本研究目標旨在發展高階轉折理論(Higher-order refined zigzag theory, HRZT)於疊層板結構之應用，包含推導HRZT板結構之平衡方程式，與發展以HRZT為理論基礎之板元素。近期，有學者已針對三明治複合樑發展出高階轉折理論，以解決其靜態彎曲響應的問題。本研究延伸了這一理論的應用範疇，將其應用於三明治複合板中。
本研究中，面內位移假設為高階轉折函數，使得本理論能夠滿足上、下自由表面之面外剪應力為零，以及層與層交界面上的剪應力連續性。為解決線性靜態橫向負載下的位移和應力，我們開發了三種四邊形板元素：HRZT4N36(具有4個主要結點和總共36個自由度之HRZT板元素)、HRZT8N72(具有8個主要結點和總共72個自由度之HRZT板元素)和HRZT4N40(具有4個主要結點和總共40個自由度之HRZT板元素)。其中HRZT4N40在不顯著增加計算量的同時，可有效解決剪力自鎖問題。
透過與FSDT板元素、HSDT板元素、RZT板元素之有限元素模型和ANSYS三維有限元素模型的結果進行比較，驗證了HRZT板元素在三明治複合板中包含撓度、面內外移、正向應力、面內剪應力、面外剪應力和剪力的準確性。此外本研究也對不同的面外剪應力和剪力的計算方法進行了比較，並根據結果提出推薦方法。
根據本計畫中呈現的數值結果，證明了HRZT板元素能夠準確描述三明治複合板的靜態線性現象，其有限元素公式及其數值結果可應用於航空工程、海洋工程、土木工程和機械工程等多個領域。

This study aims at developing the applications of sandwich plates based on higher-order refined zigzag theory (HRZT). It involves derivations of the equilibrium equations of HRZT plates, and development of plate elements based on HRZT. Recently, the HRZT for static bending response of sandwich composite beams has been developed. This study extends the application range of this theory to sandwich plate structures.
In order to solve the linear static responses of displacements and stresses under transverse load, we have developed three types of quadrilateral plate elements, including HRZT4N36, HRZT8N72, and HRZT4N40. Among these, HRZT4N40 effectively resolves the shear locking phenomenon with slight increase in computational cost.
The in-plane displacements, deflections, normal stresses, in-plane shear stresses, out-of-plane shear stresses and shear forces calculated by HRZT plate elements have been compared with those of FSDT, HSDT, RZT plate elements and 3-D FEM model. It is proved that the solutions based on HRZT are reliable to linear static analysis for sandwich plates. This study also compared different methods for calculating the out-of-plane shear stresses and shear forces. A suggested method is provided according to the results.
Based on the numerical results in this study, it has been demonstrated that HRZT plate elements can accurately describe the static linear behavior of sandwich plates. The formulations of HRZT plates developed in this study are applicable to aerospace engineering, naval engineering, civil engineering and mechanical engineering, etc.

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