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).

scholarly journals On the cell-dependent vibrations and wave propagation in uniperiodic cylindrical shells

2019 ◽  
Vol 32 (4) ◽  
pp. 1197-1216 ◽  
Author(s):  
Barbara Tomczyk ◽  
Marcin Gołąbczak ◽  
Anna Litawska ◽  
Andrzej Gołąbczak
Keyword(s):  
Wave Propagation ◽  
Periodic Structures ◽  
Cylindrical Shells ◽  
Heterogeneous Structure ◽  
Combined Model ◽  
Asymptotic Models ◽  
Constant Coefficients ◽  
A Cell ◽  
Circular Cylindrical Shells ◽  
Averaged Model

Abstract The objects of consideration are thin linearly elastic Kirchhoff–Love-type circular cylindrical shells having a periodically micro-heterogeneous structure in circumferential direction (uniperiodic shells). The aim of this contribution is to study certain problems of micro-vibrations and of wave propagation related to micro-fluctuations of displacement field caused by a periodic structure of the shells. These micro-dynamic problems will be analysed in the framework of a certain mathematical averaged model derived by means of the combined modelling procedure. The combined modelling includes both the asymptotic and the tolerance non-asymptotic modelling techniques, which are conjugated with themselves under special conditions. Contrary to the starting exact shell equations with highly oscillating, non-continuous and periodic coefficients, governing equations of the combined model have constant coefficients depending also on a cell size. Hence, this model takes into account the effect of a microstructure size on the dynamic behaviour of the shells (the length-scale effect). It will be shown that the micro-periodic heterogeneity of the shells leads to cell-depending micro-vibrations and to exponential waves as well as to dispersion effects, which cannot be analysed in the framework of the asymptotic models commonly used for investigations of vibrations and wave propagation in the periodic structures.

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.

scholarly journals Micro-Vibrations and Wave Propagation in Biperiodic Cylindrical Shells

2020 ◽  
Vol 22 (3) ◽  
pp. 789-808
Author(s):  
Barbara Tomczyk ◽  
Anna Litawska
Keyword(s):  
Wave Propagation ◽  
Periodic Structures ◽  
Cylindrical Shells ◽  
Combined Model ◽  
Asymptotic Models ◽  
Wave Propagation Problem ◽  
Modelling Procedure ◽  
Constant Coefficients ◽  
A Cell ◽  
Averaged Model

AbstractThe objects of consideration are thin linearly elastic 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 study a certain long wave propagation problem related to micro-fluctuations of displacement field caused by a periodic structure of the shells. This micro-dynamic problem will be analysed in the framework of a certain mathematical averaged model derived by means of the combined modelling procedure. The combined modelling applied here includes two techniques: the asymptotic modelling procedure and a certain extended version of the known tolerance non-asymptotic modelling technique based on a new notion of weakly slowly-varying function. Both these procedures are conjugated with themselves under special conditions. Contrary to the starting exact shell equations with highly oscillating, non-continuous and periodic coefficients, governing equations of the averaged combined model have constant coefficients depending also on a cell size. It will be shown that the micro-periodic heterogeneity of the shells leads to exponential micro-vibrations and to exponential waves as well as to dispersion effects, which cannot be analysed in the framework of the asymptotic models commonly used for investigations of vibrations and wave propagation in the periodic structures.

Fabrication of Nanoscale Hydrophobic Regions on Anodic Alumina for Selective Adhesion of Biologic Molecules

2003 ◽  
Vol 773 ◽  
Author(s):  
Xiefan Lin ◽  
Anthony S. W. Ham ◽  
Natalie A. Villani ◽  
Whye-Kei Lye ◽  
Qiyu Huang ◽  
...  
Keyword(s):  
Anodic Alumina ◽  
Biological Molecules ◽  
Spatial Density ◽  
Length Scale ◽  
Adhesion Sites ◽  
A Cell ◽  
Adhesive Molecules ◽  
Receptor Clusters ◽  
Molecular Bonding ◽  
Fabrication Parameters

AbstractStudies of selective adhesion of biological molecules provide a path for understanding fundamental cellular properties. A useful technique is to use patterned substrates, where the pattern of interest has the same length scale as the molecular bonding sites of a cell, in the tens of nanometer range. We employ electrochemical methods to grow anodic alumina, which has a naturally ordered pore structure (interpore spacing of 40 to 400 nm) controlled by the anodization potential. We have also developed methods to selectively fill the alumina pores with materials with contrasting properties. Gold, for example, is electrochemically plated into the pores, and the excess material is removed by backsputter etching. The result is a patterned surface with closely separated islands of Au, surrounded by hydrophilic alumina. The pore spacing, which is determined by fabrication parameters, is hypothesized to have a direct effect on the spatial density of adhesion sites. By attaching adhesive molecules to the Au islands, we are able to observe and study cell rolling and adhesion phenomena. Through the measurements it is possible to estimate the length scale of receptor clusters on the cell surface. This information is useful in understanding mechanisms of leukocytes adhesion to endothelial cells as well as the effect of adhesion molecules adaptation on transmission of extracellular forces. The method also has applications in tissue engineering, drug and gene delivery, cell signaling and biocompatibility design.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

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