Direct and inverse problems in the mechanics of composite plates and shells

Golushko, Sergey

doi:10.1007/3-540-32376-7_12

Cited by 10 publications

(14 citation statements)

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“…The present state of the different divisions of shell theory is well represented in review articles and monographs by Carrera [1], Qu [24], Reddy [25], Ventsel and Krauthammer [10], Golushko and Nemirovsky [4], Karpov [26,27], Grigolyuk and Kulikov [28], Maksimyuk and Chernyshenko [21] et al [29][30][31][32]. A number of publications is devoted to the review on works on shell stability [33][34][35].…”

Section: Introductionmentioning

confidence: 98%

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Strength and stability of geometrically nonlinear orthotropic shell structures

Semenov

2016

Thin-Walled Structures

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Section: Introductionmentioning

confidence: 98%

“…In modern building, as well as in shipbuilding, mechanical engineering, aviation, and other industries, structures in the form of shells have wide application [1][2][3][4][5][6][7][8][9][10][11][12]. Currently there are composite materials [13][14][15][16][17][18][19] (CFRP, GRP etc.…”

Section: Introductionmentioning

confidence: 99%

Strength and stability of geometrically nonlinear orthotropic shell structures

Semenov

2016

Thin-Walled Structures

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“…Features of using this method in the theory of shells are outlined in [16] where it was also shown that the memory requirements can be substantially reduced by somewhat modifying the algorithm. The efficiency and high accuracy of the method when applied to the theory of shells is noted in [4,26] and confirmed in [7].…”

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confidence: 95%

Static and Dynamic Problems for Anisotropic Inhomogeneous Shells with Variable Parameters and Their Numerical Solution (Review)

Grigorenko¹,

Grigorenko

2013

Int Appl Mech

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Studies on the static and dynamic deformation of isotropic and anisotropic elastic shell-like bodies of complex shape performed using classical and refined problem statements are reviewed. To solve two-dimensional boundary-value problems and eigenvalue problems, use is made of a nontraditional discrete-continuum approach based on the spline-approximation of the unknown functions of partial differential equations with variable coefficients. This enables reducing the original problem to a system of one-dimensional problems solved with the discrete-orthogonalization method. An analysis is made of numerical results on the distribution of stress and displacement fields and dynamic characteristics depending on the loading and boundary conditions, geometrical and mechanical parameters of elastic bodies. Emphasis is placed on the accuracy of the results Keywords: shell structures, static and dynamic problems, variable parameters, models, discrete-continuum methods Introduction.Many members of modern engineering structures have the form of intricately shaped shells fixed in various ways and subjected to various distributed and local loads. Shell elements are widely used to meet the requirements imposed by the severe operating conditions of machines, aircraft, transportation vehicles, industrial and civil facilities. The complication of the configuration of shell elements necessitates developing a theory and methods for solving static and dynamic problems for shells made of anisotropic inhomogeneous materials.A typical feature in the development of the theory of plates and shells is the relationship between the setting up of a mathematical model describing a given class of problems and the development of a method for solving them. For example, Kirchhoff's theory of thin plates [101] and the Kirchhoff-Love theory of thin shells [97] tend not only to provide a realistic description of the deformation of plates and shells, but also to make such models so simple as to solve a number of problems with available computational capability. An example of such relationship is the Donnell-Mushtari-Vlasov theory of shells [5,28,36]. Its basic equations were simplified so as to find solutions to some classes of problems over wide ranges of their characteristics, which is demonstrated by the names given to this theory: technical theory of shells, theory of shallow shells, theory of shells with highly variable stress state [2,8,9,16,20,23,24,29,37]. This relationship is even stronger nowadays when computers are widely used to solve problems in the theory of shells and mathematical models for certain classes of shells are set up so as to provide for all aspects and possibilities associated with the solution of problems [63].The solution of two-dimensional boundary-value problems of the statics and dynamics of plates, shells, and solids described by partial differential equations with variable coefficients involves severe computational difficulties. To solve them, use is sometimes made of approaches based on separation of variables and redu...

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“…(2) solution of the obtained one-dimensional boundary-value problem by the stable numerical method of discrete orthogonalization [3,5,9,16,17].…”

mentioning

confidence: 99%

“…The investigations of the characteristics of strength of these shells encounter significant difficulties of the mathematical and computational character caused by the complexity of the system of partial differential equations and the corresponding boundary conditions. Thus, it is necessary to perform calculations of the stress-strain state of shells of this kind on the basis of an improved of Timoshenko-type shell theory [4,8,15].In the present work, for the investigation of the influence of variable thickness of a toroidal shell and the curvature of its axis on its stress-strain state, we apply an approach consisting of two stages:(1) application of the method of spline approximation along a generatrix to reduce the analyzed twodimensional problem to a one-dimensional problem [1,6,7,9,10];(2) solution of the obtained one-dimensional boundary-value problem by the stable numerical method of discrete orthogonalization [3,5,9,16,17]. …”

mentioning

confidence: 99%

Analysis of the Fields of Displacements and Stresses in an Orthotropic Toroidal Shell Depending on the Changes in its Thickness and in the Curvature of its Axis

Grigorenko

Avramenko

2014

J Math Sci

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A numerical-analytic approach is used to study the stress-strain state of orthotropic toroidal shells of variable thickness. The problem is solved with the use of a nonclassical Timoshenko-type shell theory based on the model of a rectilinear element. The system of partial differential equations is reduced to a one-dimensional problem by applying the method of spline approximation in one coordinate direction. The boundary-value problem for the system of ordinary differential equations is solved by the stable numerical method of discrete orthogonalization. We also present the data on the distribution of the fields of displacements and stresses depending on the curvature of the axis of the shell and the parameter of variability of its thickness.With toughening of the requirements to contemporary structures, the shells of complex shapes with variable parameters produced of composite materials are more and more extensively applied as structural elements [5,9,13,14,18,19]. Among these shells, one especially can mention toroidal shells of variable stiffness made of orthotropic materials [2,11]. They are used in various branches of the contemporary engineering, including machine building, rocket and spacecraft engineering, etc. Note that shells of variable thickness are now extensively used parallel with the shells of constant thickness. The investigations of the characteristics of strength of these shells encounter significant difficulties of the mathematical and computational character caused by the complexity of the system of partial differential equations and the corresponding boundary conditions. Thus, it is necessary to perform calculations of the stress-strain state of shells of this kind on the basis of an improved of Timoshenko-type shell theory [4,8,15].In the present work, for the investigation of the influence of variable thickness of a toroidal shell and the curvature of its axis on its stress-strain state, we apply an approach consisting of two stages:(1) application of the method of spline approximation along a generatrix to reduce the analyzed twodimensional problem to a one-dimensional problem [1,6,7,9,10];(2) solution of the obtained one-dimensional boundary-value problem by the stable numerical method of discrete orthogonalization [3,5,9,16,17].

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Direct and inverse problems in the mechanics of composite plates and shells

Cited by 10 publications

References 1 publication

Strength and stability of geometrically nonlinear orthotropic shell structures

Strength and stability of geometrically nonlinear orthotropic shell structures

Static and Dynamic Problems for Anisotropic Inhomogeneous Shells with Variable Parameters and Their Numerical Solution (Review)

Analysis of the Fields of Displacements and Stresses in an Orthotropic Toroidal Shell Depending on the Changes in its Thickness and in the Curvature of its Axis

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