等效刚度法计算波纹夹层板弯曲变形与应力
Calculation bending deflection and stress for corrugated core sandwich panels employing equivalent stiffness method
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摘要:目的 为探索波纹夹层板弯曲问题的计算方法，求解波纹夹层板的弯曲变形与应力，提出一种等效刚度法。方法 将波纹夹层板中间芯层等效成正交异性体，应用卡氏定理求解芯层的等效弹性模量，最后应用层合板理论计算夹层板的整体刚度。依据夹层板的整体刚度，求解正交异性板的弯曲平衡方程，计算出夹层板的弯曲变形分布；通过求出的变形，应用虎克定律，即可推导夹层板的弯曲应力分布。结果 通过算例验证，与文献7的方法相比，本文方法计算的刚度误差为−6.98%；与有限元法相比，本文方法计算的夹层板变形最大误差为−2.01%，应力最大误差为3.63%。结论 这种分层累加计算整体刚度的方法，不仅可避免完全直接采用文献7的方法计算刚度时的复杂繁琐推导，而且用于弯曲计算还可获得较好的精度。Abstract:Objectives In order to develop a computation method for the corrugated core panel bending issue and solve the bending deflection and stress of such panels, an equivalent stiffness method is proposed.Methods First, the middle cores of these sandwich panels are taken as equivalent to orthotropic elastic materials, then the equivalent elastic modulus of the cores are solved by Castigliano's theorem and the integral stiffnesses of the sandwich panels are calculated by laminated plate theory. According to the solved integral stiffness constants, the distribution of bending deflection is achieved by solving the orthotropic plate bending equilibrium equations, and stress distribution is derived by adopting Hooke's law.Results It is validated that the stiffness error evaluated by this proposed method is −6.98% compared with the method in literature(Ref.7), the maximum error of deflection is −2.01% and stress is 3.63%, which correspond with the FEM results.Conclusions This proposed method for calculating integral stiffness through layered accumulation not only avoids the complicated derivation of applying the method of Ref.7 completely, but also satisfies calculation precision when computing the bending issue.
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