A novel integration scheme for solution of consistent mass matrix in free and forced vibration analysis

Yang, Gang; Hu, Dean; Ma, Guowei; Wan, Detao

doi:10.1007/s11012-015-0343-5

Cited by 13 publications

(2 citation statements)

References 23 publications

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“…Other researchers have developed various approaches for performing static and dynamic analyses on prismatic and nonprismatic Bernoulli-Euler and Timoshenko beams. Some of the scholars that have evaluated mass and stiffness matrices include [11] where examined the free vibration and stability analysis of Timoshenko beams through a finite element analysis. [12] presented a symbolic integration that combined an indefinite integral with the Gauss divergence theorem, which was used to form a novel integration scheme for a consistent mass matrix in the FEM.…”

Section: Introductionmentioning

confidence: 99%

An Alternative Approach to Obtaining Stiffness and Mass Matrices for Three-Dimensional Bernoulli-Euler and Timoshenko Beam-Columns

Aydin¹

2021

J. Civ. Eng. Constr.

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In the static analysis of beam-column systems using matrix methods, polynomials are using as the shape functions. The transverse deflections along the beam axis, including the axial- flexural effects in the beam-column element, are not adequately described by polynomials. As an alternative method, the element stiffness matrix is modeling using stability parameters. The shape functions which are obtaining using the stability parameters are more compatible with the system’s behavior. A mass matrix used in the dynamic analysis is evaluated using the same shape functions as those used for derivations of the stiffness coefficients and is called a consistent mass matrix. In this study, the stiffness and consistent mass matrices for prismatic three-dimensional Bernoulli-Euler and Timoshenko beam-columns are proposed with consideration for the axial-flexural interactions and shear deformations associated with transverse deflections along the beam axis. The second-order effects, critical buckling loads, and eigenvalues are determined. According to the author’s knowledge, this study is the first report of the derivations of consistent mass matrices of Bernoulli-Euler and Timoshenko beam-columns under the effect of axially compressive or tensile force.

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Section: Introductionmentioning

confidence: 99%

An Alternative Approach to Obtaining Stiffness and Mass Matrices for Three-Dimensional Bernoulli-Euler and Timoshenko Beam-Columns

Aydin¹

2021

J. Civ. Eng. Constr.

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“…Moreover, the strain smoothing technique cannot be directly applied to compute the terms in the consistent mass matrix, as there are no ‘gradient’ terms in the consistent mass matrix. Recently, the authors incorporated the indefinite integral into cell‐based S‐FEM for analysis of two‐dimensional (2D) plane dynamic problems, in which the consistent mass matrix can be transformed into boundary integral of elements without using the smoothing technique.…”

Section: Introductionmentioning

confidence: 99%

A fully smoothed XFEM for analysis of axisymmetric problems with weak discontinuities

Wan

Natarajan

et al. 2016

Numerical Meth Engineering

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Summary In this paper, we propose a fully smoothed extended finite element method for axisymmetric problems with weak discontinuities. The salient feature of the proposed approach is that all the terms in the stiffness and mass matrices can be computed by smoothing technique. This is accomplished by combining the Gaussian divergence theorem with the evaluation of indefinite integral based on smoothing technique, which is used to transform the domain integral into boundary integral. The proposed technique completely eliminates the need for isoparametric mapping and the computing of Jacobian matrix even for the mass matrix. When employed over the enriched elements, the proposed technique does not require sub‐triangulation for the purpose of numerical integration. The accuracy and convergence properties of the proposed technique are demonstrated with a few problems in elastostatics and elastodynamics with weak discontinuities. It can be seen that the proposed technique yields stable and accurate solutions and is less sensitive to mesh distortion. Copyright © 2016 John Wiley & Sons, Ltd.

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A nodal spacing study on the frequency convergence characteristics of structural free vibration analysis by lumped mass Lagrangian finite elements

Wang

et al. 2022

Engineering with Computers

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A novel integration scheme for solution of consistent mass matrix in free and forced vibration analysis

Cited by 13 publications

References 23 publications

An Alternative Approach to Obtaining Stiffness and Mass Matrices for Three-Dimensional Bernoulli-Euler and Timoshenko Beam-Columns

An Alternative Approach to Obtaining Stiffness and Mass Matrices for Three-Dimensional Bernoulli-Euler and Timoshenko Beam-Columns

A fully smoothed XFEM for analysis of axisymmetric problems with weak discontinuities

A nodal spacing study on the frequency convergence characteristics of structural free vibration analysis by lumped mass Lagrangian finite elements

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