This paper proposes a 3D 2-node element for beams and cables. Main improvements of the element are two new interpolation functions for beam axis and cross-sectional rotation. New interpolation functions employ implicit functions to simulate large deformations. In the translational interpolation function, two parameters which affect lateral deflection geometry are defined implicitly through nonlinear equations. The proposed translational interpolation function is shown to be more accurate than Hermitian function at large deformations. In the rotational interpolation function, twist rate is defined implicitly through a torsional continuity equation. Cross-sectional rotation which is strictly consistent to beam axis is obtained through separate bending rotation interpolation and torsional rotation interpolation. The element model fully accounts for geometric nonlinearities and coupling effects,and thus,can simulate cables with zero bending stiffness. Stiffness matrix and load vector have been derived using symbolic computation. Source code has been generated automatically.Numerical examples show that the proposed element has significantly higher accuracy than conventional 2-node beam elements under the same meshes for geometrically nonlinear problems.
The heaviest rainfall in recent six decades fell in Beijing on 21 July 2012, reaching a record of 460 mm within 18 h. This rainfall was a typical remote precipitation event related to Typhoon Vicente(1208).Observational analysis indicates that Vicente influenced distant heavy rainfall by transporting water vapor northward to the Beijing area. This moisture transport was mainly driven by the interaction between Vicente and the western Pacific subtropical high(WPSH) associated with the formation of a low-level southeasterly moisture channel. A set of numerical sensitivity experiments were performed with prescribed typhoons of different intensities to investigate the interaction between Vicente and the WPSH and its effects on this rainstorm process. The results indicate that the WPSH interacting with typhoons of different intensities may exert varying degrees of influence on the development of a southeasterly moisture channel, resulting in a change in rain rate and location over the Beijing area. Specifically, in the presence of an enhanced typhoon,the WPSH shows remarkable withdrawal to the east, which is favorable for a northward extension of the southeasterly moisture channel, thereby increasing moisture supply for the rainstorm. The WPSH tends to stretch westward in a zonal pattern if the typhoon is weakened or removed, hindering the northward extension of the moisture channel. Thus, the rainfall area may be expected to expand or contract, with corresponding increases or decreases in rain rate over the Beijing area with a strengthened or weakened typhoon, respectively.
