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A simple and accurate sandwich plate theory accounting for transverse normal strain and interfacial stress continuity

机译：一种简单而精确的夹心板理论，说明了横向法向应变和界面应力连续性

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This paper presents a simple and accurate sandwich plate theory accounting for the transverse normal strain and interfacial stress continuity. A refined cubic polynomial is used for the transverse shear function and a linear function is adopted for the transverse normal strain. The Heaviside step function and stress continuity coefficients are employed respectively to enforce the interfacial continuity of the in-plane displacements and transverse stresses. By the enforcement of the traction conditions on the plate surfaces, there are only five independent field variables in the present sandwich plate theory. The varia-tional consistent equilibrium equations and boundary conditions in terms of both displacements and stress resultants are derived by utilizing the variational principle. The analytical solutions of the bending analyses of sandwich plates with different aspect ratios and stiffness ratios are solved to demonstrate the accuracy of this new sandwich plate theory. The resulting analytical solutions of deflections, normal stresses and transverse shear stresses are compared with the 3D elasticity solutions, the numerical results and the results given by other sandwich plate theories. The comparison study shows that this equivalent single layer sandwich plate theory is not only simple, but also capable of achieving the accuracy of layerwise sandwich plate theories.
机译：本文提出了一种简单而精确的夹心板理论，该理论考虑了横向法向应变和界面应力连续性。精细的三次多项式用于横向剪力函数，线性函数用于横向法向应变。分别采用Heaviside阶跃函数和应力连续性系数来增强平面内位移和横向应力的界面连续性。通过在板表面上施加牵引条件，在当前的夹层板理论中只有五个独立的场变量。利用变分原理推导了在位移和应力合成两方面的变化一致的平衡方程和边界条件。解决了不同纵横比和刚度比的夹心板弯曲分析的解析解，以证明这种新的夹心板理论的准确性。将所得的挠度，法向应力和横向剪应力的解析解与3D弹性解，数值结果以及其他夹心板理论给出的结果进行比较。比较研究表明，这种等效的单层夹心板理论不仅简单，而且能够达到层状夹心板理论的精度。

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