双曲旋转薄壳弯曲问题理论计算方法研究

Research on theoretical calculation method of hyperbolic rotating thin shell bending problem

    摘要
  • 摘要:
    目的 为分析双曲旋转薄壳的弯曲特性，基于欧拉−伯努利梁理论，将双曲旋转薄壳弯曲这一复杂的二维力学问题简化为一维壳带梁弯曲问题。
    方法 通过分析壳带梁受力及变形特点，建立结构力学模型；结合板壳弹性变形的物理方程以及单跨梁复杂弯曲微分方程，建立双曲旋转薄壳弯曲微分方程；选取跨中中面环向应力这一耐压结构常用的标志性应力，提出典型的应力计算经验公式；基于ANSYS开展双曲旋转薄壳弯曲问题仿真，验证典型应力计算公式的准确性。
    结果 结果显示，所提跨中中面环向应力计算经验公式的计算结果与数值仿真结果间的误差约为2.3%，表明该公式在预报典型应力方面具有较高的精度，验证了所提双曲旋转薄壳弯曲问题理论计算方法的正确性。
    结论 所提方法可为类似结构的设计与优化提供借鉴。

     

    Abstract:
    Objectives In order to analyze the bending characteristics of a hyperbolic rotating thin shell, the complex two-dimensional mechanical problem is simplified into a one-dimensional bending problem based on Euler's Bernoulli beam theor.
    Methods By analyzing the force and deformation characteristics of shells and belt beams, a structural mechanical model is established, and a double curvature rotating thin shell bending differential equation is obtained by combining the physical equation of plate and shell theory with the bending differential equation of a single-span beam. An empirical formula for typical stress is proposed and its accuracy verified by an ANSYS-based simulation.
    Results The results show that the error between the simulation and the formula is about 2.3%, which demonstrates the high accuracy of the formula in predicting typical stress and verifies the correctness of the theoretical calculation method.
    Conclusions The proposed method can provide useful references for the design and optimization of similar structure.

     

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