A new approach for treating concentrated loads in doubly-curved composite deep shells with variable radii of curvature

Tornabene, Francesco; Fantuzzi, Nicholas; Bacciocchi, Michele; Viola, Erasmo

doi:10.1016/j.compstruct.2015.05.049

Cited by 62 publications

(19 citation statements)

References 93 publications

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“…Therefore, many researchers had recourse to the GDQ method in order to find an approximate solution to this kind of structural problems . The works [97][98][99][100][101][102][103] have proven that the numerical results given by the application of the GDQ method are stable and accurate. In these papers the GDQ technique has been employed to solve both the static and dynamic analyses of plates, singly-curved and doubly-curved shells and panels of revolution.…”

Section: Introductionmentioning

confidence: 96%

Higher-order theories for the free vibrations of doubly-curved laminated panels with curvilinear reinforcing fibers by means of a local version of the GDQ method

Tornabene

Fantuzzi

Bacciocchi

et al. 2015

Composites Part B: Engineering

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113

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Section: Introductionmentioning

confidence: 96%

Higher-order theories for the free vibrations of doubly-curved laminated panels with curvilinear reinforcing fibers by means of a local version of the GDQ method

Tornabene

Fantuzzi

Bacciocchi

et al. 2015

Composites Part B: Engineering

Self Cite

113

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“…By regularizing the Dirac-delta function, such singular function is treated as non-singular functions and can be easily and directly discretized using the DQM. Jung (2009), Jung and Don (2009), , Wang et al (2014), Eftekhari (2015a), and Tornabene et al (2015b) have successfully applied this technique in conjunction with the point discretization methods to solve various partial differential equations involving the Dirac-delta function. However, this technique involves a regularization parameter that should be carefully adjusted before the problem being solved.…”

Section: Introductionmentioning

confidence: 99%

A Differential Quadrature Procedure with Direct Projection of the Heaviside Function for Numerical Solution of Moving Load Problem

Eftekhari

2016

Lat. Am. j. solids struct.

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Owing to its particular characteristics, the direct discretization of the Dirac-delta function is not feasible when point discretization methods like the differential quadrature method (DQM) are applied. A way for overcoming this difficulty is to approximate (or regularize) the Dirac-delta function with simple mathematical functions. By regularizing the Dirac-delta function, such singular function is treated as non-singular functions and can be easily and directly discretized using the DQM. On the other hand, it is possible to combine the DQM with the integral quadrature method (IQM) to handle the Dirac-delta function. Alternatively, one may use another definition of the Dirac-delta function that the derivative of the Heaviside function, H(x), is the Dirac-delta function, δ(x), in the distribution sense, namely, dH(x)/dx = δ(x). This approach has been referred in the literature as the direct projection approach. It has been shown that although this approach yields highly oscillatory approximation of the Dirac-delta function, it can yield a non-oscillatory approximation of the solution. In this paper, we first present a modified direct projection approach that eliminates such difficulty (oscillatory approximation of the Dirac-delta function). We then demonstrate the applicability and reliability of the proposed method by applying it to some moving load problems of beams and rectangular plates.

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“…However, the previous studies are most confined to the signer geometric configuration, that is, panels and shells, the difficulty of which is that the admissible functions of the panels do not fit to the shells. As we all know, in addition to the external boundary conditions, the kinematic and physical compatibility should be satisfied at the common meridian of = 0 and 2 , if a complete shell of revolution needs considering [3,[53][54][55]. The kinematic compatibility conditions include the continuity 8 Mathematical Problems in Engineering of displacements.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition

Pang

et al. 2017

Mathematical Problems in Engineering

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The aim of this paper is to extend the modified Fourier-Ritz approach to evaluate the free vibration of four-parameter functionally graded moderately thick cylindrical, conical, spherical panels and shells of revolution with general boundary conditions. The first-order shear deformation theory is employed to formulate the theoretical model. In the modified Fourier-Ritz approach, the admissible functions of the structure elements are expanded into the improved Fourier series which consist of two-dimensional (2D) Fourier cosine series and auxiliary functions to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges regardless of boundary conditions and then solve the natural frequencies by means of the Ritz method. As one merit of this paper, the functionally graded cylindrical, conical, spherical shells are, respectively, regarded as a special functionally graded cylindrical, conical, spherical panels, and the coupling spring technology is introduced to ensure the kinematic and physical compatibility at the common meridian. The excellent accuracy and reliability of the unified computational model are compared with the results found in the literatures.

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A new approach for treating concentrated loads in doubly-curved composite deep shells with variable radii of curvature

Cited by 62 publications

References 93 publications

Higher-order theories for the free vibrations of doubly-curved laminated panels with curvilinear reinforcing fibers by means of a local version of the GDQ method

Higher-order theories for the free vibrations of doubly-curved laminated panels with curvilinear reinforcing fibers by means of a local version of the GDQ method

A Differential Quadrature Procedure with Direct Projection of the Heaviside Function for Numerical Solution of Moving Load Problem

The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition

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