结构工程
振动
有限元法
能量(信号处理)
材料科学
几何学
机械
物理
工程类
声学
数学
量子力学
出处
期刊:AIAA Journal
[American Institute of Aeronautics and Astronautics]
日期:2024-09-25
卷期号:: 1-18
被引量:1
摘要
A novel numerical method, the energy element method, is proposed for the three-dimensional vibration analysis of stiffened plates with complex geometries. The problem is modeled in a cuboidal domain, and a cuboidal energy element is developed for the simulation of the structural components. To simulate the energy distribution of the structure, stiffened plates are treated as discrete energy systems, where variable stiffness is used to characterize their energy distribution in a cuboidal domain and a global admissible function is used to approximate their vibrational behavior. With extended interval integral, Gauss quadrature, variable stiffness, and Legendre polynomials used for numerical integration in the cuboidal domain, the cuboidal energy element can offer sufficient precision with sufficient Gauss points for simulating the strain energy of stiffened plates with complex geometries. The Gauss–Legendre quadrature will provide accurate integration results if the integral domain is cuboidal. Otherwise, small cuboidal energy elements are generated with denser Gauss points to capture the geometric boundaries. As the numerical model is constructed on a standard geometric domain, all energy functionals and computational procedures are standard. Three-dimensional vibration problems are investigated for variously shaped stiffened plates with straight or curvilinear stiffeners. The present results are compared with analytical, numerical, and experimental results published in the literature.
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