A fiber-section model based Timoshenko beam element is proposed in this study that is founded on the nonlinear analysis of frame elements considering axial,flexural,and shear deformations.This model is achieved using a shear-bending interdependent formulation(SBIF).The shape function of the element is derived from the exact solution of the homogeneous form of the equilibrium equation for the Timoshenko deformation hypothesis.The proposed element is free from shear-locking.The sectional fiber model is constituted with a multi-axial plasticity material model,which is used to simulate the coupled shear-axial nonlinear behavior of each fiber.By imposing deformation compatibility conditions among the fibers,the sectional and elemental resisting forces are calculated.Since the SBIF shape functions are interactive with the shear-corrector factor for different shapes of sections,an iterative procedure is introduced in the nonlinear state determination of the proposed Timoshenko element.In addition,the proposed model tackles the geometric nonlinear problem by adopting a corotational coordinate transformation approach.The derivation procedure of the corotational algorithm of the SBIF Timoshenko element for nonlinear geometrical analysis is presented.Numerical examples confirm that the SBIF Timoshenko element with a fiber-section model has the same accuracy and robustness as the flexibility-based formulation.Finally,the SBIF Timoshenko element is extended and demonstratedin a three-dimensional numerical example.
High rates of fertilizer nitrogen (N) are applied in greenhouse vegetable fields in southeastern China to maximize production;however,the N budgets of such intensive vegetable production remain to be explored.The goal of this study was to determine the annual N balance and loss in a greenhouse vegetable system of annual rotation of tomato,cucumber,and celery at five N (urea) application rates (0,348,522,696,and 870 kg N ha-1 year-1).Total N input to the 0-50 cm soil layer ranged from 531 to 1 053 kg ha-1,and N fertilizer was the main N source,accounting for 66%-83% of the total annual N input.In comparison,irrigation water,wet deposition,and seeds in total accounted for less than 1% of the total N input.The fertilizer N use efficiency was only 18% under the conventional application rate of 870 kg N ha-1 and decreased as the application rate increased from 522 to 870 kg N ha-1.Apparent N losses were 196-201 kg N ha-1,of which 71%-86% was lost by leaching at the application rates of 522-870 kg N ha-1.Thus,leaching was the primary N loss pathway at high N application rates and the amount of N leached was proportional to the N applied during the cucumber season.Moreover,dissolved organic N accounted for 10% of the leached N,whereas NH3 volatilization only contributed 0.1%-0.6% of the apparent N losses under the five N application rates in this greenhouse vegetable system.
MIN Ju ZHAO Xu SHI Wei-Ming XING Guang-Xi ZHU Zhao-Liang
