梯度弹性基础上正交异性薄板的弯曲

BENDING ANALYSIS OF ORTHOTROPIC THIN PLATE ON GRADED ELASTIC FOUNDATION

基于能量法和变分原理,采用双参数弹性基础模型,研究了梯度弹性基础上正交异性薄板在分布载荷作用下的弯曲问题.首先,根据能量法与变分原理,给出了梯度弹性基础上正交异性薄板的弯曲微分平衡方程,并得到了梯度弹性基础刚度系数K1与K2的计算表达式;进而,假设z向正应力在厚度方向上均匀分布,推导了弹性基础z向位移衰减函数φ(z)的计算式.在算例中,通过将梯度弹性基础退化为均质基础,并与Vlazov模型对比,证明了论文理论的正确性;最后,求解了弹性模量呈幂律分布的梯度基础上薄板的挠度分布,分析了基础上下表层材料弹性模量比λ与体积分数指数n对薄板挠度分布的影响.

Based on the energy method and variation principle,the bending analysis is presented for orthotropic thin plates on graded elastic foundations subjected to distributed loads using two-parameter foundation model.Firstly,the bending differential equilibrium equation of orthotropic thin plates on graded elastic foundations and the expressions of two elastic parameters of elastic foundation are given by introducing the energy method and variation principle.Then,the displacement reduced function φ（z） is derived based on the assumption that the normal stress in z-direction is uniform through foundation thickness.In the example,the proposed solution is validated by comparing the degenerated results for homogeneous isotropic foundation with Vlazov model.Finally,this paper studies the displacements distributions of the orthotropic thin plate on a graded elastic foundation,whose Young＇s modulus obeys a power law through the thickness.The effects of top-bottom surfaces＇ Young＇s modulus ratio λ and volume fraction exponent n on the variation of deflection of the plate are also examined.