Boris Semenov | Saint-Petersburg State University (original) (raw)
Papers by Boris Semenov
Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
The paper presents the results of a study of the bifurcation of axisymmetric equilibrium forms of... more The paper presents the results of a study of the bifurcation of axisymmetric equilibrium forms of round plates under various conditions for fixing the outer edge. It is shown that for the case of sliding edge, the analytical, asymptotic and finite element approaches give close results. When the edge of the plate is hinged, the buckling to a non-axisymmetric state occurs at a much higher load and with the formation of a smaller number of waves than for a sliding boundary conditions. Difficulties in obtaining a numerical solution based on the analytical approach are apparently associated with the need for a more accurate description of the stress-strain subcritical state of the plate.
Applied Sciences
The review presents data on the synthesis, properties of carbon-containing compounds, and their a... more The review presents data on the synthesis, properties of carbon-containing compounds, and their application in the technology of obtaining functional and structural composites. Such materials are widely used in recent years due to their good physical and mechanical properties. The review discusses in detail the influence of the chemical composition of various carbon-containing substances and the size of the dispersed phase on the mechanical and physical properties of produced metal matrix composite. The review also concerns methods for the modern synthesis of graphene, carbon nanotubes, and metallic functional and structural composites with reinforcing carbon-containing compounds. Additionally, the results of metal matrix composite modeling are presented. They show that the improved mechanical properties of CNT–Al composites can be attributed to three factors: CNT hardening, matrix grain refinement, and layered architecture.
Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019
Рассматривается прямолинейная трещина в тонкой упругой пластине. При растяжении пластины в направ... more Рассматривается прямолинейная трещина в тонкой упругой пластине. При растяжении пластины в направлении, перпендикулярном трещине, в окрестности трещины появляются сжимающие напряжения, которые при определенном уровне растяжения приводят к потере устойчивости плоской формы равновесия пластины. Целью исследования является выяснение вопроса о том, способствует ли потеря устойчивости росту трещины или приводит к стабилизации деформаций. В работе исследуется напряженное состояние пластины в начальной послекритической стадии. Предложено приближенное аналитическое решение. Методом конечных элементов построено решение задачи растяжения пластинки после потери устойчивости. Оценено влияние потери плоской формы деформирования при растяжении пластины с центральной трещиной на уровень напряженного состояния в окрестности вершины трещины. Анализ напряженного состояния в окрестности вершины центральной трещины при одноосном растяжении дает основания утверждать, что при возможной локальной потере устойчивости вблизи трещины происходит повышение уровня растягивающих напряжений в окрестности кончика трещины, и, как следствие, снижается нагрузка, приводящая к разрушению. Ключевые слова: потеря плоской формы деформирования, пластина, метод конечных элементов.
In modern constructions, thin-layer coats are often used as protecting or strengthening elements.... more In modern constructions, thin-layer coats are often used as protecting or strengthening elements. Deformations of such constructions may cause significant stresses on the interface between the base and the coat because of the difference in their physical-mechanical properties, which leads to the destruction or delamination of the cover. Of special interest is strength analysis under dynamical or vibrational impacts because of the possibility of localizing oscillations in a neighborhood of the initial inhomogeneities (such as inclusions, defects, construction elements, etc.). In this paper, on the example of the delamination of a string from an elastic substrate, the possibility of localizing oscillations on a delamination defect is demonstrated and the effect of this localization on the growth of the delamination zone is analyzed. A simplified setting of the problem is considered. The possibility of localizing oscillations on a delamination defect is demonstrated and an approximate ...
Acta Mechanica, 2021
The present paper is devoted to the development of the method for searching an approximate soluti... more The present paper is devoted to the development of the method for searching an approximate solution of non-stationary problems on a variable interval. This method was first proposed by L.I. Slepyan. Here, the field of its applicability has been expanded to systems of equations, including equations of both hyperbolic and parabolic type. We describe the procedure of such approach in detail on a number of classical partial differential equations and compare the obtained results with exact analytical solution. Also, we consider a dynamic non-coupled thermoelastic problem. The method of expansion on a variable interval allows us to estimate the material response to a thermal disturbance at a large distance from the source.
This paper deals with the problem of local buckling caused by uniaxial stretching of an infinite ... more This paper deals with the problem of local buckling caused by uniaxial stretching of an infinite plate with a circular hole or with circular inclusion made of another material. As the Young’s modulus of the inclusion approaches that of the plate, the critical load increases substantially. When these moduli coincide, stability loss is not possible. This paper also shows the difference between them when the inclusion is softer than the plate and when the inclusion is stiffer than the plate. Computational models show that instability modes are different both when the inclusion is softer than the plate and when the inclusion is stiffer than the plate. The case when plate and inclusion have the same modulus of elasticity, but different Poisson’s ratio is investigated too. It is also discussed here the case when a plate with inclusion is under biaxial tension. For each ratio of the modulus of elasticity of plate versus inclusion it’s obtained the range of the load parameters for which the...
A two-component model of material with a nonlinear internal interaction force is proposed for des... more A two-component model of material with a nonlinear internal interaction force is proposed for describing its structural transformations. An analogy between the equations of a continuous medium and their discrete representation allows demonstrating the effect of quenching of a non-stationary wave, caused by the transfer of energy to internal degrees of freedom. The parameters of the external impact at which the transformation of crystalline lattice takes place are determined. Analytical results are compared with numerical calculations, performed by using the finite difference method.
Vestnik St. Petersburg University, Mathematics
Решается задача о потере плоской формы равновесия бесконечной пластины с круговой вставкой из дру... more Решается задача о потере плоской формы равновесия бесконечной пластины с круговой вставкой из другого материала, находящейся под действием одноосного растяжения. Исследуется влияние модуля упругости вставки на значение критической нагрузки. Для нахождения минимального собственного числа, соответствующего первой критической нагрузке, применяется вариационный принцип. Расчеты проводятся в пакете Maple и сравниваются с результатами, полученными методом конечных элементов в пакете ANSYS 13.1. Проведенные расчеты показывают, что потеря устойчивости при вставке более мягкой, чем пластина, и при вставке более жесткой, чем пластина происходят по разным формам. При приближении значения модуля Юнга вставки к значению модуля Юнга пластины критическая нагрузка существенно увеличивается. При совпадении модулей упругости пластины и вставки потеря устойчивости невозможна. Библиогр. 10 назв. Ил. 5. Табл. 1. Ключевые слова: потеря устойчивости пластины, энергетический метод.
PAMM, 2011
Applanation tonometry estimates intraocular pressure (IOP) by quantifying the force needed to cre... more Applanation tonometry estimates intraocular pressure (IOP) by quantifying the force needed to create a defined amount of deformation of the cornea (Goldmann tonometer) or by estimating the diameter of the circular contact area of the cornea and flat tonometer of defined load (Maklakov tonometer). The first simplest models of the applanation method for measurement of the IOP were based on approach, in which an eyeball is modelled as a thin-walled spherical liquid-filled soft shell with corneal biomechanical properties. It was usually supposed that these properties were the same for all patients. In this work numerical simulation have been carried out using finite element code ANSYS. The eye shell is modeled as two joint shells (cornea and sclera) with different mechanical properties. The results are obtained for numerous sets of parameters and were compared to clinical data. For statistics the measurements of IOP for both eyes of 120 patients before and one month after refractive surgery are used. All parameter of refractive surgery (depth, the width and the place of ablation -refractive surgery for myopia or hypermetropia) have effect on IOP reading obtained with both Goldmann and Maklakov tonometry. The results obtained by Goldmann tonometer are significantly more sensitive to all parameters of refractive surgery than those found with Maklakov tonometer with load 10 g.
PAMM, 2011
In modern constructions, thin-layer coats are often used as protecting or strengthening elements.... more In modern constructions, thin-layer coats are often used as protecting or strengthening elements. Deformations of such constructions may cause significant stresses on the interface between the base and the coat because of the difference in their physical mechanical properties, which leads to the destruction or detachment of the cover. The impact of static or shock loads on the emergence and development of delamination in multilayer constructions has been studied fairly well, but much less is known about destructions of this type under nonstationary (vibrational) loads. The interest in the latter is caused by the fact that even small variable actions may cause the localization of oscillations in a neighborhood of inhomogeneities (such as inclusions, defects, construction elements, etc.) [1] (and lead to the emergence and growth of defects, which strongly affects the reliability and functionality of the whole construction. The possibility of the localization of oscillations near initial delamination and the impact of localization on the growth of the delamination are studied and a model for analyzing conditions under which a detachment zone grows or ceases to grow is suggested.
Vestnik St. Petersburg University: Mathematics, 2011
In modern constructions, thin-layer coats are often used as protecting or strengthening elements.... more In modern constructions, thin-layer coats are often used as protecting or strengthening elements. Deformations of such constructions may cause significant stresses on the interface between the base and the coat because of the difference in their physical-mechanical properties, which leads to the destruction or detachment of the cover. Of special interest is strength analysis under dynamical or vibrational impacts because
Proceedings of the Annual Frequency Control Symposium, 1992
ABSTRACT The approximate analytical formulas for eigenvalues and vibration modes for homogeneous ... more ABSTRACT The approximate analytical formulas for eigenvalues and vibration modes for homogeneous anisotropic plates with varied thickness are obtained. It is supposed that the vibration modes with one or some semi-waves of deformations in the thickness direction of the plate are localized near the point of maximal thickness. The influence of the irregular heating on the working frequency of the quartz resonator is studied by the perturbation method
Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
The paper presents the results of a study of the bifurcation of axisymmetric equilibrium forms of... more The paper presents the results of a study of the bifurcation of axisymmetric equilibrium forms of round plates under various conditions for fixing the outer edge. It is shown that for the case of sliding edge, the analytical, asymptotic and finite element approaches give close results. When the edge of the plate is hinged, the buckling to a non-axisymmetric state occurs at a much higher load and with the formation of a smaller number of waves than for a sliding boundary conditions. Difficulties in obtaining a numerical solution based on the analytical approach are apparently associated with the need for a more accurate description of the stress-strain subcritical state of the plate.
Applied Sciences
The review presents data on the synthesis, properties of carbon-containing compounds, and their a... more The review presents data on the synthesis, properties of carbon-containing compounds, and their application in the technology of obtaining functional and structural composites. Such materials are widely used in recent years due to their good physical and mechanical properties. The review discusses in detail the influence of the chemical composition of various carbon-containing substances and the size of the dispersed phase on the mechanical and physical properties of produced metal matrix composite. The review also concerns methods for the modern synthesis of graphene, carbon nanotubes, and metallic functional and structural composites with reinforcing carbon-containing compounds. Additionally, the results of metal matrix composite modeling are presented. They show that the improved mechanical properties of CNT–Al composites can be attributed to three factors: CNT hardening, matrix grain refinement, and layered architecture.
Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019
Рассматривается прямолинейная трещина в тонкой упругой пластине. При растяжении пластины в направ... more Рассматривается прямолинейная трещина в тонкой упругой пластине. При растяжении пластины в направлении, перпендикулярном трещине, в окрестности трещины появляются сжимающие напряжения, которые при определенном уровне растяжения приводят к потере устойчивости плоской формы равновесия пластины. Целью исследования является выяснение вопроса о том, способствует ли потеря устойчивости росту трещины или приводит к стабилизации деформаций. В работе исследуется напряженное состояние пластины в начальной послекритической стадии. Предложено приближенное аналитическое решение. Методом конечных элементов построено решение задачи растяжения пластинки после потери устойчивости. Оценено влияние потери плоской формы деформирования при растяжении пластины с центральной трещиной на уровень напряженного состояния в окрестности вершины трещины. Анализ напряженного состояния в окрестности вершины центральной трещины при одноосном растяжении дает основания утверждать, что при возможной локальной потере устойчивости вблизи трещины происходит повышение уровня растягивающих напряжений в окрестности кончика трещины, и, как следствие, снижается нагрузка, приводящая к разрушению. Ключевые слова: потеря плоской формы деформирования, пластина, метод конечных элементов.
In modern constructions, thin-layer coats are often used as protecting or strengthening elements.... more In modern constructions, thin-layer coats are often used as protecting or strengthening elements. Deformations of such constructions may cause significant stresses on the interface between the base and the coat because of the difference in their physical-mechanical properties, which leads to the destruction or delamination of the cover. Of special interest is strength analysis under dynamical or vibrational impacts because of the possibility of localizing oscillations in a neighborhood of the initial inhomogeneities (such as inclusions, defects, construction elements, etc.). In this paper, on the example of the delamination of a string from an elastic substrate, the possibility of localizing oscillations on a delamination defect is demonstrated and the effect of this localization on the growth of the delamination zone is analyzed. A simplified setting of the problem is considered. The possibility of localizing oscillations on a delamination defect is demonstrated and an approximate ...
Acta Mechanica, 2021
The present paper is devoted to the development of the method for searching an approximate soluti... more The present paper is devoted to the development of the method for searching an approximate solution of non-stationary problems on a variable interval. This method was first proposed by L.I. Slepyan. Here, the field of its applicability has been expanded to systems of equations, including equations of both hyperbolic and parabolic type. We describe the procedure of such approach in detail on a number of classical partial differential equations and compare the obtained results with exact analytical solution. Also, we consider a dynamic non-coupled thermoelastic problem. The method of expansion on a variable interval allows us to estimate the material response to a thermal disturbance at a large distance from the source.
This paper deals with the problem of local buckling caused by uniaxial stretching of an infinite ... more This paper deals with the problem of local buckling caused by uniaxial stretching of an infinite plate with a circular hole or with circular inclusion made of another material. As the Young’s modulus of the inclusion approaches that of the plate, the critical load increases substantially. When these moduli coincide, stability loss is not possible. This paper also shows the difference between them when the inclusion is softer than the plate and when the inclusion is stiffer than the plate. Computational models show that instability modes are different both when the inclusion is softer than the plate and when the inclusion is stiffer than the plate. The case when plate and inclusion have the same modulus of elasticity, but different Poisson’s ratio is investigated too. It is also discussed here the case when a plate with inclusion is under biaxial tension. For each ratio of the modulus of elasticity of plate versus inclusion it’s obtained the range of the load parameters for which the...
A two-component model of material with a nonlinear internal interaction force is proposed for des... more A two-component model of material with a nonlinear internal interaction force is proposed for describing its structural transformations. An analogy between the equations of a continuous medium and their discrete representation allows demonstrating the effect of quenching of a non-stationary wave, caused by the transfer of energy to internal degrees of freedom. The parameters of the external impact at which the transformation of crystalline lattice takes place are determined. Analytical results are compared with numerical calculations, performed by using the finite difference method.
Vestnik St. Petersburg University, Mathematics
Решается задача о потере плоской формы равновесия бесконечной пластины с круговой вставкой из дру... more Решается задача о потере плоской формы равновесия бесконечной пластины с круговой вставкой из другого материала, находящейся под действием одноосного растяжения. Исследуется влияние модуля упругости вставки на значение критической нагрузки. Для нахождения минимального собственного числа, соответствующего первой критической нагрузке, применяется вариационный принцип. Расчеты проводятся в пакете Maple и сравниваются с результатами, полученными методом конечных элементов в пакете ANSYS 13.1. Проведенные расчеты показывают, что потеря устойчивости при вставке более мягкой, чем пластина, и при вставке более жесткой, чем пластина происходят по разным формам. При приближении значения модуля Юнга вставки к значению модуля Юнга пластины критическая нагрузка существенно увеличивается. При совпадении модулей упругости пластины и вставки потеря устойчивости невозможна. Библиогр. 10 назв. Ил. 5. Табл. 1. Ключевые слова: потеря устойчивости пластины, энергетический метод.
PAMM, 2011
Applanation tonometry estimates intraocular pressure (IOP) by quantifying the force needed to cre... more Applanation tonometry estimates intraocular pressure (IOP) by quantifying the force needed to create a defined amount of deformation of the cornea (Goldmann tonometer) or by estimating the diameter of the circular contact area of the cornea and flat tonometer of defined load (Maklakov tonometer). The first simplest models of the applanation method for measurement of the IOP were based on approach, in which an eyeball is modelled as a thin-walled spherical liquid-filled soft shell with corneal biomechanical properties. It was usually supposed that these properties were the same for all patients. In this work numerical simulation have been carried out using finite element code ANSYS. The eye shell is modeled as two joint shells (cornea and sclera) with different mechanical properties. The results are obtained for numerous sets of parameters and were compared to clinical data. For statistics the measurements of IOP for both eyes of 120 patients before and one month after refractive surgery are used. All parameter of refractive surgery (depth, the width and the place of ablation -refractive surgery for myopia or hypermetropia) have effect on IOP reading obtained with both Goldmann and Maklakov tonometry. The results obtained by Goldmann tonometer are significantly more sensitive to all parameters of refractive surgery than those found with Maklakov tonometer with load 10 g.
PAMM, 2011
In modern constructions, thin-layer coats are often used as protecting or strengthening elements.... more In modern constructions, thin-layer coats are often used as protecting or strengthening elements. Deformations of such constructions may cause significant stresses on the interface between the base and the coat because of the difference in their physical mechanical properties, which leads to the destruction or detachment of the cover. The impact of static or shock loads on the emergence and development of delamination in multilayer constructions has been studied fairly well, but much less is known about destructions of this type under nonstationary (vibrational) loads. The interest in the latter is caused by the fact that even small variable actions may cause the localization of oscillations in a neighborhood of inhomogeneities (such as inclusions, defects, construction elements, etc.) [1] (and lead to the emergence and growth of defects, which strongly affects the reliability and functionality of the whole construction. The possibility of the localization of oscillations near initial delamination and the impact of localization on the growth of the delamination are studied and a model for analyzing conditions under which a detachment zone grows or ceases to grow is suggested.
Vestnik St. Petersburg University: Mathematics, 2011
In modern constructions, thin-layer coats are often used as protecting or strengthening elements.... more In modern constructions, thin-layer coats are often used as protecting or strengthening elements. Deformations of such constructions may cause significant stresses on the interface between the base and the coat because of the difference in their physical-mechanical properties, which leads to the destruction or detachment of the cover. Of special interest is strength analysis under dynamical or vibrational impacts because
Proceedings of the Annual Frequency Control Symposium, 1992
ABSTRACT The approximate analytical formulas for eigenvalues and vibration modes for homogeneous ... more ABSTRACT The approximate analytical formulas for eigenvalues and vibration modes for homogeneous anisotropic plates with varied thickness are obtained. It is supposed that the vibration modes with one or some semi-waves of deformations in the thickness direction of the plate are localized near the point of maximal thickness. The influence of the irregular heating on the working frequency of the quartz resonator is studied by the perturbation method