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Mass-Stiffness Templates for cubic Structural Elements Dedicated to Professor Karl Stark Pister for his 95th birthday

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Computer Modeling in Engineering & Sciences 2021年第12期129卷 1209-1241页

作者： Carlos A.Felippa Department of Aerospace Engineering Sciences and Aerospace Mechanics Research Center University of Colorado at BoulderBoulderCO 80309-0429USA

1 This paper considers Lagrangian finite elements for structural dynamics constructed with cubic displacement shape *** method of templates is used to investigate the construction of accurate mass-stiffness *** method introduces free parameters that can be adjusted to customize elements according to accuracy and rank-sufficiency ***-and two-dimensional Lagrangian cubic elements with only translational degrees of freedom(DOF)carry two additional nodes on each side,herein called side nodes or *** usually placed at the third-points,the SN location may be adjusted within geometric *** adjustment effect is studied in detail using symbolic computations for a bar *** best SN location is taken to be that producing accurate approximation to the lowest natural frequencies of the continuum *** is investigated through Fourier analysis of the propagation of plane waves over a regular infinite lattice of bar *** is placed on the acoustic branch of the frequency-vs.-wavenumber dispersion *** is found that dispersion results using the fully integrated consistent mass matrix(CMM)are independent of the SN location whereas its lowfrequency accuracy order is O(κ8),whereκis the dimensionless wave *** the diagonally lumped mass matrix(DLMM)constructed through the HRZ scheme,two optimal SN locations are identified,both away from third-points and of accuracy order O(κ8).That with the smallest error coefficient corresponds to the Lobatto 4-point integration rule.A special linear combination of CMM and DLMM with nodes at the Lobatto points yields an accuracy of O(κ10)without any increase in the computational effort over *** effect of reduced integration(RI)on both mass and stiffness matrices is also *** is shown that singular mass matrices can be constructed with 2-and 3-point RI rules that display the same optimal accuracy of the exactly integrated case,at the cost of introducing spurious modes

关键词： Structural dynamics Lagrangian elements finite elements cubic shape functions bar plane stress mass stiffness vibration wave propagation Fourier analysis dispersion templates

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