一种改进的Pasternak地基模型及层合地基板的解析解

从三维弹性力学基本方程出发,建立了正交异性材料层合板的状态方程,并提出一种改进的Pasternak弹性地基模型,给出了四边简支层合地基板的解析解。此解满足层合板的基本方程和层间连续条件,适合任意厚跨比,计及了所有材料常数,考虑了基底切向接触应力的影响。算例讨论了地基参数对几种地基模型的影响。计算结果表明,随着地基刚度的增大,剪应力的影响是不可忽略的。

A modified model of Pasternak foundation and analytical solution for laminated plate on the elastic foundation

Based on three dimensional fundamental equations of elasticity,state equation for orthotropic laminated plate is established.By presenting a modified model of Pasternak elastic foundation,an analytical solution for laminated plate on the elastic foundation with four simply supported edges is presented.The solution given,which satisfies fundamental equations and inter-laminar continuity conditions of the laminates,is suitable to any thickness-span ratios.All material constants and shear stresses in contact with foundation are taken into account in the formulas.Effects of foundation parameters on some foundation models are discussed in numerical examples.The results illustrate that the effects of shear stresses are not negligible as the stiffness of the foundation increases.