: Newmark-beta method, Numerical integration, Nonlinear system, Direct integration of a beam, Superposition principle, Pile, Applied mathematics, Numerical analysis

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