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本文从厚板的内力特性出发,把Winkler地基或Pasternak地基上各种厚板模型的基本方程求解问题变为求解两个位移函数ω及ψ的问题,并导出解的一般形式。然后证明,对于弹性地基上简支多边形厚板,ψ恒为零,其基本方程组就化为一个位移函数ω的四阶偏微分方程,而这个方程与Pasternak地基上弹性薄板弯曲的方程是完全类似的。此外,文中还研究了弹性地基上厚圆板解的问题。
In this paper, starting from the characteristics of the internal forces of thick plates, the problem of solving basic equations of various thick plate models on Winkler foundation or Pasternak foundation becomes the problem of solving two displacement functions ω and ψ, and the general form of the solution is derived. It is then proved that for a simply supported polygonal slab on an elastic foundation, the enthalpy is always zero, and its basic equations are transformed into a fourth-order partial differential equation of the displacement function ω, and this equation is completely equivalent to the equation of the elastic thin plate bending on the Pasternak foundation. akin. In addition, the problem of solution of thick circular plates on elastic foundations is also studied.