A new asymptotic-tolerance model of dynamic and stability problems for longitudinally graded cylindrical shells

2018 ◽  
Vol 202 ◽  
pp. 473-481 ◽  
Author(s):  
Barbara Tomczyk ◽  
Paweł Szczerba
Keyword(s):  
Cylindrical Shells ◽  
Stability Problems ◽  
Tolerance Model

scholarly journals Length-scale effect in stability problems for thin biperiodic cylindrical shells: extended tolerance modelling

2020 ◽  
Author(s):  
B. Tomczyk ◽  
M. Gołąbczak ◽  
A. Litawska ◽  
A. Gołąbczak
Keyword(s):  
Scale Effect ◽  
Cylindrical Shells ◽  
Length Scale ◽  
Stability Problems ◽  
Constant Coefficients ◽  
A Cell ◽  
Circular Cylindrical Shells ◽  
Tolerance Modelling ◽  
Tolerance Model ◽  
Shell Equations

Abstract Thin linearly elastic Kirchhoff–Love-type circular cylindrical shells of periodically micro-inhomogeneous structure in circumferential and axial directions (biperiodic shells) are investigated. The aim of this contribution is to formulate and discuss a new averaged nonasymptotic model for the analysis of selected stability problems for these shells. This, so-called, general nonasymptotic tolerance model is derived by applying a certain extended version of the known tolerance modelling procedure. Contrary to the starting exact shell equations with highly oscillating, noncontinuous and periodic coefficients, governing equations of the tolerance model have constant coefficients depending also on a cell size. Hence, the model makes it possible to investigate the effect of a microstructure size on the global shell stability (the length-scale effect).

On the modelling of stability problems for thin cylindrical shells with two-directional micro-periodic structure

2021 ◽  
pp. 114495
Author(s):  
Barbara Tomczyk ◽  
Vazgen Bagdasaryan ◽  
Marcin Gołąbczak ◽  
Anna Litawska
Keyword(s):  
Periodic Structure ◽  
Cylindrical Shells ◽  
Stability Problems

scholarly journals Mathematical modelling of thermoelasticity problems for thin biperiodic cylindrical shells

2021 ◽  
Author(s):  
B. Tomczyk ◽  
M. Gołąbczak ◽  
A. Litawska ◽  
A. Gołąbczak
Keyword(s):  
Constitutive Relations ◽  
Cylindrical Shells ◽  
Asymptotic Model ◽  
Heat Sources ◽  
Asymptotic Models ◽  
Stationary Action ◽  
Constant Coefficients ◽  
A Cell ◽  
Fourier Heat Conduction ◽  
Tolerance Model

AbstractThe objects of consideration are thin linearly thermoelastic Kirchhoff-Love-type circular cylindrical shells having a periodically microheterogeneous structure in circumferential and axial directions (biperiodic shells). The aim of this contribution is to formulate and discuss two new averaged mathematical models for the analysis of selected dynamic thermoelasticity problems for the shells under consideration: the non-asymptotictolerance and the consistent asymptotic models. 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 in which the heat sources are neglected. For the microperiodic shells under consideration, the starting equations mentioned above have highly oscillating, non-continuous and periodic coefficients. The tolerance model is derived applying the tolerance averaging technique and a certain extension of the known stationary action principle. It has constant coefficients depending also on a cell size. Hence, this model makes it possible to study the effect of a microstructure size on the global shell thermoelasticity (the length-scale effect). The consistent asymptotic model is obtained using the consistent asymptotic approach. It has constant coefficients being independent of the period lengths. Moreover, the comparison between the tolerance model for biperiodic shells proposed here and the known tolerance model for cylindrical shells with a periodic structure in the circumferential direction only (uniperiodic shells) is presented.

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