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On the buoyancy load formulation for geometrically nonlinear analysis of flexible marine risers

机译：关于柔性船用立管几何非线性分析的浮力荷载公式

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摘要

A proper buoyancy load formulation that complements the continuum formulation with incorporated beam theory in geometrically nonlinear analysis of flexible marine risers is presented. For continuous riser pipes, the hydrostatic pressure field only covers the circumferential surfaces thus hindering the buoyancy load approach. The present buoyancy load formulation is based on a vector calculus approach and essentially agrees with the well known effective tension concept in the direct beam formulation. The gradient version of the divergence theorem (GVDT) is employed onto a continuous pipe segment subjected to circumferential hydrostatic pressure. The application of the GVDT results in the body force and cross sectional surface traction which are regarded as the buoyancy load and boundary effect respectively. Emphasis is placed on the consequences of the boundary effect and the load definition of the buoyancy load in geometrically nonlinear analysis. The boundary effect occurs if either boundary end of the pipe system were uncapped. Further consequences of the boundary effect depends on the corresponding restraining locations and directions. Furthermore, the buoyancy load is ascertained to have weak nonlinearity hence the derivation of the augmented tangent stiffness matrix is deemed unnecessary. Finite element formulation of the corresponding external nodal load vectors is also presented using the iso-parametric beam elements for discretization.
机译：提出了一种合适的浮力载荷公式，该公式通过弹性梁的几何非线性分析中的结合梁理论补充了连续体公式。对于连续的立管，静水压力场仅覆盖圆周表面，因此阻碍了浮力的接近。当前的浮力载荷公式基于矢量演算方法，并且基本上与直接梁公式中众所周知的有效张力概念一致。将散度定理（GVDT）的梯度形式应用到承受周向静水压力的连续管段上。 GVDT的应用导致体力和横截面表面牵引力分别被视为浮力载荷和边界效应。在几何非线性分析中，重点放在边界效应的结果和浮力载荷的载荷定义上。如果未封闭管道系统的任一边界端，则会发生边界效应。边界效应的其他后果取决于相应的约束位置和方向。此外，确定浮力负载具有弱的非线性，因此认为不需要增加切线刚度矩阵。还使用等参梁单元进行离散化，给出了相应的外部节点载荷矢量的有限元公式。

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