Exact Elasticity Solution for the Density Functionally Gradient Beam by Using Airy Stress Function

Daneshmehr, Alireza; Momeni, Saeed; Akhloumadi, Mahdi

doi:10.4028/www.scientific.net/amm.110-116.4669

Cited by 3 publications

(1 citation statement)

References 12 publications

(10 reference statements)

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“…In a number of recent works [6][7][8][9][10][11][12], the efforts of scientists were directed to solving the problems of bending anisotropic functionally gradient beams, the material of which has continuous nonuniformity over the height of the section.…”

Section: Introductionmentioning

confidence: 99%

Exact Solution of the Problem of Elastic Bending of a Multilayer Beam under the Action of a Normal Uniform Load

Ковальчук

Goryk

2019

MSF

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An exact solution of the theory of elasticity is presented for the problem of a narrow multilayer bar section transverse bending under the action of a normal uniform load on longitudinal faces. The solution is built using the principle of superposition, by imposing common solutions to the problems of bending a multilayer cantilever with uniform loads on the longitudinal faces and an arbitrary load on the free end, and allows to take into account the orthotropy of the materials of the layers, as well as transverse shear deformation and compression. On the basis of a built-in general solution, a number of particular solutions are obtained for multi-layer beams with various ways of the ends fixing.

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Section: Introductionmentioning

confidence: 99%

Exact Solution of the Problem of Elastic Bending of a Multilayer Beam under the Action of a Normal Uniform Load

Ковальчук

Goryk

2019

MSF

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Exact Solution of the Problem on Elastic Bending of the Segment of a Narrow Multilayer Beam by an Arbitrary Normal Load

Ковальчук

2020

Mech Compos Mater

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An analytical solution to the problem of thermoelastic bending of a multilayer beam with different temperature of longitudinal faces

Ковальчук

Goryk

2021

IOP Conf. Ser.: Mater. Sci. Eng.

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An exact analytical solution of the quasistatic problem of thermoelasticity is presented for a section of a narrow multilayer beam with different temperatures of the longitudinal lower and upper faces and a heat flow of arbitrary height across the sections through the lateral faces. The solution was obtained for the entire package of layers by sequentially solving the heat equation for an inhomogeneous beam, taking into account the ideal thermal contact of the layers and the system of equations of the plane problem of the theory of elasticity under the assumption of a rigid connection of the layers. To take into account the inhomogeneity of the beam, a continuum approach is used, in which the multilayer material is considered continuous with variable physical and mechanical characteristics. The resulting relations take into account the orthotropy of the physico-mechanical properties of the materials of the layers and their compliance with the transverse shear and compression strains. An example of implementation of a solution for a five-layer beam with combined rigid and articulated fastening of the ends is given.

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Exact Elasticity Solution for the Density Functionally Gradient Beam by Using Airy Stress Function

Cited by 3 publications

References 12 publications

Exact Solution of the Problem of Elastic Bending of a Multilayer Beam under the Action of a Normal Uniform Load

Exact Solution of the Problem of Elastic Bending of a Multilayer Beam under the Action of a Normal Uniform Load

Exact Solution of the Problem on Elastic Bending of the Segment of a Narrow Multilayer Beam by an Arbitrary Normal Load

An analytical solution to the problem of thermoelastic bending of a multilayer beam with different temperature of longitudinal faces

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