A novel mixed finite element method is developed and implemented for analyzing the vibration and buckling behavior of general composite beams which consists both transversely layered and axially jointed materials. The governing state-space equations are derived using the Hamilton's principle, where both displacements and stresses are treated as fundamental variables. This semi-analytical method uses transfer relations in the transverse direction and finite element meshing in the longitudinal direction, overcoming the difficulties for general composite beams analysis and providing computational efficiency and analyzing flexibilities. The developed mixed finite element model ensures continuity of both displacements and stresses across the material interface, thereby resolving interfacial stress singularity issues and offering more reliable simulations of boundary conditions at both ends. The proposed method is formulated and validated for the free vibration and buckling analysis of general composite beams. Additionally, it is observed that material properties such as Young's modulus and density, as well as the stiffness of the interface connecting layers, have significant effects on the free vibration and buckling responses of the composite beams. Analysis of periodically distributed and bi-directional composite beams demonstrates the versatility of this method in handling two types of combination forms. The proposed method serves as a valuable reference for obtaining accurate vibration and buckling results while ensuring stress-compatibility for composite beams in practical applications.

中文翻译：

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使用混合有限元的通用组合梁的动态行为


开发并实施了一种新颖的混合有限元方法，用于分析由横向层状材料和轴向接合材料组成的通用组合梁的振动和屈曲行为。控制状态空间方程是使用汉密尔顿原理导出的，其中位移和应力都被视为基本变量。这种半解析方法利用横向传递关系和纵向有限元网格划分，克服了一般组合梁分析的困难，提供了计算效率和分析灵活性。开发的混合有限元模型确保了材料界面上位移和应力的连续性，从而解决了界面应力奇异性问题，并为两端的边界条件提供了更可靠的模拟。所提出的方法针对一般组合梁的自由振动和屈曲分析进行了阐述和验证。此外，据观察，杨氏模量和密度等材料特性以及界面连接层的刚度对复合梁的自由振动和屈曲响应具有显着影响。对周期性分布和双向组合梁的分析证明了该方法在处理两种类型的组合形式方面的多功能性。该方法为获得准确的振动和屈曲结果同时确保实际应用中组合梁的应力兼容性提供了有价值的参考。