A lumped mass Chebyshev spectral element method and its application to structural dynamic problems  

作　　者：Wang Jingxiong Li Hongjing Xing Haojie 

机构地区：[1]Engineering Mechanics Institute,Nanjing Tech University,Nanjing 211816,China [2]Institute of Geophysics,China Earthquake Administration,Beijing 100081,China

出　　处：《Earthquake Engineering and Engineering Vibration》2022年第3期843-859,共17页地震工程与工程振动（英文刊）

基　　金：Supported by:Joint Research Fund for Earthquake Science,launched by the National Natural Science Foundation of China and the China Earthquake Administration under Grant No.U2039208。

摘　　要：A diagonal or lumped mass matrix is of great value for time-domain analysis of structural dynamic and wave propagation problems,as the computational efforts can be greatly reduced in the process of mass matrix inversion.In this study,the nodal quadrature method is employed to construct a lumped mass matrix for the Chebyshev spectral element method(CSEM).A Gauss-Lobatto type quadrature,based on Gauss-Lobatto-Chebyshev points with a weighting function of unity,is thus derived.With the aid of this quadrature,the CSEM can take advantage of explicit time-marching schemes and provide an efficient new tool for solving structural dynamic problems.Several types of lumped mass Chebyshev spectral elements are designed,including rod,beam and plate elements.The performance of the developed method is examined via some numerical examples of natural vibration and elastic wave propagation,accompanied by their comparison to that of traditional consistent-mass CSEM or the classical finite element method(FEM).Numerical results indicate that the proposed method displays comparable accuracy as its consistent-mass counterpart,and is more accurate than classical FEM.For the simulation of elastic wave propagation in structures induced by high-frequency loading,this method achieves satisfactory performance in accuracy and efficiency.

关 键 词：mass lumping Chebyshev spectral element method Gauss-Lobatto-Chebyshev points Gauss-Lobatto type quadrature structural dynamic analysis elastic wave propagation 

分 类 号：TU311.3[建筑科学—结构工程]