基于谱位移格式的复杂切口功能梯度板自由振动等几何分析  

Isogeometric analysis for free vibration of functionally graded plates with complex cutouts using spectral displacement formulation

作　　者：杨少伟 孙贤波 蔡志勤[1] 卢海龙 杨志勋 YANG Shaowei;SUN Xianbo;CAI Zhiqin;LU Hailong;YANG Zhixun(Department of Engineering Mechanics,Dalian University of Technology,Dalian 116024,China;College of Mechanical and Electrical Engineering,Harbin Engineering University,Harbin 150001,China)

机构地区：[1]大连理工大学工程力学系,大连116024 [2]哈尔滨工程大学机电工程学院,哈尔滨150001

出　　处：《科技导报》2024年第13期36-47,共12页Science & Technology Review

基　　金：国家自然科学基金项目(52271269,52001088,U2241263,U1906233)。

摘　　要：为分析具有复杂切口的功能梯度板自由振动响应,基于一种新的准三维高阶剪切变形理论(谱位移格式)的等几何分析方法被用来预测带切口板的动力特性。谱位移格式将未知位移场展开为厚度方向上特殊形式的切比雪夫级数,具有精度高,以及避免剪切闭锁问题的特性,对薄厚板的分析具有很好的通用性。利用达朗贝尔原理和虚功原理推导了功能梯度板自由振动的控制方程,并利用等几何方法对方程进行离散和求解。通过对数值算例的计算,以及与现有参考结果的比较,证明了提出的分析方法能够准确有效地分析具有复杂切口的功能梯度板自由振动问题。This paper aims to analyze the free vibration response of functionally graded plates with complex cutouts.An isogeometric analysis method based on a novel quasi-three-dimensional higher-order shear deformation theory called the spectral displacement formulation(SDF)is employed to predict the free vibration characteristics of the plates.The SDF can deal with the three-dimensional elasticity solution and naturally avoid the shear-locking problem,making it suitable for plates with varying thicknesses.The governing equations for free vibration of the plates are derived using the D'Alembert principle and the principle of virtual work,and the equations are discretized using isogeometric method.The results of several numerical examples are compared with existing reference solutions.It is concluded that the proposed analysis method can accurately and effectively analyze the free vibration of functionally graded plates with complex cutouts.

关 键 词：功能梯度板 复杂切口 谱位移格式 等几何分析 自由振动 

分 类 号：TB34[一般工业技术—材料科学与工程] O32[理学—一般力学与力学基础]