ABSTRACT

For the purpose of engineering application in the design of offshore structure, an analytical approximation is presented. The solution is based on a Fourier series expansion and contains some dimensionless constants determined by regression analysis. For the regression analysis, all field quantities are represented in dimensionless forms and the required data are numerically calculated with a set of nonlinear equations formulated by tensor analysis. The set of equations is solved by Newton's method. Thus, a numerical method to determine the constants is also made. Unlike the other numerical methods, the numerical method is valid for all waves including those in the solitary wave limit and in the deep water wave limit. Because there is a wave height limit, the constants can be presented with continuous and bounded functions of two dimensionless variables whose domain is also bounded. In the domain, sufficient data are calculated with the numerical method. Applying regression analysis to the data, the functions are presented with closed forms equivalent to analytical solutions. The functions provide an analytical approximation to the problem. Because of its simplicity, it is suitable for engineering application. Some waves in the breaking limits are calculated. The results are compared with the known results and found to be closely accorded. Applying regression analysis to the results, the breaking limit is also presented with a closed form. Results for fluid velocities are compared with experiment and agreement found to be good. Some profiles are calculated and compared with those calculated by the other wave theories.

INTRODUCTION

A structure design is to determine structural configuration, material and dimension. In order to verify structural integrity, a structural analysis is definitely necessary. But the outputs of a structure design are considered as input data for a structural analysis. The outputs of a structural analysis such as stress, strain and displacement etc., are merely referenced data in a structural design. Because of the reasons, a structural design is a nonlinear process. There are two basic methods to overcome the non-linearity. One of these uses the conservative scheme in which design loads are greater than actual values and design strength and stiffness are less than actual values. Therefore, the integrity of an actual structure can be guaranteed when we use the scheme for a structure analysis and the result satisfies integrity requirements. The reason for using the scheme is that a structural analysis is simple and the determination of a structural design is easy. If approximations satisfy the scheme and are simpler than exact solutions, they can be acceptable to a structural analysis. The other is to use analytical solutions instead of numerical solutions. Structural designers prefer analytical solutions instead of numerical solutions because it is possible to determine a structural design without a structural analysis when analytical solutions are available. Therefore, it is obvious that approximations should be made as simple as possible, analytically and close to the exact solutions. The objective of this study is to provide an analytical approximation accorded with the scheme.

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