Nonlinear deformations of a cylindrical pipe with pre-stressed thin coatings

2022 ◽  
pp. 108128652110635
Author(s):  
Leonid Zubov ◽  
Mikhail Karyakin
Keyword(s):  
Shell Theory ◽  
Large Deformations ◽  
Three Dimensional ◽  
Surface Coatings ◽  
Cylindrical Pipe ◽  
Thin Coatings ◽  
Axial Tension ◽  
Incompressible Body ◽  
Nonlinear Deformations ◽  
Constitutive Material

The paper presents an exact solution for the problem of large deformations of torsion, axial tension–compression, and radial expansion or shrinkage of an elastic hollow circular cylinder equipped with pre-stressed elastic coatings. Surface coatings are modeled using the six-parameter nonlinear shell theory. The constitutive material of the cylinder is described by a three-dimensional nonlinear model of the isotropic incompressible body of the general form. Special boundary conditions describe the interaction of this material with thin coatings on the inner and outer surface of the pipe. Based on the solution obtained, numerical calculations were performed on the effect of preliminary stresses in coatings on the stress–strain state of a cylindrical pipe.

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

Model of the Evaporating Meniscus in a Capillary Tube

1992 ◽  
Vol 114 (2) ◽  
pp. 434-441 ◽  
Author(s):  
L. W. Swanson ◽  
G. C. Herdt
Keyword(s):  
Marangoni Convection ◽  
Tube Wall ◽  
Capillary Tube ◽  
Mass Transfer Rate ◽  
Three Dimensional ◽  
Surface Coatings ◽  
Apparent Effect ◽  
A Value ◽  
Dispersion Number ◽  
Meniscus Profile

A mathematical model describing the evaporating meniscus in a capillary tube has been formulated incorporating the full three-dimensional Young–Laplace equation, Marangoni convection, London–van der Waals dispersion forces, and nonequilibrium interface conditions. The results showed that varying the dimensionless superheat had no apparent effect on the meniscus profile. However, varying the dispersion number produced a noticeable change in the meniscus profile, but only at the microscopic level near the tube wall. No change in the apparent contact angle was observed with changes in the dimensionless superheat or dispersion number. In all cases, the dimensionless mean curvature was asymptotic to a value equal to that for a hemispherical meniscus. The local interfacial mass flux and total mass transfer rate increased dramatically as the dispersion number was increased, suggesting that surface coatings can play an important role in improving or degrading capillary pumping. The model also predicted that the local capillary pressure remains constant and equal to 2σ/rc regardless of changes in the dimensionless superheat and dispersion number. It should be noted that the results in this study are theoretical in nature and require experimental verification.

More hyperelastic models for rubber-like materials: consistent tangent operators and comparative study

2013 ◽  
Vol 22 (1-2) ◽  
pp. 27-50 ◽  
Author(s):  
Mokarram Hossain ◽  
Paul Steinmann
Keyword(s):  
Large Deformations ◽  
Pure Shear ◽  
Three Dimensional ◽  
Network Models ◽  
Polymeric Materials ◽  
Chain Molecules ◽  
Current Contribution ◽  
Dimensional Network ◽  
Analytical Expressions ◽  
Order Tangent

AbstractRubber-like materials can deform largely and nonlinearly upon loading, and they return to the initial configuration when the load is removed. Such rubber elasticity is achieved due to very flexible long-chain molecules and a three-dimensional network structure that is formed via cross-linking or entanglements between molecules. Over the years, to model the mechanical behavior of such randomly oriented microstructures, several phenomenological and micromechanically motivated network models for nearly incompressible hyperelastic polymeric materials have been proposed in the literature. To implement these models for polymeric material (undoubtedly with widespread engineering applications) in the finite element framework for solving a boundary value problem, one would require two important ingredients, i.e., the stress tensor and the consistent fourth-order tangent operator, where the latter is the result of linearization of the former. In our previous work, 14 such material models are reviewed by deriving the accurate stress tensors and tangent operators from a group of phenomenological and micromechanical models at large deformations. The current contribution will supplement some further important models that were not included in the previous work. For comparison of all selected models in reproducing the well-known Treloar data, the analytical expressions for the three homogeneous defomation modes, i.e., uniaxial tension, equibiaxial tension, and pure shear, have been derived and the performances of the models are analyzed.

scholarly journals Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium

2016 ◽  
Vol 472 (2185) ◽  
pp. 20150790 ◽  
Author(s):  
F. dell’Isola ◽  
I. Giorgio ◽  
M. Pawlikowski ◽  
N. L. Rizzi
Keyword(s):  
Large Deformations ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Beam Theory ◽  
Beam Model ◽  
Computationally Efficient ◽  
Nonlinear Beam ◽  
Pantographic Structures ◽  
Diffusion Of Technology ◽  
Second Gradient

The aim of this paper is to find a computationally efficient and predictive model for the class of systems that we call ‘pantographic structures’. The interest in these materials was increased by the possibilities opened by the diffusion of technology of three-dimensional printing. They can be regarded, once choosing a suitable length scale, as families of beams (also called fibres) interconnected to each other by pivots and undergoing large displacements and large deformations. There are, however, relatively few ‘ready-to-use’ results in the literature of nonlinear beam theory. In this paper, we consider a discrete spring model for extensible beams and propose a heuristic homogenization technique of the kind first used by Piola to formulate a continuum fully nonlinear beam model. The homogenized energy which we obtain has some peculiar and interesting features which we start to describe by solving numerically some exemplary deformation problems. Furthermore, we consider pantographic structures, find the corresponding homogenized second gradient deformation energies and study some planar problems. Numerical solutions for these two-dimensional problems are obtained via minimization of energy and are compared with some experimental measurements, in which elongation phenomena cannot be neglected.

Three-Dimensional Vibration Analysis of Thick, Complete Conical Shells

2004 ◽  
Vol 71 (4) ◽  
pp. 502-507 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Present Method ◽  
Shell Theory ◽  
Ritz Method ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Algebraic Polynomials ◽  
Shells Of Revolution ◽  
Conical Shells ◽  
Thin Shell Theory ◽  
Time Periodic

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution. Unlike conventional shell theories, which are mathematically two-dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components ur,uz, and uθ in the radial, axial, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the r and z-directions. Potential (strain) and kinetic energies of the conical shells are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the conical shells. Novel numerical results are presented for thick, complete conical shells of revolution based upon the 3D theory. Comparisons are also made between the frequencies from the present 3D Ritz method and a 2D thin shell theory.

Effect of truck position and multiple truck loading on response of long-span metal culverts

2014 ◽  
Vol 51 (2) ◽  
pp. 196-207 ◽  
Author(s):  
Tamer M. Elshimi ◽  
Richard W.I. Brachman ◽  
Ian D. Moore
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Shell Theory ◽  
Orthotropic Shell ◽  
Three Dimensional ◽  
Element Analysis ◽  
Long Span ◽  
Dimensional Finite Element ◽  
Current Design ◽  
Three Dimensional Finite Element

Long-span metal culverts have been used for almost 50 years as an economical alternative to short-span bridges. Current design methods are based on two-dimensional finite element analysis using beam theory to represent the structure, or three-dimensional analysis employing orthotropic shell theory. However, neither analysis has been used to investigate the most critical position for trucks at the surface of long-span metal culverts. This paper shows results of three-dimensional finite element analysis, employing orthotropic shell theory and explicitly modeling the geometry of corrugated plates for a specific box culvert tested using a fully loaded dump truck. The analysis was then extended to study the effect of truck position on the response of long-span box and arch culverts. The finite element models, employing orthotropic shell theory and explicitly modeling the geometry of corrugated plates, successfully produced the behaviour of the culvert under truck loading for different truck positions. Culvert deformations were calculated within 7%–13% of the measured values at different locations. The bending moment at the crown was within 4%–17% of the values calculated using the measured strains. If three-dimensional finite element analysis is used to design these culverts, two design trucks should be considered (current design considers a single design truck). The highest moment or thrust is obtained when the truck tandem axles are located above the crown of the culvert.

scholarly journals Efficient and Tunable Three-Dimensional Functionalization of Fully Zwitterionic Antifouling Surface Coatings

Langmuir ◽  
2016 ◽  
Vol 32 (40) ◽  
pp. 10199-10205 ◽  
Author(s):  
Stefanie C. Lange ◽  
Esther van Andel ◽  
Maarten M. J. Smulders ◽  
Han Zuilhof
Keyword(s):  
Three Dimensional ◽  
Surface Coatings

Bifurcation of Equilibrium in Thick Orthotropic Cylindrical Shells Under Axial Compression

1995 ◽  
Vol 62 (1) ◽  
pp. 43-52 ◽  
Author(s):  
G. A. Kardomateas
Keyword(s):  
Axial Compression ◽  
Orthotropic Material ◽  
Shell Theory ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Elasticity Solution ◽  
Timoshenko Theory ◽  
Cylinder Axis ◽  
Dimensional Theory ◽  
Nonshallow Shell

The bifurcation of equilibrium of an orthotropic thick cylindrical shell under axial compression is studied by an appropriate formulation based on the three-dimensional theory of elasticity. The results from this elasticity solution are compared with the critical loads predicted by the orthotropic Donnell and Timoshenko nonshallow shell formulations. As an example, the cases of an orthotropic material with stiffness constants typical of glass/epoxy and the reinforcing direction along the periphery or along the cylinder axis are considered. The bifurcation points from the Timoshenko formulation are always found to be closer to the elasticity predictions than the ones from the Donnell formulation. For both the orthotropic material cases and the isotropic one, the Timoshenko bifurcation point is lower than the elasticity one, which means that the Timoshenko formulation is conservative. The opposite is true for the Donnell shell theory, i.e., it predicts a critical load higher than the elasticity solution and therefore it is nonconservative. The degree of conservatism of the Timoshenko theory generally increases for thicker shells. Likewise, the Donnell theory becomes in general more nonconservative with thicker construction.

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