On the non-classical mathematical models of coupled problems of thermo-elasticity for multi-layer shallow shells with initial imperfections

Kirichenko, Valeriy F.; Awrejcewicz, Jan; Kirichenko, Aleksandr V.; Krysko, Anton V.; Krysko, Vadim A.

doi:10.1016/j.ijnonlinmec.2015.03.011

Cited by 18 publications

(11 citation statements)

References 8 publications

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“…In particular, the multi-layer flexible Euler-Bernoulli and Timoshenko beams were investigated in reference [40], whereas multi-layer beams with a clearance have been studied in references [41,42]. Also, the non-classical mathematical models of coupled problems of thermoelasticity were derived and studied for multi-layer shells with initial imperfections in [43]. This paper extends the former investigations.…”

Section: Introductionmentioning

confidence: 76%

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On the mathematical models of the Timoshenko-type multi-layer flexible orthotropic shells

et al. 2018

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Mathematical models of multi-layer orthotropic shells were reconsidered based on the Timoshenko hypothesis. A new mathematical model with ε-regularisation was proposed, and the theorem regarding the existence of a generalised solution to the model was formulated and proved. The algorithms of numerical investigation of models studied with the aid of the variational-difference method were developed. The associated stability problem was also addressed. A comparison of the results yielded by the considered models was carried out and discussed for numerous factors and parameters.

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Section: Introductionmentioning

confidence: 76%

“…where: 2 -biharmonic operator, -Laplace operator, ρ-radius of the contour ∂ curvature, ν=const > 0 [43]. By the general solution, one should understand a vector u ε = u 3ε , γ xε , γ yε , F ε ∈ H 2 satisfying the following integral identities:…”

Section: Modification Of the Timoshenko Mm2 And The ε-Regularisation Mm3mentioning

confidence: 99%

On the mathematical models of the Timoshenko-type multi-layer flexible orthotropic shells

et al. 2018

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“…A generalized solution of problem A is the vector of generalized displacements a = (w1, w2, w3, 1, 2)  Wp (2) (), p  2, which satisfies the system (1) and point wise boundary conditions (2)-( 4) almost everywhere.…”

Section: Definitionmentioning

confidence: 99%

“…The representation for Sd[Φ1] + (t) is found in [22]. For the function Φ'2(z) (z  K ̅ ) from ( 9), using the representation d[g] from (6) and taking into account that ((t+z)/(t-z)) = 2t/(t-z) 2 we have the following:…”

Section: Definitionmentioning

confidence: 99%

“…Currently, there are a large number of works devoted to the strength of thin-walled shell structures, taking into account the geometric and/or physical nonlinearity [1][2][3][4][5][6][7][8][9]. This is due to the widespread use of elastic thin-walled shell structures in aviation, space technology, shipbuilding, mechanical engineering and construction.…”

Section: Introductionmentioning

confidence: 99%

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Stress state of hinged supported thin-wall elastic structures

Kharasova

Timergaliev

2021

E3S Web Conf.

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The paper studies the stress-strain state of flat elastic isotropic thin-walled shell structures in the framework of the S. P. Timoshenko shear model with pivotally supported edges. The stress-strain state of shell structures is described by a system of five second-order nonlinear partial differential equations under given static boundary conditions with respect to generalized displacements. The system of equations under study is linear in terms of tangential displacements, rotation angles, and nonlinear in terms of normal displacement. To find a solution to the system that satisfies the given static boundary conditions, integral representations for generalized displacements containing arbitrary holomorphic functions are used. Finding holomorphic functions is one of the main and difficult points in the proposed study. The integral representations constructed in this way allow us to reduce the original problem to a single nonlinear operator equation with respect to the deflection, the solvability of which is established using the principle of compressed maps.

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