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通过分析得到了现浇混凝土空心板正交各向异性主刚度存在着D3=D1D2~(1/2)的关系;从正交各向异性板挠曲面的偏微分方程出发,保持一个主方向尺寸不变x1=x,将另一主方向的尺寸做线性缩放y1=k-14y,并保持弹性模量与第一主方向相同E=E1,泊松比μ=μ1μ2~(1/2),将原来的正交各向异性板等效为一块各向同性板,通过分析得到:各向同性板任意点的挠度就是原正交各向异性板对应点的挠度,各对应点内力存在简单的对应关系:Mx=Mx1、My=k1/2My1、Mxy=k1/4Mx1y1。最后,通过算例验证了该方法的正确性。
The relationship between the main stiffness of cast-in-situ concrete hollow slab with orthogonal anisotropy is obtained by the analysis of D3 = D1D2 ~ (1/2). Based on the PDE of the flexural surface of orthotropic slab, one principal dimension Constant x1 = x, linearly scaling y1 = k-14y in the other principal direction and maintaining the same elastic modulus as the first main direction E = E1, Poisson’s ratio μ = μ1μ2 ~ (1/2) The original orthotropic plate is equivalent to an isotropic plate. The analysis shows that the deflection at any point of the isotropic plate is the deflection of the corresponding point of the original orthotropic plate, and the internal forces at each corresponding point are simple Corresponding relationship: Mx = Mx1, My = k1 / 2My1, Mxy = k1 / 4Mx1y1. Finally, an example is given to verify the correctness of the method.