Carlos A. Felippa^*

CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.3, pp. 1209-1241, 2021, DOI:10.32604/cmes.2021.016803

Abstract This paper considers Lagrangian finite elements for structural dynamics constructed with cubic displacement shape functions. The method of templates is used to investigate the construction of accurate mass-stiffness pairs. This method introduces free parameters that can be adjusted to customize elements according to accuracy and rank-sufficiency criteria. One- 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 SN. Although usually placed at the third-points, the SN location may be adjusted within geometric limits. The adjustment effect is studied in detail using symbolic computations for a… More >

Gouravaraju Saipraneeth¹, Ranjan Ganguli²

Structural Durability & Health Monitoring, Vol.7, No.1&2, pp. 23-64, 2011, DOI:10.3970/sdhm.2011.007.023

Abstract In this paper, the effect of damage on mode shape related parameters of a beam is investigated. The damage is represented by a localized reduction in beam stiffness. The damage location and amount is varied using a finite element model of the beam to obtain the mode shapes. A beam which is simply supported at both ends is used for the numerical results. The periodic nature of the beam is exploited to obtain spatial Fourier coefficients of the mode shapes. As the damage location and size are varied, it is found that the Fourier coefficients also change and are found… More >

Michely Laís de Oliveira^1,*, Marcio Augusto Villela Pinto², Simone de Fátima Tomazzoni Gonçalves², Grazielli Vassoler Rutz³

CMES-Computer Modeling in Engineering & Sciences, Vol.117, No.2, pp. 251-270, 2018, DOI:10.31614/cmes.2018.04237

Abstract Studies of problems involving physical anisotropy are applied in sciences and engineering, for instance, when the thermal conductivity depends on the direction. In this study, the multigrid method was used in order to accelerate the convergence of the iterative methods used to solve this type of problem. The asymptotic convergence factor of the multigrid was determined empirically (computer aided) and also by employing local Fourier analysis (LFA). The mathematical model studied was the 2D anisotropic diffusion equation, in which ε > 0 was the coefficient of a nisotropy. The equation was discretized by the Finite Difference Method (FDM) and Central… More >

A. P. S. Selvadurai¹, Wenjun Dong

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 41-54, 2006, DOI:10.3970/cmes.2006.012.041

Abstract A Fourier analysis conducted on both the spatial and the temporal discretizations of the governing partial differential equation shows that the Courant number as well as the time marching scheme have significant influences on the numerical behaviour of a Modified Least Squares (MLS) method for the solution of the advection equation. The variations of the amplification factor and the relative phase velocity with the Courant number and the dimensionless wave number indicate that when Courant number is equal to unity, the MLS method with the specified time-weighting and upwind function gives accurate results. This conclusion is confirmed by the numerical… More >

Kanchi Venkatesulu Reddy¹, Ranjan Ganguli²

CMC-Computers, Materials & Continua, Vol.5, No.2, pp. 79-98, 2007, DOI:10.3970/cmc.2007.005.079

Abstract This paper investigates the effect of damage on beams with fixed boundary conditions using Fourier analysis of the mode shapes in spatial domain. A finite element model is used to obtain the mode shapes of a damaged fixed-fixed beam. Then the damaged beams are studied using a spatial Fourier analysis. This approach contrasts with the typical time domain application of Fourier analysis for vibration problems. It is found that damage causes considerable change in the Fourier coefficients of the mode shapes. The Fourier coefficients, especially the higher harmonics, are found to be sensitive to both damage size and location and… More >