A hierarchic high-order Timoshenko beam finite element

Tai, C.-Y.; Chan, Yum Ji

doi:10.1016/j.compstruc.2015.12.002

Cited by 16 publications

(8 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where ρ, G and E are respectively the density, the shear modulus and Young's modulus of the constitutive material of the beam; A and I are the area and quadratic momentum of the cross-section; κ is the shear correction factor, which depends on the shape of the cross-section [40,29]; andq andm are the spatial amplitudes of time-harmonic linear densities of forces and moments, respectively. In these equations, the shear forceN and the bending momentM have been expressed in terms of the kinematic variables (ū, θ) thanks to the classical linear elastic constitutive relations…”

Section: Notations and Available Exact Solutions To The Timoshenko Symentioning

confidence: 99%

“…and the right-hand side vector F is left unchanged and is defined by (29). Contrary to the system (24), the system (43) is not symmetric, due to the contribution of D.…”

Section: Discretizationmentioning

confidence: 99%

“…The traditional FEM [26,27] featuring low-order polynomial shape functions (also called h-FEM) is a reliable choice for static or low-frequency problems and slowly varying heterogeneities, but fails at addressing higher frequencies or sharper heterogeneities [27,28]. To tackle these difficulties, two improvements are often considered: (i) using higher-order polynomial shape functions, the resulting method being sometimes called the hp-FEM [27,29] or spectral FEM [30,28], or (ii) enriching the finite element basis with problem-related functions chosen to approximate the exact solution better than polynomials. This second approach is adopted in this paper.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Enriched finite elements and local rescaling for vibrations of axially inhomogeneous Timoshenko beams

Cornaggia

Darrigrand

Marrec

et al. 2020

Journal of Sound and Vibration

View full text Add to dashboard Cite

This work presents a new enriched finite element method dedicated to the vibrations of axially inhomogeneous Timoshenko beams. This method relies on the "half-hat" partition of unity and on an enrichment by solutions of the Timoshenko system corresponding to simple beams with a homogeneous or an exponentially-varying geometry. Moreover, the efficiency of the enrichment is considerably increased by introducing a new formulation based on a local rescaling of the Timoshenko problem, that accounts for the inhomogeneity of the beam. Validations using analytical solutions and comparisons with the classical high-order polynomial FEM, conduced for several inhomogeneous beams, show the efficiency of this approach in the time-harmonic domain. In particular low error levels are obtained over ranges of frequencies varying from a factor of one to thirty using fixed coarse meshes. Possible extensions to the research of natural frequencies of beams and to simulations of transient wave propagation are highlighted.

show abstract

Section: Notations and Available Exact Solutions To The Timoshenko Symentioning

confidence: 99%

“…and the right-hand side vector F is left unchanged and is defined by (29). Contrary to the system (24), the system (43) is not symmetric, due to the contribution of D.…”

Section: Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Enriched finite elements and local rescaling for vibrations of axially inhomogeneous Timoshenko beams

Cornaggia

Darrigrand

Marrec

et al. 2020

Journal of Sound and Vibration

View full text Add to dashboard Cite

show abstract

“…The structures are numerically simulated as layers within which the seismic wave travels and reflects . The phenomenon of wave propagation inside the structure is also studied based on the theory of Timoshenko beam, and the comparison with the experimental results is conducted as well . The elastic investigated lump method decomposes structure/media into elastic lumps, and the structural/media dynamic response is computed in the time domain.…”

Section: Introductionmentioning

confidence: 99%

Explicit fiber element and its application to piers under multipulse near‐fault earthquake motion

Chunxu

2018

Structural Design Tall Build

View full text Add to dashboard Cite

Summary The time delay effect is prominent for the slender structures under the action of near‐fault pulse‐like earthquake excitation. It takes time for the earthquake motion to transfer from the base to other portions of the structure. This paper proposes an explicit‐based fiber line element with its analytical framework to capture the time delay effect when excitated by earthquake motion. The object‐oriented technique (C++) is used to code the integrated analysis framework. Newly designed classes are integrated to perform the explicit analysis parallelly. The nonlinear material model is also incorporated into the proposed element. The verification of the proposed element shows the time delay effect can be spotted inside the structure. The proposed element can provide a reasonable transient dynamic response under both static and dynamic loadings. The basic and higher vibration model can be aroused if the proper frequency is inputted. A slender reinforced concrete bridge pier is numerically modeled by the proposed element, and its seismic response characteristic under the action of the qualified multipulse near‐fault earthquake motion is analyzed. The results show the seismic response within the pier is transferred from bottom to top in a distinct time delay. In a statistical sense, the typical increasing ratio of relative displacement for S/R and P/S is 4.9% and 8.1%, respectively. Directly using the earthquake motion recorded at the seismic station may underestimate the seismic demand.

show abstract

“…Yu et al [43] used hierarchical finite beam elements to static and dynamic analysis. The rate of convergence in Timoshenko beam improved by Tai and Chan [44] by considering Legendre based hierarchic shape functions. Green's-function-based finite element formulation (HSF-FEM) is utilized by Wang and Qin [45] for simulating bioheat transfer in the human eye and by Cao et al [46] for analyzing three-dimensional elastic problems with body forces.…”

mentioning

confidence: 99%

Hybrid integral transform and p-version FEM for thermo-mechanical analysis of a functionally graded piezoelectric hollow cylinder subjected to asymmetric loads

2021

View full text Add to dashboard Cite

As the first endeavor, a combination of fast Fourier transform (FFT) and p-version of finite element method is proposed for electro-thermo-elastic analysis of a thick hollow cylinder under asymmetric thermal loadings. In shells of revolution, the proposed FFT-pFE method is accompanied by a significant decrease in the computational costs. Due to the problem periodicity in such structures, the FFT technique is used to discretize the governing equations into a set of harmonics. Each harmonic is then partitioned using higher order finite elements. Hierarchical finite elements based on Legendre polynomial interpolation functions are utilized to discretize 2D governing equations of a functionally graded piezoelectric (FGP) cylinder. 3D governing equations of a FGP hollow cylinder are then discretized by using the higher-order Lagrangian finite elements. The effects of FFT grid-size as well as the order of the interpolation functions are investigated on convergence behavior of the proposed mixed FFT-pFE method. The material properties, with the exception of the Poisson's ratio, are considered to vary along the radius of the cylinder. The governing equations are derived using the principle of virtual displacements. For a 3D FGP hollow cylinder, the influence of axially and circumferentially non-symmetric thermal loadings is presented in contour plots.

show abstract

A hierarchic high-order Timoshenko beam finite element

Cited by 16 publications

References 22 publications

Enriched finite elements and local rescaling for vibrations of axially inhomogeneous Timoshenko beams

Enriched finite elements and local rescaling for vibrations of axially inhomogeneous Timoshenko beams

Explicit fiber element and its application to piers under multipulse near‐fault earthquake motion

Hybrid integral transform and p-version FEM for thermo-mechanical analysis of a functionally graded piezoelectric hollow cylinder subjected to asymmetric loads

Contact Info

Product

Resources

About