In the present work, a new higher-order zigzag theory is proposed for the analysis of laminated sandwich beams under static and free vibration conditions. Fourth-order in-plane and transverse displacement fields are chosen along with linear unit Heaviside step function. The present theory satisfies interlaminar transverse stress continuity conditions along with zero value at the top and bottom surface for transverse shear stresses. The proposed approach is also free from any kind of C-1 or penalty requirements. A three-noded one-dimensional finite element having eight degrees of freedom per node is used during analysis. The efficiency of the proposed model is carried out by comparing the present results with those available based on elasticity solutions and zigzag theories in the literature. New results are also reported in the present work, which will serve as a benchmark for future studies. The influence of boundary condition on the nature of stress distribution across the length of beam and frequencies of the beam with different end conditions is also carried out. A comparative study has also been carried out between symmetric and unsymmetric laminated sandwich beam.

中文翻译：

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用于层合夹层梁分析的新型高阶锯齿理论

在目前的工作中，提出了一种新的高阶之字形理论，用于在静态和自由振动条件下分析层压夹层梁。选择四阶平面内和横向位移场以及线性单位 Heaviside 阶跃函数。本理论满足层间横向应力连续性条件以及横向剪切应力在顶面和底面的零值。提议的方法也没有任何类型的 C-1 或惩罚要求。在分析期间使用每个节点具有八个自由度的三节点一维有限元。所提出模型的效率是通过将当前结果与基于弹性解决方案和文献中的之字形理论的可用结果进行比较来实现的。目前的工作还报告了新的结果，这将作为未来研究的基准。还进行了边界条件对梁长度上应力分布的性质和梁在不同端部条件下的频率的影响。还对对称和非对称层合夹层梁进行了比较研究。