吴 晓, 黄 翀, 杨立军, 孙 晋. 拉压模量不同圆板的非线性弯曲计算[J]. 工程力学, 2011, 28(4): 23-027,.
引用本文: 吴 晓, 黄 翀, 杨立军, 孙 晋. 拉压模量不同圆板的非线性弯曲计算[J]. 工程力学, 2011, 28(4): 23-027,.
WU Xiao, HUANG Chong, YANG Li-jun, SUN Jin. NONLINEAR BENDING CALCULATION OF BIMODULUS CIRCULAR PLATE[J]. Engineering Mechanics, 2011, 28(4): 23-027,.
Citation: WU Xiao, HUANG Chong, YANG Li-jun, SUN Jin. NONLINEAR BENDING CALCULATION OF BIMODULUS CIRCULAR PLATE[J]. Engineering Mechanics, 2011, 28(4): 23-027,.

拉压模量不同圆板的非线性弯曲计算

NONLINEAR BENDING CALCULATION OF BIMODULUS CIRCULAR PLATE

  • 摘要: 拉压弹性模量不同的圆板在均布外载荷作用下,会形成拉压弹性模量不相同的拉伸区和压缩区,把拉压弹性模量不同的圆板看成两种材料组成的层合板,采用弹性力学理论建立了拉压模量不同圆板在均布外载荷作用下的静力平衡方程,利用静力平衡方程确定了拉压弹性模量不同圆板的中性面位置。在此基础上,建立了拉压弹性模量不同圆板的非线性弯曲微分方程,求得了圆板中心挠度与均布荷载的关系式,并把该方法计算结果与有限元方法计算结果进行比较,验证了该计算方法可靠性。算例分析表明:当圆板材料拉压弹性模量相差较大时,其挠度计算不宜采用相同弹性模量弹性理论,而应该采用拉压弹性模量不同的弹性理论。

     

    Abstract: A bimodulus circular plate could form a compression and tensile area under external uniform loads. And it was regarded as a laminated plate composited of two kinds of materials. The static equilibrium equation of a bimodulus circular plate under external uniform loads was established using elasticity theory. Then the location of a neutral plane was determined by static equilibrium equation. The nonlinear bending deformation differential equation of a bimodulus circular plate was derived, and the relation between the circular plate center deflection and uniform loads was obtained. The FEM analysis shows that the method was reliable. The example shows that the deflection calculation of the circular plate which has a larger difference between tensile elastic modulus and compressive elastic modulus may as well not apply classical elastic theory with the same elastic modulus, and should use elastic theory with different elastic moduli in tension and compression.

     

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