Solving physically nonlinear equilibrium problems for sandwich plates with a transversally soft core

Badriev, I. B.; Garipova, G. Z.; Makarov, M. V.; Паймушин, В. Н.; Хабибуллин, Р. Ф.

doi:10.1134/s1995080215040216

Cited by 45 publications

(14 citation statements)

References 8 publications

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“…Обобщенные постановки физически нелинейных и геометрически линейных задач рассмотрены в [15][16][17][18][19]. Нелинейные задачи теории мягких сетчатых оболочек изучены в [20][21][22][23][24][25][26][27][28].…”

Section: рис 1 трехслойная конструкция заполнители: 1 -пенопласт; unclassified

Производная Гато Оператора Геометрически Нелинейной Задачи Об Изгибе Трехслойной Пластины

Бадриев¹,

Буянов²,

Макаров³

2017

Тенденции Развития Науки И Образования

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Section: рис 1 трехслойная конструкция заполнители: 1 -пенопласт; unclassified

Производная Гато Оператора Геометрически Нелинейной Задачи Об Изгибе Трехслойной Пластины

Бадриев¹,

Буянов²,

Макаров³

2017

Тенденции Развития Науки И Образования

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“…We note that a numerical study of the geometrically and physically nonlinear problem of the three-point bending of test samples from layered fibrous composites having a rectangular cross-section was carried out in [1]. The problems of the bending of sandwich plates with a transversally soft core are discussed in [2][3][4][5][6].…”

Section: Statement Of the Problemmentioning

confidence: 99%

Theoretical and experimental investigations of the formation mechanisms of residual deformations of fibrous layered structure composites

2017

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Abstract. On the example of a unidirectional fibrous composite made of unidirectional carbon fibre composite and cold-hardening epoxy XT-118, tests of specimens with a stacking scheme [+45 0 /-45 0 ]2s, where s is the number of monolayers, were carried out for cyclic loading by tension and compression. When the samples are stretched, both the fibers and the epoxy of composite are under shear stresses and stretching in the transverse direction by normal stresses, and under compression, under shear stresses and compression by normal stresses across the fibers. It is shown that in each loading cycle there is a consolidation of the material associated with the rearrangement of its microstructure, an increase in the secant modulus of elasticity and a decrease in the magnitude of the deformation increment at each cycle. The mechanism of accumulation of residual deformations under multiple loading of test samples was qualitatively studied and their level formed in the composite after each loading cycle was quantitatively found. Statement of the problemIn the products of space technology for special purposes, nowadays, structural elements from fibrous composite materials (CM), in particular, carbon plastic, are widely used. Such structural elements in the process of operation under multiple (multi-cycle) loading (in particular, thermal loading) should preserve the stability of geometric sizes and shapes. It was found that when ground-based testing of such products and during their operation, distortions of the measured parameters are always fixed, apparently due to the formation of residual deformations in the design. All the formation mechanisms of such residual deformations in fibrous composites in the process of exploitation of the structural elements made from them have not yet been fully revealed, which raises an urgent problem in the world science in the field of mechanics and machine building. We note that a numerical study of the geometrically and physically nonlinear problem of the three-point bending of test samples from layered fibrous composites having a rectangular cross-section was carried out in [1]. The problems of the bending of sandwich plates with a transversally soft core are discussed in [2-6]. Experiments on cyclic deformationAn extensive scientific literature [7][8][9][10][11][12], etc is devoted to the study of nonlinear deformation under cyclic loading of unidirectional fibrous composites. In particular, in work [12] such a study is carried out for a unidirectional composite on the basis of glass fibers under shearing conditions and repeated cyclic loading of specimens with a stacking scheme [+45 0 /-45 0 ]2s (s is the number of monolayers). On the basis of the obtained experimental data, the secant shear modulus G12 is calculated and a conclusion is made about its fall after loading the sample with ten cycles. The authors explain the fall of the shear modulus by the degradation of the composite under conditions of shear deformations forming in the composite.The carried out studies on the shear ...

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“…The theoretical basis for the study of nonlinear spectral problems is results obtained for linear eigenvalues problems [17][18][19][20][21][22][23]. In the papers [24][25][26][27][28][29][30], numerical methods for solving applied nonlinear boundary value problems and variational inequalities have been studied.…”

Section: Introductionmentioning

confidence: 99%

Eigenvibrations of a bar with load

Samsonov

́ev

2017

MATEC Web Conf.

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Abstract. The differential eigenvalue problem describing eigenvibrations of an elastic bar with load is investigated. The problem has an increasing sequence of positive simple eigenvalues with limit point at infinity. To the sequence of eigenvalues, there corresponds a complete orthonormal system of eigenfunctions. We formulate limit differential eigenvalue problems and prove the convergence of the eigenvalues and eigenfunctions of the initial problem to the corresponding eigenvalues and eigenfunctions of the limit problems as load mass tending to infinity. The original differential eigenvalue problem is approximated by the finite difference method on a uniform grid. Error estimates for approximate eigenvalues and eigenfunctions are established. Investigations of this paper can be generalized for the cases of more complicated and important problems on eigenvibrations of beams, plates and shells with attached loads.

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Solving physically nonlinear equilibrium problems for sandwich plates with a transversally soft core

Cited by 45 publications

References 8 publications

Производная Гато Оператора Геометрически Нелинейной Задачи Об Изгибе Трехслойной Пластины

Производная Гато Оператора Геометрически Нелинейной Задачи Об Изгибе Трехслойной Пластины

Theoretical and experimental investigations of the formation mechanisms of residual deformations of fibrous layered structure composites

Eigenvibrations of a bar with load

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