Nonlinear Numerical Simulation of Finite Elements Based on Fiber Beam Elements With Shear Effects for Structures
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摘要:
基于Euler-Bernoulli梁理论的经典纤维模型忽略了剪切变形给截面带来的影响，为了得到更加精确的梁单元模型，该文基于考虑剪切效应的纤维梁单元，根据Timoshenko梁理论，推导了该纤维梁单元的刚度矩阵，并结合弹塑性增量理论，同时考虑了几何非线性和材料非线性的双重影响，建立了压弯剪复杂应力状态下结构非线性有限元分析理论。该文最后利用MATLAB编制了相关计算程序，对钢筋混凝土和矩形钢管混凝土的典型压弯剪构件进行有限元数值模拟，得到了构件的荷载-位移非线性全过程曲线。典型算例的验证结果表明：该文建立的非线性有限元分析理论是通用、可行和正确的。
Abstract:The classical fiber beam model based on the Euler-Bernoulli beam theory ignores the influence of shear deformation on the section. To get a more accurate beam element model, based on the fiber beam element with shear effects and the Timoshenko beam theory, the stiffness matrix of the fiber beam element was deduced, and the dual effects of geometric nonlinearity and material nonlinearity were considered at the same time, combined with the elastoplastic incremental theory. Then, the nonlinear finite element analysis theory for the structure under the complex stress state of compression, bending and shear was established. Finally, a program was coded on MATLAB to conduct finite element numerical simulation of the typical compression-bending-shear members of reinforced concrete and rectangular concrete-filled steel tube, and the nonlinear full-process load-displacement curves were obtained. The analysis of the numerical examples show that, the established nonlinear finite element analysis theory is universal, feasible and correct.
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Key words:
- fiber beam element /
- structural nonlinearity /
- shear effect /
- finite element analysis
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图 2 增量理论应力更新流程图
Figure 2. The flow chart for stress updating with the incremental theory
图 8 矩形钢管混凝土压弯剪试件计算模型
Figure 8. The calculation model for the rectangular CFST column under the compression-bending-shear loading condition
表 1 计算参数
Table 1. Calculation parameters
parameter value compressive strength of concrete $ f_{\rm{c}}^\prime = 32.1\;{\text{MPa}} $ Poisson’s ratio of concrete $ {\nu _{\rm{c}}} = 0.2 $ yield strength of rebar $ {f_{\rm{y}}} = 510\;{\text{MPa}} $ sectional shear coefficient $ {\kappa _y} = {\kappa _z} = 6/5 $ elastic modulus of concrete $ {E_{\rm{c}}} = 2.64 \times {10^4}\;{\text{MPa}} $ Poisson’s ratio of rebar $ {\nu _{\rm{s}}} = 0.3 $ elastic modulus of rebar $ {E_{\rm{s}}} = 2 \times {10^5}\;{\text{MPa}} $ peak compressive strain of the member $ \varepsilon {\text{ = }}0.005\;2 $ shear modulus of concrete $ {G_{\rm{c}}} = 1.1 \times {10^4}\;{\text{MPa}} $ moment of inertia $ I = 7.63 \times {10^{ - 3}}\;{{\text{m}}^4} $ shear modulus of rebar $ {G_{\rm{s}}} = 7.7 \times {10^4}\;{\text{MPa}} $ equivalent weight of the element $ P = 3\;539.25\;{\text{kN}} $ 
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表 2 数值模拟结果
Table 2. Numerical simulation results
displacement u/mm ref. [15] FR/kN numerical simulation FN/kN error δ/% 2 167.16 156.02 6.66 4 313.14 294.85 5.84 6 417.97 409.75 1.97 8 490.91 487.48 0.70 10 540.35 537.67 0.50 12 568.83 558.61 1.80 14 577.99 570.97 1.22 16 573.22 555.43 3.10 18 562.80 534.98 4.94 20 552.04 515.57 6.61 22 538.23 497.12 7.64 24 517.62 479.59 7.35
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