A differential quadrature procedure for linear and nonlinear steady state vibrations of infinite beams traversed by a moving point load

Eftekhari, S. A.

doi:10.1007/s11012-016-0373-7

Cited by 9 publications

(7 citation statements)

References 42 publications

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“…(69). Following the procedure suggested by references [90,91], the GDQ and GIQ rules are adopted for the implementation of the concentrated load in the present strong form problem according to Eq. ( 69), assuming that the vector at issue is applied in one of the selected discrete computational points.…”

Section: Numerical Implementation With the Gdq Methodsmentioning

confidence: 99%

“…As a consequence, a concentrated force pretends to be a boundary condition within the differential model. On the other hand, in the case of a problem developed within a single domain, in references [89][90][91], an interesting procedure based on GDQ and GIQ methods accounts for a differential-integral implementation on a rectangular plate under a concentrated load, taking into account the main features of the well-known Dirac-Delta function [92]. On the other hand, a concentrated load can be seen as a particular case of a surface pressure acting on a very small area.…”

Section: Introductionmentioning

confidence: 99%

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Static Analysis of Anisotropic Doubly-Curved Shell Subjected to Concentrated Loads Employing Higher Order Layer-Wise Theories

Tornabene¹,

Viscoti²,

Dimitri³

2023

Computer Modeling in Engineering &Amp; Sciences

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In the present manuscript, a Layer-Wise (LW) generalized model is proposed for the linear static analysis of doublycurved shells constrained with general boundary conditions under the influence of concentrated and surface loads. The unknown field variable is modelled employing polynomials of various orders, each of them defined within each layer of the structure. As a particular case of the LW model, an Equivalent Single Layer (ESL) formulation is derived too. Different approaches are outlined for the assessment of external forces, as well as for non-conventional constraints. The doubly-curved shell is composed by superimposed generally anisotropic laminae, each of them characterized by an arbitrary orientation. The fundamental governing equations are derived starting from an orthogonal set of principal coordinates. Furthermore, generalized blending functions account for the distortion of the physical domain. The implementation of the fundamental governing equations is performed by means of the Generalized Differential Quadrature (GDQ) method, whereas the numerical integrations are computed employing the Generalized Integral Quadrature (GIQ) method. In the post-processing phase, an effective procedure is adopted for the reconstruction of stress and strain through-the-thickness distributions based on the exact fulfillment of three-dimensional equilibrium equations. A series of systematic investigations are performed in which the static response of structures with various curvatures and lamination schemes, calculated by the present methodology, have been successfully compared to those ones obtained from refined finite element three-dimensional simulations. Even though the present LW approach accounts for a two-dimensional assessment of the structural problem, it is capable of well predicting the three-dimensional response of structures with different characteristics, taking into account a reduced computational cost and pretending to be a valid alternative to widespread numerical implementations.

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Section: Numerical Implementation With the Gdq Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Static Analysis of Anisotropic Doubly-Curved Shell Subjected to Concentrated Loads Employing Higher Order Layer-Wise Theories

Tornabene¹,

Viscoti²,

Dimitri³

2023

Computer Modeling in Engineering &Amp; Sciences

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“…The applications of the method are numerous and include the numerical solution of ordinary differential equations (ODEs), partial differential equations (PDEs), and integro-differential equations (IDEs) that arise in various engineering and applied mechanics problems [28,29]. More recently, the DQM has been applied to some type of moving load problem [31][32][33][34][35][36]. In the moving load problem, the position and movement of the load can be described by means of a time-dependent Dirac-delta function.…”

Section: Introductionmentioning

confidence: 99%

“…To overcome the difficulties in the discretization of the Dirac-delta function, in Refs. [31][32][33][34][35][36][37][38][39][40], various procedures have been proposed. Although the proposed approaches were shown to be accurate and reliable, as discussed in Refs.…”

Section: Introductionmentioning

confidence: 99%

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An accurate differential quadrature procedure for the numerical solution of the moving load problem

Eftekhari

2020

J Braz. Soc. Mech. Sci. Eng.

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In moving load-type problems, the moving point load is modeled mathematically by a time-dependent Dirac-delta function. A key and difficult step in solving this type of problems using a point discrete method such as the differential quadrature method is the discretization of the Dirac-delta function in a simple and accurate manner. This paper is conducted to facilitate this step and to present a new way to do this task. In this way, the Dirac-delta function is approximated by orthogonal polynomials such as the Legendre and Chebyshev polynomials. Unlike the original Dirac-delta function, which is a generalized singularity function, the resulting approximation function is a non-singular function which can be discretized simply and efficiently. The proposed procedure is applied herein to solve the moving load problem in beams and rectangular plates. Comparisons with available analytical and numerical solutions prove that the proposed approach is highly accurate and efficient.

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Dynamics of a beam on a bilinear elastic foundation under harmonic moving load

et al. 2018

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A differential quadrature procedure for linear and nonlinear steady state vibrations of infinite beams traversed by a moving point load

Cited by 9 publications

References 42 publications

Static Analysis of Anisotropic Doubly-Curved Shell Subjected to Concentrated Loads Employing Higher Order Layer-Wise Theories

Static Analysis of Anisotropic Doubly-Curved Shell Subjected to Concentrated Loads Employing Higher Order Layer-Wise Theories

An accurate differential quadrature procedure for the numerical solution of the moving load problem

Dynamics of a beam on a bilinear elastic foundation under harmonic moving load

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