Mathematical modelling of physically/geometrically non-linear micro-shells with account of coupling of temperature and deformation fields

Awrejcewicz, Jan; Кrysko, V.А.; Сопенко, А А; Zhigalov, Maxim V.; Kirichenko, Aleksandr V.; Krysko, Anton V.

doi:10.1016/j.chaos.2017.09.008

Cited by 19 publications

(6 citation statements)

References 10 publications

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“…Awrejcewicz et al [48] presented a new mathematical model for elastoplastic beams, rigidly clamped at the ends, under the action of transverse pressure. The model took into account traveling elastic bending waves, stationary and nonstationary plastic hinges, elastic-plastic tension and shear deformation.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical modeling of physically nonlinear 3D beams and plates made of multimodulus materials

et al. 2021

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In this work, mathematical models of physically nonlinear plates and beams made from multimodulus materials are constructed. Our considerations are based on the 3D deformation theory of plasticity, the von Mises plasticity criterion and the method of variable parameters of the theory of elasticity developed by Birger. The proposed theory and computational algorithm enable for solving problems of three types of boundary conditions, edge conditions and arbitrary lateral load distribution. The problem is solved by the finite element method (FEM), and its convergence and the reliability of the results are investigated. Based on numerical experiments, the influence of multimodulus characteristics of the material of the beam and the plate on their stress–strain states under the action of transverse loads is illustrated and discussed.

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Section: Introductionmentioning

confidence: 99%

“…In [48], a mathematical model of flexible physically nonlinear micro-shells was created taking into account the connectedness of the temperature and strain fields. Geometric nonlinearity was introduced according to Kármán's theory, and the shells were flat.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of physically nonlinear 3D beams and plates made of multimodulus materials

et al. 2021

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“…Awrejcewicz et al [8–10] studied the influence of temperature fields in the theory of plates and shells. Awrejcewicz et al [8] is devoted to the nonlinear dynamics of thin plates and shells with thermosensitive excitation.…”

Section: Introductionmentioning

confidence: 99%

“…Awrejcewicz et al [10] constructed a mathematical model of flexible shallow geometrically and physically nonlinear shells, taking into account the relationship between the temperature and deformation fields. Geometric nonlinearity was introduced using the von Karman theory of shells.…”

Section: Introductionmentioning

confidence: 99%

Identifying inclusions in a non-uniform thermally conductive plate under external flows and internal heat sources using topological optimization

Krysko

Awrejcewicz

Bodyagina³

et al. 2021

Mathematics and Mechanics of Solids

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We propose applying topological optimization methods based on measuring temperature and heat fluxes to estimate the thermal conductivity of inhomogeneous thermally conductive plates and determine the shape and location of foreign inclusions. Examples of plates subjected to external heat fluxes and heat sources are considered. The solutions are obtained with the help of the finite element method combined with the method of moving asymptotes. The results show that identification accuracy depends on the defined boundary conditions, the source intensity value, heat fluxes, temperature distribution and the shape of the inclusions. For the problem of 18 circular inclusions under different heat fluxes, identification accuracy increases with increasing source intensity values.

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“…Progress in micro-and nano-technologies leads to the interest of scientists not only to the behavior of full-size mechanical systems in the form of plates and shells [13,14,16], but also the need to create mathematical models that take into account the scale effects at the micro and nano level [10,12,19]. In most works on this subject linear models are used for numerical analysis [15,17,18,21,22].…”

Section: Introductionmentioning

confidence: 99%

Visualization of Scenarios for the Transition of Oscillations from Harmonic to Chaotic for a Micropolar Kirchhoff-Love Cylindrical Meshed Panel

Krylova¹,

Папкова²,

Салтыкова³

et al. 2019

GraphiCon'2019 Proceedings. Volume 2

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On the basis of the kinematic hypotheses of the Kirchhoff-Love built a mathematical model of micropolar cylindrical meshed panels vibrations under the action of a normal distributed load. In order to take into account the size-dependent behavior, the panel material is considered as a Cosser’s pseudocontinuum with constrained particle rotation. The mesh structure is taken into account by the phenomenological continuum model of G. I. Pshenichnov. For a cylindrical panel consisting of two systems of mutually perpendicular edges, a scenario of transition of oscillations from harmonic to chaotic is constructed. It is shown that in the study of the behavior of cylindrical micropolar meshed panels it is necessary to study the nature of the oscillations of longitudinal waves.

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Mathematical modelling of physically/geometrically non-linear micro-shells with account of coupling of temperature and deformation fields

Cited by 19 publications

References 10 publications

Mathematical modeling of physically nonlinear 3D beams and plates made of multimodulus materials

Mathematical modeling of physically nonlinear 3D beams and plates made of multimodulus materials

Identifying inclusions in a non-uniform thermally conductive plate under external flows and internal heat sources using topological optimization

Visualization of Scenarios for the Transition of Oscillations from Harmonic to Chaotic for a Micropolar Kirchhoff-Love Cylindrical Meshed Panel

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