The complete hydrostatic stiffness and geometrically nonlinear beam finite element analysis of floating structures

Abstract

In this study, the complete hydrostatic tangent stiffness for geometrically nonlinear beam finite element model is introduced. Based on consistent global hydrostatic restoring stiffness analysis, the complete form of hydrostatic tangent stiffness is developed. In addition, a surface integration parameterization method for shear-deformable beams is discussed with classifications of two special types of cross-sections, i.e., elliptical and rectangular. The presence of rigid-body load stiffness (RBLS) complementing the lacking part of geometric stiffness is observed and found to be essential to fulfill objectivity of the hydrostatic tangent stiffness. The developed method is validated with well-established cantilever quadrant and deployable ring examples and then applied to various nonlinear hydrostatic problems for floating structures including floating spheres, rigid and flexible box-barges and fish-cage collars.