This paper presents an analytical model to investigate the static behaviour of sandwich plates comprised of two isotropic face sheets and a honeycomb core. Through-thickness transverse shear stresses were considered using a unified displacement field with which various plate theories were implemented, i.e., exponential, third-order, hyperbolic, sinusoidal, fifth-order, Mindlin, and the classic plate theory. The equilibrium equations of a simply-supported sandwich panel were derived using the principle of virtual work and Navier solution was obtained under static transverse loading. After validating of the model, various mechanical and geometrical parameters were varied to characterise the behaviour of the structure under regular and auxetic response. It was found that the auxeticity of the core strongly affects the mechanical response, e.g., in controlling deflection, in-plane anisotropy, and Poisson’s ratio. Cell wall angle was found to be most critical parameter that can be used to adjust anisotropy, out-of-plane shear modulus, transverse shear stress distribution, and deflection of the panel. Also the cell aspect ratio controls the sensitivity of the core response to other geometrical variations. In terms of the higher-order theories, the deflection-dependent parameter of the unified formulation seems to have more control of maximum deflection compared to independent rotations. Auxeticity of the core showed some benefits in controlling anisotropy, deflection and providing additional out-of-plane shear rigidity. Overall, since there is not one-to-one relationship between specific values of Poisson’s ratio, anisotropy, and shear rigidity, careful design considerations must be invested to obtain a correct mechanical response.

本文提出了一个分析模型来研究由两个各向同性面板和蜂窝芯组成的夹层板的静态行为。使用统一的位移场来考虑厚度方向的横向剪应力，通过该位移场实现了各种板理论，即指数、三阶、双曲、正弦、五阶、Mindlin 和经典板理论。利用虚功原理推导了简支夹芯板的平衡方程，并得到了静横向载荷作用下的Navier解。模型验证后，改变各种机械和几何参数来表征结构在规则和拉胀响应下的行为。研究发现核心的拉胀性强烈影响机械响应，例如，控制偏转、面内各向异性和泊松比。细胞壁角度被发现是最关键的参数，可用于调整面板的各向异性、面外剪切模量、横向剪切应力分布和偏转。单元纵横比还控制核心响应对其他几何变化的敏感性。就高阶理论而言，与独立旋转相比，统一公式的偏转相关参数似乎对最大偏转有更多的控制。核心的拉胀性在控制各向异性、偏转和提供额外的面外剪切刚度方面显示出一些好处。总体而言，由于泊松比、各向异性和剪切刚度的具体值之间不存在一对一的关系，