Deformation of Piecewise-Homogeneous Plates

Bespalova, E. I.; Kitaigorodskii, A. B.

doi:10.1023/a:1023969817246

Cited by 9 publications

(11 citation statements)

References 5 publications

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“…Here these problems are three-dimensional and for each ψ θ mn s ( , )from (2) are formulated as (12) and reduces to a one-dimensional problem in ς for each pair of harmonics i and k [5].…”

Section: Applicability Of the Methods To Contact Problemsmentioning

confidence: 99%

“…As is seen, the materials of the layers strongly differ by elastic characteristics and have different orders of symmetry. It is assumed that the distribution of the contact pressure along the cylinder length is described by one term of series (12) 2 .…”

Section: Applicability Of the Methods To Contact Problemsmentioning

confidence: 99%

“…The pseudo-force method for rod (beam) structures in problems with bilateral constraints and a known one-dimensional contact region was generalized in [11,12] to stationary problems for plate systems. To further generalize this method to contact problems for shells of revolution and rigid or elastic surfaces, it is necessary:…”

Section: Problem Formulation and Solution Techniquementioning

confidence: 99%

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Contact Interaction Between a Laminated Shell of Revolution and a Rigid or Elastic Foundation

2005

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A method is proposed to solve the contact problem for laminated anisotropic shells of revolution. The method is based on a two-dimensional model that accounts for transverse shears and reduction. Also the method is based on the method of successive approximations, the generalized pseudo-force method, and a numerical-analytical method of solving boundary-value problems. The results obtained for a cylindrical shell of complex thickness structure are compared with those obtained in three-dimensional formulation Keywords: contact problem, anisotropic shell, laminated structure Introduction. In analyzing the stress-strain state of thin-walled structures on rigid or elastic foundations, it is necessary to describe the deformation of a shell and the mechanism of its interaction with the foundation [1-3, 6-10, 13].The model chosen to describe the deformation of a laminated shell should strike a reasonable balance between accuracy and implementability. The spatial theory of elasticity can adequately describe processes of interest, but may involve certain computational difficulties because of the high dimension of the corresponding problems. Approximate two-dimensional models of shells materially simplify the way the final result is obtained, but describe the contact interaction of bodies with different degrees of adequacy. For example, the classical theory of shells requires introducing concentrated forces at the contact boundary, which distort the contact pressure distribution. Allowing for transverse-shear strains eliminates the discontinuity of the shearing forces, but does not make the normal reactions at the boundary vanish. Additional tricks, such as an elastic layer between contacting surfaces, allow us to describe contact interaction more accurately, though describing the properties of such a layer involves difficulties [6,7]. A natural way to solve the contact problem for thin-walled shells is to allow for all kinds of transverse strains.In describing the interaction of contacting elements, the contact conditions are formulated as inequalities reflecting the nonnegativity of the constraint reactions in the contact region. In the absence of tangential forces, the geometrical contact condition is usually equality of displacements (strains) or curvatures of these elements [8].Expanding upon the studies [1, 2, 13], we propose here a method to solve static problems for laminated anisotropic shells of revolution contacting with rigid or elastic planes. The method is based on the nonclassical theory of shells and accounts for transverse-shear strains and reduction. To test the method, we will compare the results it produces with the exact solutions of some problems.

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Section: Applicability Of the Methods To Contact Problemsmentioning

confidence: 99%

Section: Applicability Of the Methods To Contact Problemsmentioning

confidence: 99%

Section: Problem Formulation and Solution Techniquementioning

confidence: 99%

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Contact Interaction Between a Laminated Shell of Revolution and a Rigid or Elastic Foundation

2005

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“…The results obtained there are rather approximate and cannot be used to estimate the number of laminas required to minimize the effect of unbalanced laminate. One possible solution is to develop a numerical method for stability analysis of anisotropic shells based on the approach from [5][6][7]9]. This way was used in [8].…”

Section: Introductionmentioning

confidence: 99%

Stability of Cylindrical Shells Made of Fibrous Composites with One Symmetry Plane

2005

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Cylindrical shells produced by single-layer or cross winding are analyzed for stability. An approximate analytical solution is proposed. It allows evaluating the effect of an unbalanced laminate on the critical values of the axial load, intensity of external pressure, and shear forces. It is shown that the effect of imbalance weakens with increase in the number of laminas. In each specific case, the number of laminas at which the material can be considered orthotropic is determined

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“…At each ith approximation (i I = 1 2 , , ... , ) out of I approximations needed to determine the unknown functions (18) with prescribed accuracy, the systems of differential equations (22) and (23) with given boundary conditions are integrated by the Runge-Kutta method with discrete orthogonalization and Godunov normalization. This method is widely used to solve elastic problems [11] and plastic problems [8][9][10]. At an arbitrary ith approximation, the system (22) is integrated first.…”

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confidence: 99%

Thermoelastoplastic Stress-Strain State of Rectangular Plates

Shevchenko

Prokhorenko

2005

Int Appl Mech

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A technique is proposed to solve a thermoplastic problem for rectangular plates of varying thickness with arbitrary boundary conditions at all edges. The technique is based on the hypothesis of rectilinear element, the theory of simple loading, and the method of complete systems Keywords: thermoplasticity, theory of simple loading, method of complete systemsThe problems of thermoelasticity and thermoplasticity for a rectangular plate of varying thickness with arbitrary boundary conditions at all edges are rather complicated [2]. Moreover, when the hypothesis of rectilinear element is used, the combination of unknown functions and a method of solving boundary-value problems may result in an unstable computational process [4].The present paper proposes an algorithm for thermoelastoplastic stress-strain analysis of rectangular plates of varying thickness with arbitrary boundary conditions based on the hypothesis of rectilinear element and the theory of simple loading. Combining the method of complete systems [5] and unknown functions, we can develop a stable algorithm for determining the thermoelastoplastic stress-strain state of rectangular plates of varying thickness. It is assumed that the plate fixed in one way or another, which is in a stress-free and strain-free state at temperature T T = 0 at the initial time t t = 0 , is subjected to distributed loads reduced to the mid-surface of the plate, boundary loads, and nonuniform heating. The thermoplastic problem is solved using the hypothesis of rectilinear element and the theory of simple loading processes linearized by the method of variable elasticity parameters.We will consider loading processes in which creep strains are small compared with instantaneous elastoplastic strains and may be neglected. The temperature field of the plate is assumed given. The plate is referred to an orthogonal coordinate system x y , ,ζ , where the coordinates x and y run along the orthogonal boundary lines of the mid-surface of the plate, and the ζ-axis is orthogonal to the mid-surface.To solve the problem posed, we will use the equilibrium equations, geometrical equations, and plasticity equations. If the coordinates q 1 and q 2 coincide with the coordinates x and y, respectively, and A A

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Deformation of Piecewise-Homogeneous Plates

Cited by 9 publications

References 5 publications

Contact Interaction Between a Laminated Shell of Revolution and a Rigid or Elastic Foundation

Contact Interaction Between a Laminated Shell of Revolution and a Rigid or Elastic Foundation

Stability of Cylindrical Shells Made of Fibrous Composites with One Symmetry Plane

Thermoelastoplastic Stress-Strain State of Rectangular Plates

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