Analyzing static and dynamic problems including composite structures has been of high significance in research efforts and industrial applications. In this article, equivalent single layer approach is utilized for dynamic finite element procedures of 3D composite beam as the building block of numerous composite structures. In this model, both displacement and strain fields are decomposed into cross-sectional and longitudinal components, called consistent geometric decomposition theorem. Then, the model is discretized using finite element procedures. Two local coordinate systems and a global one are defined to decouple mechanical degrees of freedom. Furthermore, from the viewpoint of consistent geometric decomposition theorem, the transformation and element mass matrices for those systems are introduced here for the first time. The same decomposition idea can be used for developing element stiffness matrix. Finally, comprehensive validations are conducted for the theory against experimental and numerical results in two case studies and for various conditions.

中文翻译：

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基于实验和数值分析的一致几何分解定理在3D复合梁动力有限元中的应用

分析包括复合结构在内的静态和动态问题在研究工作和工业应用中具有重要意义。在本文中，等效单层方法用于3D复合梁的动态有限元过程，作为许多复合结构的基础。在该模型中，位移场和应变场都分解为横截面和纵向分量，称为一致几何分解定理。然后，使用有限元程序离散化模型。定义了两个局部坐标系和一个全局坐标系以解耦机械自由度。此外，从一致的几何分解定理的角度出发，这里首次引入了这些系统的变换和元素质量矩阵。相同的分解思想可用于开发单元刚度矩阵。最后，在两个案例研究和各种条件下，针对实验和数值结果对该理论进行了全面验证。