Finite deformation higher-order shell models and rigid-body motions

Куликов, Г. М.; Carrera, Erasmo

doi:10.1016/j.ijsolstr.2008.01.020

Cited by 58 publications

(35 citation statements)

References 25 publications

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“…The sampling surface technique was originally proposed by Kulikov et al [33][34][35]. A brief resume and application of this technique are included in this section.…”

Section: Application Of Sampling Surfacementioning

confidence: 99%

Effects of Transverse Deformation on Free Vibration of 2D Curved Beams with General Restraints

Wang

Miao

et al. 2017

Shock and Vibration

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An efficient modified Fourier series-based sampling surface approach is proposed for the analytical evaluation of the vibration characteristics of thick curved beams subjected to general restraints. The theoretical models of the beams are formulated by the theory of elasticity in two dimensions, which allows arbitrary thickness configurations to be tackled. As an innovation of this work, the approach is based upon the sampling surface method combined with the use of modified Fourier series approximation. In particular, the transverse beam domain is discretized by a set of sampling surfaces with unequal spaces, and the displacement components in beam domain coinciding with these surfaces are mathematically described as a set of modified Fourier series in which certain supplementary functions are included to remove all the relevant discontinuities with the displacements and their derivatives at the boundaries to form a mathematically complete set and guarantee the results convergent to the exact solutions. The final results are numerically solved using a modified variational principle by means of Lagrange multipliers and penalty method for the sake of arbitrary boundary conditions. The influences of transverse normal and shear deformation on the vibration characteristics with respect to the geometrical dimension and boundary conditions are systematically evaluated.

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“…The sampling surface technique was originally proposed by Kulikov et al [33][34][35]. A brief resume and application of this technique are included in this section.…”

Section: Application Of Sampling Surfacementioning

confidence: 99%

Effects of Transverse Deformation on Free Vibration of 2D Curved Beams with General Restraints

Wang

Miao

et al. 2017

Shock and Vibration

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“…For the sake of completeness, it should be noted that the displacement field (9) without the Murakami's function is equivalent to the displacement approximation of the sampling surfaces (SaS) formulation presented in the works [104,105], if the Lagrange polynomials (17)- (18) are employed as thickness functions.…”

Section: Higher-order Equivalent Layer-wise Approachmentioning

confidence: 99%

An Equivalent Layer-Wise Approach for the Free Vibration Analysis of Thick and Thin Laminated and Sandwich Shells

et al. 2016

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Abstract:The main purpose of the paper is to present an innovative higher-order structural theory to accurately evaluate the natural frequencies of laminated composite shells. A new kinematic model is developed starting from the theoretical framework given by a unified formulation. The kinematic expansion is taken as a free parameter, and the three-dimensional displacement field is described by using alternatively the Legendre or Lagrange polynomials, following the key points of the most typical Layer-wise (LW) approaches. The structure is considered as a unique body and all the geometric and mechanical properties are evaluated on the shell middle surface, following the idea of the well-known Equivalent Single Layer (ESL) models. For this purpose, the name Equivalent Layer-Wise (ELW) is introduced to define the present approach. The governing equations are solved numerically by means of the Generalized Differential Quadrature (GDQ) method and the solutions are compared with the results available in the literature or obtained through a commercial finite element program. Due to the generality of the current method, several boundary conditions and various mechanical and geometric configurations are considered. Finally, it should be underlined that different doubly-curved surfaces may be considered following the mathematical framework given by the differential geometry.

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“…It means in turn that the solutions based on the SaS technique asymptotically approach the 3D exact solutions of elasticity as the number of SaS goes to infinity. Note also that the origins of the SaS concept can be found in contributions [8,9] in which three, four and five equally spaced SaS are employed. The SaS formulation with the arbitrary number of equispaced SaS is considered in [10].…”

Section: Introductionmentioning

confidence: 99%

Exact geometry solid-shell element based on a sampling surfaces technique for 3D stress analysis of doubly-curved composite shells

Куликов

Mamontov

Плотникова

et al. 2015

Curved and Layered Structures

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A hybrid-mixed ANS four-node shell element by using the sampling surfaces (SaS) technique is developed. The SaS formulation is based on choosing inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell in order to introduce the displacements of these surfaces as basic shell variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree In − 1 in the thickness direction for each layer permits the presentation of the layered shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that allows one to minimize uniformly the error due to the Lagrange interpolation. To implement the efficient analytical integration throughout the element, the enhanced ANS method is employed. The proposed hybrid-mixed four-node shell element is based on the Hu-Washizu variational equation and exhibits a superior performance in the case of coarse meshes. It could be useful for the 3D stress analysis of thick and thin doubly-curved shells since the SaS formulation gives the possibility to obtain numerical solutions with a prescribed accuracy, which asymptotically approach the exact solutions of elasticity as the number of SaS tends to infinity.

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Finite deformation higher-order shell models and rigid-body motions

Cited by 58 publications

References 25 publications

Effects of Transverse Deformation on Free Vibration of 2D Curved Beams with General Restraints

Effects of Transverse Deformation on Free Vibration of 2D Curved Beams with General Restraints

An Equivalent Layer-Wise Approach for the Free Vibration Analysis of Thick and Thin Laminated and Sandwich Shells

Exact geometry solid-shell element based on a sampling surfaces technique for 3D stress analysis of doubly-curved composite shells

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