Determination of nonstationary temperature fields and stress state in bidirectionally tapered shells of revolution

Merzlyakov, V. A.

doi:10.1007/bf02209099

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“…To simplify the solution of the nonstationary heat-conduction problem, we introduce a function F [24]:…”

Section: Determining Nonstationary Temperature Fieldsmentioning

confidence: 99%

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Thermoelastoplastic deformation of noncircular cylindrical shells

Merzlyakov

2008

Int Appl Mech

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A method to determine the nonstationary temperature fields and the thermoelastoplastic stress-strain state of noncircular cylindrical shells is developed. It is assumed that the physical and mechanical properties are dependent on temperature. The heat-conduction problem is solved using an explicit difference scheme. The temperature variation throughout the thickness is described by a power polynomial. For the other two coordinates, finite differences are used. The thermoplastic problem is solved using the geometrically nonlinear theory of shells based on the Kirchhoff-Love hypotheses. The theory of simple processes with deformation history taken into account is used. Its equations are linearized by a modified method of elastic solutions. The governing system of partial differential equations is derived. Variables are separated in the case where the curvilinear edges are hinged. The partial case where the stress-strain state does not change along the generatrix is examined. The systems of ordinary differential equations obtained in all these cases are solved using Godunov's discrete orthogonalization. The temperature field in a shell with elliptical cross-section is studied. The stress-strain state found by numerical integration along the generatrix is compared with that obtained using trigonometric Fourier series. The effect of a Winkler foundation on the stress-strain state is analyzed Keywords: thermoelastoplasticity, noncircular cylindrical shell, Kirchhoff-Love hypotheses, linearization method, explicit difference scheme, Godunov's discrete orthogonalization, cylindrical shell of elliptical cross-section Introduction.Methods and elastic problems of designing noncircular cylindrical shells with arbitrary cross-section and arbitrary thickness are addressed in [3-6, 8]. These methods were further developed and some problems were solved in [14][15][16][17][18][19][20][21]29]. The thermoelastoplastic stress-strain state (SSS) of this class of inelastic shells is analyzed below. To calculate thermal stresses, we will preliminarily solve the nonstationary heat-conduction problem for shells that transfer heat to the environment by convection.1. Problem Formulation. Basic Equations. Let us determine the thermoelastoplastic SSS of a cylindrical shell with arbitrary cross-section and thickness varying in two directions. The shell can be coupled with an elastic foundation so that there can be no separation between them. At time zero, the shell, which is unstressed at temperature Ò 0 , is subjected to mechanical and thermal loads that do not cause buckling. We will formulate a noncoupled quasistatic problem and use the geometrically nonlinear theory of shells to solve it. The meridian and thickness of the shell and the applied loads permit accepting the Kirchhoff-Love hypotheses. The physical and mechanical characteristics of the shell material are assumed temperature-dependent.The position of points on the mid-surface of the shell is defined by the longitudinal coordinate s (s 0 £ s £ s N ) and the circumferential coordi...

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“…To simplify the solution of the nonstationary heat-conduction problem, we introduce a function F [24]:…”

Section: Determining Nonstationary Temperature Fieldsmentioning

confidence: 99%

“…In solving Eq. (2.6), we approximate the function F by a power polynomial of order n in the thickness coordinate [1,7,23,24], which makes it possible to reduce the solution of the problem to the determination of integral functions independent of the coordinate z:…”

Section: Determining Nonstationary Temperature Fieldsmentioning

confidence: 99%

Thermoelastoplastic deformation of noncircular cylindrical shells

Merzlyakov

2008

Int Appl Mech

Self Cite

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show abstract

Determination of nonstationary temperature fields and stress state in bidirectionally tapered shells of revolution

Cited by 1 publication

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Thermoelastoplastic deformation of noncircular cylindrical shells

Thermoelastoplastic deformation of noncircular cylindrical shells

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