This paper presents a numerical and experimental assessment of the static behaviour of thick sandwich beams using the mixed {3,2}-Refined Zigzag Theory (RZT{3,2}(m)). The displacement field of the RZT{3,2}(m) assumes a piecewise continuous cubic zigzag distribution for the axial contribution and a smoothed parabolic variation for the transverse one. At the same time, the out-of-plane stresses are assumed continuous a-priori: the transverse normal stress is given as a third-order power series expansion of the thickness coordinate, whereas the transverse shear one is derived through the integration of Cauchy's equation. The equilibrium equations and consistent boundary conditions are derived through a mixed variational statement based on the Hellinger-Reissner (HR) theorem and a penalty functional to enforce the strain compatibilities between the assumed independent stress fields and those obtained with the constitutive equations. Based on the proposed model, a simple C0-continuous two-node beam finite element is formulated (2B−RZT{3,2}(m)). Firstly, the analytical and FE model accuracies of the presented formulation are addressed, and comparisons with the available three-dimensional elasticity solutions are performed. Subsequently, an experimental campaign is conducted to evaluate the static response of various thick sandwich beam specimens in three- and four-point bending configurations. The thick beam specimens are equipped with Distributed Fibre Optic Sensors (DFOS) embedded in the sandwich layup to measure axial deformation at the sandwich interfaces directly. Finally, the experimental data are compared with the available numerical models, highlighting the formulated numerical model's performances and limitations.

中文翻译：

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使用混合 {3,2}-RZT 公式对厚夹层梁的静态行为进行数值和实验预测


本文使用混合 {3,2} 精炼之字形理论 （RZT{3,2}（m）） 对厚夹层梁的静态行为进行了数值和实验评估。RZT{3,2}（m） 的位移场假设轴向贡献为分段连续的三次锯齿形分布，横向贡献为平滑的抛物线变化。同时，假设平面外应力是连续的先验应力：横向法向应力是厚度坐标的三阶幂级数展开，而横向剪切应力是通过 Cauchy 方程的积分得出的。平衡方程和一致的边界条件是通过基于 Hellinger-Reissner （HR） 定理的混合变分陈述和罚函数得出的，以加强假设的独立应力场与使用本构方程获得的应力场之间的应变兼容性。基于所提出的模型，公式化了一个简单的 C0 连续双节点梁有限元 （2B−RZT{3,2}（m））。首先，解决了所提公式的解析精度和有限元模型精度，并与可用的三维弹性解进行了比较。随后，进行了一次实验活动，以评估各种厚夹层梁试样在三点和四点弯曲配置下的静态响应。厚梁试样配备了嵌入夹层中的分布式光纤传感器 （DFOS），以直接测量夹层界面处的轴向变形。最后，将实验数据与可用的数值模型进行比较，突出了所构建的数值模型的性能和局限性。