A new combined asymptotic-tolerance model of thermoelasticity problems for thin biperiodic cylindrical shells

Tomczyk, Barbara; Bagdasaryan, Vazgen; Gołąbczak, M.; Litawska, Anna

doi:10.1016/j.compstruct.2023.116708

Cited by 5 publications

(2 citation statements)

References 33 publications

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“…Not all of them take into account the microstructure parameter, in contrast to the Tolerance Averaging Technique, which is used in this work [ 9 , 10 ]. This method is used in the analysis of a variety of structures, such as beams [ 11 , 12 ], plates [ 13 ] and shells [ 14 , 15 ]. The main reason for utilizing the Tolerance Averaging Technique in this study was the great alignment of its results to the exact solution when it comes to the stationary problem of heat conduction [ 16 ].…”

Section: Introductionmentioning

confidence: 99%

Influence of Composite Structure on Temperature Distribution—An Analysis Using the Finite Difference Method

Kubacka

Ostrowski

2023

Materials

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Among composites, we can distinguish periodic structures, biperiodic structures, and structures with a functional gradation of material properties made of two or more materials. The selection of the composite’s constituent materials and the way they are distributed affects the weight of the composite, its strength, and other properties, as well as the way it conducts heat. This work is about studying the temperature distribution in composites, depending on the type of component material and its location. For this purpose, the Tolerance Averaging Technique and the Finite Difference Method were used. Differential equations describing heat conduction phenomena were obtained using the Tolerance Averaging Technique, while the Finite Difference Method was used to solve them. In terms of results, temperature distribution plots were produced showing the effect of the structure of the composite on the heat transfer properties.

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Section: Introductionmentioning

confidence: 99%

Influence of Composite Structure on Temperature Distribution—An Analysis Using the Finite Difference Method

Kubacka

Ostrowski

2023

Materials

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“…After formulating the buckling problem of functionally graded nanocomposite cylindrical shells under separate external pressures in thermal environments in Shen's study [23,24], the buckling problem of nanocomposite cylindrical shells under combined loads was investigated by Shen and Xiang [25] using boundary layer theory and a singular perturbation procedure. In the literature, in most studies devoted to solving the problem of buckling of nanocomposite circular shells, separate action loads were considered, and the number of studies is limited due to the difficulties of mathematically modeling the combined loads and solving their problems [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Stability Problem of Nanocomposite Cylindrical Shells under Combined Loadings in Thermal Environments

Avey,

Fantuzzi,

Sofiyev

2023

Mathematics

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The mathematical modeling of the stability problem of nanocomposite cylindrical shells is one of the applications of partial differential equations (PDEs). In this study, the stability behavior of inhomogeneous nanocomposite cylindrical shells (INH-NCCSs), under combined axial compression and hydrostatic pressure in the thermal environment, is investigated by means of the first-order shear deformation theory (FSDT). The nanocomposite material is modeled as homogeneous and heterogeneous and is based on a carbon nanotube (CNT)-reinforced polymer with the linear variation of the mechanical properties throughout the thickness. In the heterogeneous case, the mechanical properties are modeled as the linear function of the thickness coordinate. The basic equations are derived as partial differential equations and solved in a closed form, using the Galerkin procedure, to determine the critical combined loads for the selected structure in thermal environments. To test the reliability of the proposed formulation, comparisons with the results obtained by finite element and numerical methods in the literature are accompanied by a systematic study aimed at testing the sensitivity of the design response to the loading parameters, CNT models, and thermal environment.

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A new combined asymptotic-tolerance model of thermoelasticity problems for thin uniperiodic cylindrical shells

Tomczyk,

Gołąbczak,

Gołąbczak

2023

Continuum Mech. Thermodyn.

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The objects of consideration are thin linearly thermoelastic Kirchhoff–Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential direction (uniperiodic shells). The aim of this contribution is to formulate and discuss a new averaged mathematical model for the analysis of selecteddynamic thermoelasticity problemsfor the shells under consideration. This so-called combined asymptotic-tolerance model is derived by applying the combined modelling including the consistent asymptotic and the tolerance non-asymptotic modelling techniques, which are conjugated with themselves into a newprocedure. The starting equations are the well-known governing equations of linear Kirchhoff–Love theory of thin elastic cylindrical shells combined with Duhamel–Neumann thermoelastic constitutive relations and coupled with the known linearized Fourier heat conduction equation. For the periodic shells, the starting equations have highly oscillating, non-continuous and periodic coefficients, whereas equations of the proposed model have constant coefficients dependent also on a cell size.

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A new combined asymptotic-tolerance model of thermoelasticity problems for thin biperiodic cylindrical shells

Cited by 5 publications

References 33 publications

Influence of Composite Structure on Temperature Distribution—An Analysis Using the Finite Difference Method

Influence of Composite Structure on Temperature Distribution—An Analysis Using the Finite Difference Method

Analytical Solution of Stability Problem of Nanocomposite Cylindrical Shells under Combined Loadings in Thermal Environments

A new combined asymptotic-tolerance model of thermoelasticity problems for thin uniperiodic cylindrical shells

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