| 1. |
- Ahlkrona, Josefin, et al.
(författare)
-
A numerical study of scaling relations for non-Newtonian thin film flows with applications in ice sheet modelling
- 2013
-
Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford University Press (OUP). - 0033-5614 .- 1464-3855. ; 66:4, s. 417-435
-
Tidskriftsartikel (refereegranskat)abstract
- This article treats the viscous, non-Newtonian thin-film flow of ice sheets, governed by the Stokes equations, and the modelling of ice sheets with asymptotic expansion of the analytical solutions in terms of the aspect ratio, which is a small parameter measuring the shallowness of an ice sheet. An asymptotic expansion requires scalings of the field variables with the aspect ratio. There are several, conflicting, scalings in the literature used both for deriving simplified models and for analysis. We use numerical solutions of the Stokes equations for varying aspect ratios in order to compute scaling relations. Our numerically obtained results are compared with three known theoretical scaling relations: the classical scalings behind the Shallow Ice Approximation, the scalings originally used to derive the so-called Blatter-Pattyn equations, and a non-uniform scaling which takes into account a high viscosity boundary layer close to the ice surface. We find that the latter of these theories is the most appropriate one since there is indeed a boundary layer close to the ice surface where scaling relations are different than further down in the ice. This boundary layer is thicker than anticipated and there is no distinct border with the inner layer for aspect ratios appropriate for ice sheets. This makes direct application of solutions obtained by matched asymptotic expansion problematic.
|
|
| 2. |
- Argatov, Ivan, et al.
(författare)
-
Rayleigh surface waves in functionally graded materials : long-wave limit
- 2019
-
Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford Univeristy Press. - 0033-5614 .- 1464-3855. ; 72:2, s. 197-211
-
Tidskriftsartikel (refereegranskat)abstract
- A first-order asymptotic model for describing waves propagating along the surface of a functionally graded isotropic elastic half-space is constructed in the long-wave limit under the assumption of a finitely supported perturbation of the half-space properties. Explicit approximations for the Rayleigh waves are derived under the assumption that the semi-infinite elastic medium is slightly inhomogeneous
|
|
| 3. |
- Boström, Anders E, 1951, et al.
(författare)
-
Elastic SH wave propagation in a layered anisotropic plate with interface damage modelled by spring boundary conditions
- 2009
-
Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford University Press (OUP). - 0033-5614 .- 1464-3855. ; 62:1, s. 39-52
-
Tidskriftsartikel (refereegranskat)abstract
- Elastic SH wave propagation in a layered anisotropic plate withinterface damage is modelled in several steps. A single interfacecrack between two half-spaces is first studied and an explicitsolution for the crack-opening displacement is obtained at lowfrequencies. This is then generalized to a random distribution ofcracks at the interface and the result is reformulated as a springboundary condition. As an example of its usefulness,this boundary condition is then used in thederivation of a plate equation by expanding the displacements inpower series in the thickness coordinate.
|
|
| 4. |
- Boström, Anders E, 1951
(författare)
-
Scattering of In-plane Elastic Waves by an Anisotropic Circle
- 2018
-
Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford University Press (OUP). - 0033-5614 .- 1464-3855. ; 71:2, s. 139-155
-
Tidskriftsartikel (refereegranskat)abstract
- The 2D scattering of in-plane elastic waves by a circle is considered when the surrounding medium is isotropic and the medium inside the circle is anisotropic (orthotropic). The equations inside the circle are transformed to polar coordinates and then depend explicitly on the azimuthal angle through trigonometric functions. Making expansions in trigonometric series in the azimuthal coordinate give a coupled system of ordinary differential equations in the radial coordinate that is solved by power series expansions. With the solution inside the circle complete the scattering problem is solved essentially as in the classical case. The elements of the transition (T) matrix of the circle are given explicitly for low frequencies (long wavelengths). For low frequencies some numerical examples are given showing the strong influence of anisotropy.
|
|
| 5. |
- Folkow, Peter D., et al.
(författare)
-
Time domain Green functions for the homogeneous Timoshenko beam
- 1998
-
Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford University Press (OUP). - 0033-5614 .- 1464-3855. ; 51:1, s. 125-141
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper a wave splitting technique is applied to a homogeneous Timoshenko beam. The purpose is to obtain a diagonal equation in terms of the split fields. These fields are calculated in the time domain from an appropriate set of boundary conditions. The fields along the beam are represented as a time convolution of Green functions with the excitation. The Green functions do not depend on the wave fields but only on the parameters of the beam. Green functions for a Timoshenko beam are derived, and the exponential behaviour of these functions as well as the split modes are discussed. A transformation that extracts the exponential part is performed. Some numerical examples for various loads are presented and compared with results appearing in the literature.
|
|
| 6. |
- Folkow, Peter, 1968, et al.
(författare)
-
Dynamic higher-order equations for finite rods
- 2010
-
Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford University Press (OUP). - 0033-5614 .- 1464-3855. ; 63:1, s. 1-21
-
Tidskriftsartikel (refereegranskat)abstract
- This work considers longitudinal wave propagation in circular cylindrical rods adopting Bostrom's power series expansion method in the radial coordinate. Equations of motion together with consistent sets of general lateral and end boundary conditions are derived in a systematic fashion up to arbitrary order using a generalized Hamilton's principle. Analytical comparisons are made between the present theory to low order and several classic theories. Numerical examples for eigenfrequencies, displacement and stress distributions are given for a number of finite rod structures. The results are presented for series expansion theories of different order and various classical theories, from which one may conclude that the present method generally models the rod accurately.
|
|
| 7. |
- Ghosh, Arpan, et al.
(författare)
-
A TWO-DIMENSIONAL MODEL OF THE THIN LAMINAR WALL OF A CURVILINEAR FLEXIBLE PIPE
- 2018
-
Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : OXFORD UNIV PRESS. - 0033-5614 .- 1464-3855. ; 71:3, s. 349-367
-
Tidskriftsartikel (refereegranskat)abstract
- We present a two-dimensional model describing the elastic behaviour of the wall of a curved flexible pipe. The wall has a laminate structure consisting of several anisotropic layers of varying thickness and is assumed to be much smaller in thickness than the radius of the channel which itself is allowed to vary. Our two-dimensional model takes the interaction of the wall with any surrounding or supporting material and the fluid flow into account and is obtained via a dimension reduction procedure. The curvature and twist of the pipes axis as well as the anisotropy of the laminate wall present the main challenges in applying the dimension reduction procedure so plenty of examples of canonical shapes of pipes and their walls are supplied with explicit systems of differential equations at the end.
|
|
| 8. |
- Kozlov, Vladimir, et al.
(författare)
-
BOUNDS FOR SOLUTIONS TO THE PROBLEM OF STEADY WATER WAVES WITH VORTICITY
- 2017
-
Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : OXFORD UNIV PRESS. - 0033-5614 .- 1464-3855. ; 70:4, s. 497-518
-
Tidskriftsartikel (refereegranskat)abstract
- The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. Bounds for stream functions as well as free-surface profiles and the total head are obtained under the assumption that the vorticity distribution is a locally Lipschitz function. It is also shown that wave flows have countercurrents in the case when the infimum of the free surface profile exceeds a certain critical value.
|
|
| 9. |
- Kozlov, Vladimir, et al.
(författare)
-
Fields in non-degenerate 1D-3D elastic multi-structures
- 2001
-
Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford University Press (OUP). - 0033-5614 .- 1464-3855. ; 54:2, s. 177-212
-
Tidskriftsartikel (refereegranskat)abstract
- We analyse 1D-3D elastic multi-structures defined as solids involving finite-size three-dimensional elastic regions connected with thin rods. In the limit, when the thickness of the thin rods tends to zero, one has a union of a three-dimensional region and a set of thin rods. Classes of degenerate and non-degenerate multi-structures are specified, and asymptotic expansions of solutions of mixed boundary-value problems of linear elasticity are constructed. Asymptotic analysis, given in this work, provides rigorous justification of the existing engineering pile-structure models, and it also enables one to construct new models of high accuracy.
|
|
| 10. |
- Kozlov, Vladimir, et al.
(författare)
-
Steady Free-Surface Vortical Flows Parallel to the Horizontal Bottom
- 2011
-
Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford University Press (OUP). - 0033-5614 .- 1464-3855. ; 64:3, s. 371-399
-
Tidskriftsartikel (refereegranskat)abstract
- Steady, free-surface, vortical flows of an inviscid, incompressible, heavy fluid over a horizontal, rigid bottom are considered. All flows of constant depth are described for any Lipschitz vorticity distribution. It is shown that the values of Bernoullis constant, for which such flows exist, are greater than or equal to some critical value depending on the vorticity. For the critical value, only one flow exists and it is unidirectional. Supercritical flows exist for all values of Bernoullis constant greater than the critical one; every such flow is also unidirectional and its depth is smaller than that of the critical flow. Furthermore, at least one flow other than supercritical does exist for every value of Bernoullis constant greater than the critical one. It is found that for some vorticity distributions, the number of constant depth flows increases unrestrictedly as Bernoullis constant tends to infinity. However, all these flows, except for one or two, have counter-currents; their number depends on Bernoullis constant and increases by at least two every time when this constant becomes greater than a critical value (the above mentioned is the smallest of them), belonging to a sequence defined by the vorticity. A classification of vorticity distributions is presented; it divides all of them into three classes in accordance with the behaviour of some integral of the distribution on the interval [0, 1]. For distributions in the first class, a unidirectional subcritical flow exists for all admissible values of Bernoullis constant. For vorticity distributions belonging to the other two classes such a flow exists only when Bernoullis constant is less than a certain value. If Bernoullis constant is greater than this value, then at least one flow with counter-currents does exist along with the unidirectional supercritical flow. The second and third classes of vorticity distributions are distinguished from one another by the character of the counter-currents. If a distribution is in the second class, then a near-bottom counter-current is always present for sufficiently large values of Bernoullis constant. For distributions in the third class, a near-surface counter-current is always present for such values of the constant. Several examples illustrating the results are considered.
|
|
| 11. |
- Kroon, Martin
(författare)
-
An Efficient Method for Material Characterisation of Hyperelastic Anisotropic Inhomogeneous Membranes Based on Inverse Finite-Element Analysis and an Element Partition Strategy
- 2010
-
Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford University Press (OUP). - 0033-5614 .- 1464-3855. ; 63:2, s. 201-225
-
Tidskriftsartikel (refereegranskat)abstract
- An inverse method for estimating the distributions of the nonlinear elastic properties of inhomogeneous and anisotropic membranes is investigated. The material description of the membrane is based on a versatile constitutive model, including four material parameters: two initial stiffness values pertaining to the principal directions of the material, the angle between these principal directions and a reference coordinate system and a parameter related to the level of nonlinearity of the material. The estimation procedure consists of the following three steps: (i) perform experiments on the membranous structure whose properties are to be determined, (ii) define a corresponding finite-element (FE) model and (iii) minimise an error function (with respect to the unknown parameters) that quantifies the deviation between the numerical predictions and the experimental data. For this finite deformation problem, an FE framework for membranous structures exposed to a pressure boundary loading is outlined: the principle of virtual work, its linearisation and the related spatial discretisation. To achieve a robust parameter estimation, an element partition method is employed. In numerical examples, the proposed procedure is assessed by attempting to reproduce given random reference distributions of material fields in a reference membrane. The deviations between the estimated material parameter distributions and the related reference fields are within a few percent in most cases. The standard deviation for the resulting maximum principal stress was consistently below 1%.
|
|
| 12. |
- Needham, D. J., et al.
(författare)
-
THE DEVELOPMENT OF A WAX LAYER ON THE INTERIOR WALL OF A CIRCULAR PIPE TRANSPORTING HEATED OIL
- 2014
-
Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford University Press (OUP): Policy A - Oxford Open Option A. - 0033-5614 .- 1464-3855. ; 67:1, s. 93-125
-
Tidskriftsartikel (refereegranskat)abstract
- In this article we develop a simple model to describe the evolution of a depositional wax layer on the inner surface of a circular pipe transporting heated oil, which contains dissolved wax. When the outer pipe surface is cooled sufficiently, the growth of a wax layer is initiated on the inner pipe wall, and this evolves to a saturated steady state thickness. The model proposed is based on fundamental balances of heat flow from the oil, into the wax layer, and across the pipe wall. We present an analysis of the model, examine a relevant asymptotic limit in which the full details of the solution to the model are available and develop an efficient numerical method (based on the method of fundamental solutions) for producing approximations of the model solution. The mathematical structure of the model is that of a free boundary evolution problem of generalised Stefan type.
|
|
| 13. |
|
|
| 14. |
- Sohl, Christian, et al.
(författare)
-
A priori estimates on the partial realized gain of ultra-wideband (UWB) antennas
- 2008
-
Ingår i: Quarterly Journal of Mechanics and Applied Mathematics. - : Oxford University Press (OUP). - 0033-5614 .- 1464-3855. ; 61:3, s. 415-430
-
Tidskriftsartikel (refereegranskat)abstract
- A sum rule valid for a large class of linear and reciprocal antennas is presented in terms of the electric and magnetic polarizability dyadics. The identity is based on the holomorphic properties of the forward scattering dyadic and includes arbitrarily shaped antennas modelled by linear and time-translational invariant constitutive relations. In particular, a priori estimates on the partial realized gain are introduced, and lower bounds on the onset frequency are derived for two important archetypes of ultra-wideband antennas: those with a constant partial realized gain and those with a constant effective antenna aperture. The theoretical findings are illustrated by an equiangular spiral antenna, and comparison with numerical simulations show great potential for future applications in antenna design.
|
|
