共查询到20条相似文献,搜索用时 109 毫秒
1.
Angelo Marcello Tarantino Andrea Nobili 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(4):659-678
The equilibrium problem of nonlinear, isotropic and hyperelastic square membranes, stretched by a double symmetric system
of dead loads, is investigated. Depending on the form of the stored energy function, the problem considered may admit asymmetric
solutions in addition to the expected symmetric solutions. For compressible materials, the mathematical condition allowing
the computation of these asymmetric solutions is given. Moreover, explicit expressions for evaluating critical loads and bifurcation
points are derived. Results and basic relations obtained for general isotropic materials are then specialized for a compressible
Mooney–Rivlin material and a broad numerical analysis is performed. The qualitatively more interesting branches of asymmetric
equilibrium are shown and the influence of the material parameters is discussed. Finally, using the energy criterion, some
stability considerations are made. 相似文献
2.
Zhimin Zhang 《Numerische Mathematik》1995,69(4):509-522
Summary.
In this paper we discuss locking and robustness of the finite element
method for a model circular arch problem. It is shown that in the
primal variable (i.e., the standard displacement formulation), the
p-version is free from locking and uniformly robust with order
and hence exhibits optimal rate of convergence. On the other hand, the
h-version shows locking of order , and is uniformly
robust with
order for which explains the fact that the
quadratic element
for some circular arch problems suffers from locking for thin arches
in computational
experience. If mixed method is used, both the h-version and the p-version
are free from locking. Furthermore, the mixed method even converges
uniformly with an optimal rate for the stress.
Received June 5, 1992 / Revised version received May 17,
1994 相似文献
3.
Grant M. Cox James M. Hill 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(1):92-106
Gravity flow of granular materials through hoppers occurs in many industrial processes. For an ideal cohesionless granular material, which satisfies the Coulomb-Mohr yield condition, the number of known analytical solutions is limited. However, for the special case of the angle of internal friction equal to ninety degrees, there exist exact parametric solutions for the governing coupled ordinary differential equations for both two-dimensional wedges and three-dimensional cones, both of which involve two arbitrary constants of integration. These solutions are the only known analytical solutions of this generality. Here, we utilize the double-shearing theory of granular materials to determine the velocity field corresponding to these exact parametric solutions for the two problems of gravity flow through converging wedge and conical hoppers. An independent numerical solution for other angles of internal friction is shown to coincide with the analytical solution.Received: July 24, 2002 相似文献
4.
Ngamta Thamwattana Grant M. Cox James M. Hill 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(2):330-356
The practice of storing granular materials in stock
piles occurs throughout the world in many industrial situations.
As a result, there is much interest in predicting the stress
distribution within a stock pile. In 1981, it was suggested from
experimental work that the peak force at the base does not occur
directly beneath the vertex of the pile, but at some intermediate
point resulting in a ring of maximum pressure. With this in mind,
any analytical solution pertaining to this problem has the
potential to provide useful insight into this phenomenon. Here, we
propose to utilize some recently determined exact parametric
solutions of the governing equations for the continuum mechanical
theory of granular materials for two and three-dimensional stock
piles. These solutions are valid provided sin = 1, where
is the angle of internal friction, and we term such
materials as highly frictional. We note that there exists
materials possessing angles of internal friction around 60 to 65
degrees, resulting in values of sin equal to around 0.87 to
0.91. Further, the exact solutions presented here are potentially
the leading terms in a perturbation solution for granular
materials for which 1- sin is close to zero. The model
assumes that the stock pile is composed of two regions, namely an
inner rigid region and an outer yield region. The exact parametric
solution is applied to the outer yield region, and the solution is
extended continuously into the inner rigid region. The results
presented here extend previous work of the authors to the case of
highly frictional granular solids. 相似文献
5.
Xabier Garaizar 《Acta Appl Math》1989,14(3):259-268
The specific internal energy defines the constitutive relation (stress-strain function) in elastic deformations. We introduce a form for the specific internal energy that expresses the idea of small anisotropy. In this formulation, only one parameter is needed to specify the anisotropic part of the deformation.Supported in part by AFOSR-88-0025. 相似文献
6.
Tuong Ha-Duong 《Integral Equations and Operator Theory》1992,15(3):427-453
The boundary integral equations for the crack opening displacement in acoustic and elastic scattering problems are discussed in the case of flat cracks by means of the Fourier analysis technique. The pseudo-differential nature of the hypersingular integral operators is shown and their symbols explicited. It is then proved that the variational problems assocaited with these BIE are well-posed in a Sobolev functional framework which is closely linked with the elastic energy. A decomposition of the vector integral equation in the elastic case into scalar integral equations is obtained as a by-product of the variational formulation. 相似文献
7.
D. Natroshvili 《Georgian Mathematical Journal》1996,3(3):239-262
The paper deals with the two-dimensional exterior boundary value problems of the steady-state oscillation theory for anisotropic elastic bodies. By means of the limiting absorption principle the fundamental matrix of the oscillation equations is constructed and the generalized radiation conditions of Sommerfeld-Kupradze type are established. Uniqueness theorems of the basic and mixed type boundary value problems are proved. 相似文献
8.
M. Svanadze 《Georgian Mathematical Journal》1996,3(2):177-200
The asymptotic behavior of eigenoscillation and eigen-vector-function is studied for the internal boundary value problems of oscillation of the linear theory of a mixture of two isotropic elastic media. 相似文献
9.
10.
Mircea Merca 《Quaestiones Mathematicae》2016,39(4):457-469
In this paper, we prove that the Stirling numbers of both kinds can be written as sums over integer partitions. As corollaries, we rewrite some identities with Stirling numbers of both kinds without Stirling numbers. 相似文献
11.
John H. Cushman 《Acta Appl Math》1985,3(3):239-254
Many multiphase transport problems are characterized by a random mixing of the phases (e.g., transport in porous media). In general, because of this randomness, instrumentation windows are designed such that only averages of field properties over the various phases are measured. In this article we identify an instrument window with a compact distribution. If the field property being filtered lies in the space of tempered distributions, then constraints may be derived on the structure of the filter. Distributional equations are derived which represent transport of a filtered property. The equations are general enough to allow for the use of different instruments to measure different properties. An equation representing the relationship between phase properties and filtered properties is derived when the filter is given by a measure with compact support. 相似文献
12.
In this paper we give some congruences on the r-derangement polynomials (defined below), Lah polynomials and some versions of Bell numbers and polynomials. 相似文献
13.
Dual extremum principles are established in this paper for the variational boundary-value problem of elasto-perfect plasticity with large deformation. There exists a duality gap between the primal and dual variational problems. Our application to nonlinear limit analysis yields a pair of dual bounding theorems for the safety factor, when the gap has the right sign. It is proved that both the upper and lower bounds directly depend on the properties of the dual gap function.This research was supported by Army Research Office grant DAAL 03-86-K 0171 and National Science Foundation grant DMS-87-03313. 相似文献
14.
Summary In this paper, we approximate the solution of a problem of a general arch by a nonconforming method using straight beam elements and taking into account numerical integration. Compatibility conditions which have to be satisfied at the mesh points are given. These conditions ensure for this method the same order of convergence as usual conforming finite element methods. 相似文献
15.
Pierre Hillion 《Acta Appl Math》1993,30(1):35-45
We prove that the homogeneous wave equation has different kinds of nondispersive solutions all defined in terms of an arbitrary functionF(u), whereu is a solution of the corresponding characteristic equation. 相似文献
16.
Diego Dominici 《Journal of Computational and Applied Mathematics》2009,233(3):708-718
We analyze the Bell polynomials Bn(x) asymptotically as n→∞. We obtain asymptotic approximations from the differential-difference equation which they satisfy, using a discrete version of the ray method. We give some examples showing the accuracy of our formulas. 相似文献
17.
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19.
The problem of a stressed state in a nonhomogeneous infinite plane consisting of two different anisotropic half-planes and having slits of finite number on the interface line is investigated. It is assumed that the difference between the displacement and stress vector values is given on the interface line segments; on the edges of the slits we have the following data: boundary values of stress vector (problem of stress) or displacement vector values on one side of the slits, and stress vector values on the other side (mixed problem). Solutions are constructed in quadratures. 相似文献
20.
Juhani Pitkäranta 《Numerische Mathematik》1992,61(1):523-542
Summary We analyse the problem of membrane locking in (h, p) finite element models of a thin hemicylindrical shell roof loaded by a smoothly varying normal pressure distribution. We show that in the standard finite element method, locking occurs especially at low values ofp and when the finite element grid is not aligned with the axis of the cylinder. A general strategy of avoiding locking by using modified bilinear forms is introduced, and a special implementation of this strategy on aligned rectangular grids is considered. 相似文献