共查询到20条相似文献,搜索用时 0 毫秒
1.
Omar Anza Hafsa Jean-Philippe Mandallena 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2008
Relaxation theorems which apply to one, two and three-dimensional nonlinear elasticity are proved. We take into account the fact an infinite amount of energy is required to compress a finite line, surface or volume into zero line, surface or volume. However, we do not prevent orientation reversal. 相似文献
2.
The traditional method of fundamental solutions (MFS) based on the “global” boundary discretization leads to dense and non-symmetric coefficient matrices that, although smaller in sizes, require huge computational cost to compute the system of equations using direct solvers. In this study, a localized version of the MFS (LMFS) is proposed for the large-scale modeling of two-dimensional (2D) elasticity problems. In the LMFS, the whole analyzed domain can be divided into small subdomains with a simple geometry. To each of the subdomain, the traditional MFS formulation is applied and the unknown coefficients on the local geometric boundary can be calculated by the moving least square method. The new method yields a sparse and banded matrix system which makes the method very attractive for large-scale simulations. Numerical examples with up to 200,000 unknowns are solved successfully using the developed LMFS code. 相似文献
3.
4.
The basic results are overviewed concerning the formulation of nonlinear elasticity equations in the form of symmetric hyperbolic systems in long-time studies performed under the direction of the first author. The underlying principles developed in those studies are stated, and some inaccuracies and errors are corrected. Procedures are described for computing the coefficient matrices of the equations from a given equation of state. 相似文献
5.
Quasi-Newton iterations are constructed for the finite element solution of small-strain nonlinear elasticity systems in 3D. The linearizations are based on spectral equivalence and hence considered as variable preconditioners arising from proper simplifications in the differential operator. Convergence is proved, providing bounds uniformly w.r.t. the FEM discretization. Convenient iterative solvers for linearized systems are also proposed. Numerical experiments in 3D confirm that the suggested quasi-Newton methods are competitive with Newton's method. 相似文献
6.
High-order dual-parametric finite element methods for cavitation computation in nonlinear elasticity
Weijie Huang Weijun Ma Liang Wei Zhiping Li 《Numerical Methods for Partial Differential Equations》2020,36(5):1012-1027
In this paper, we present the numerical analysis on high order dual parametric finite element methods for the cavitation computation problems in nonlinear elasticity, which leads to a meshing strategy assuring high efficiency on numerical approximations to cavity deformations. Furthermore, to cope with the high order approximation of the finite element methods, properly chosen weighted Gaussian type numerical quadrature is applied to the singular part of the elastic energy. Our numerical experiments show that the high order dual parametric finite element methods work well when coupled with properly designed weighted Gaussian type numerical quadratures for the singular part of the elastic energy, and the convergence rates of the numerical cavity solutions are shown to be significantly improved as expected. 相似文献
7.
Michael Bildhauer Martin Fuchs 《Calculus of Variations and Partial Differential Equations》2005,24(3):309-340
We establish several smoothness results for local minimizers of non-autonomous variational integrals with anisotropic growth
conditions.
Mathematics Subject Classification (2000) 49N60, 49N99 相似文献
8.
Under some generic assumptions we prove the unique continuation property for the two-dimensional inhomogeneous anisotropic elasticity system. Having established the unique continuation property, we then investigate the inverse problem of reconstructing the inclusion or cavity embedded in a plane elastic body with inhomogeneous anisotropic medium by infinitely many localized boundary measurements.
9.
A Fourier-Chebyshev spectral method is proposed in this paper for solving the cavitation problem in nonlinear elasticity. The interpolation error for the cavitation solution is analyzed, the elastic energy error estimate for the discrete cavitation solution is obtained, and the convergence of the method is proved. An algorithm combined a gradient type method with a damped quasi-Newton method is applied to solve the discretized nonlinear equilibrium equations. Numerical experiments show that the Fourier-Chebyshev spectral method is efficient and capable of producing accurate numerical cavitation solutions. 相似文献
10.
Consider the variational integral
where Ω⊂ℝ
n
andp≥n≥2. H: (0, ∞)→[0, ∞) is a smooth convex function such that
. We approximateJ by a sequence of regularized functionalsJ
δ whose minimizers converge strongly to anJ-minimizing function and prove partial regularity results forJ
δ-minimizers. 相似文献
11.
Jerzy Kyparisis 《Annals of Operations Research》1990,27(1):143-173
This paper surveys the main results in the area of sensitivity analysis for finite-dimensional variational inequality and nonlinear complementarity problems. It provides an overview of Lipschitz continuity and differentiability properties of perturbed solutions for variational inequality problems, defined on both fixed and perturbed sets, and for nonlinear complementarity problems. 相似文献
12.
Stefan Hildebrandt Heiko von der Mosel 《Calculus of Variations and Partial Differential Equations》1999,9(3):249-267
Let be a two-dimensional parametric variational integral the Lagrangian F(x,z) of which is positive definite and elliptic, and suppose that is a closed rectifiable Jordan curve in . We then prove that there is a conformally parametrized minimizer of in the class of surfaces of the type of the disk B which are bounded by . An immediate consequence of this theorem is that the Dirichlet integral and the area functional have the same infima, a
result whose proof usually requires a Lichtenstein-type mapping theorem or else Morrey's lemma on -conformal mappings. In addition we show that the minimizer of is H?lder continuous in B, and even in if satisfies a chord-arc condition. In Section 1 it is described how our results are related to classical investigations, in
particular to the work of Morrey. Without difficulty our approach can be carried over to two-dimensional surfaces of codimension
greater than one.
Received July 20, 1998 / Accepted October 23, 1998 相似文献
13.
We are interested in variational problems of the form min ∝W(?u) dx, withW nonconvex. The theory of relaxation allows one to calculate the minimum value, but it does not determine a well-defined “solution” since minimizing sequences are far from unique. A natural idea for determining a solution is regularization, i.e. the addition of a higher order term such as ε|??u|2. But what is the behavior of the regularized solution in the limit as ε→0? Little is known in general. Our recent work [19, 20, 21] discusses a particular problem of this type, namely min u y=±1 ∝∝u x 2 +ε|u yy|dxdy with various boundary conditions. The present paper gives an expository overview of our methods and results. 相似文献
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15.
Byong-hun Ahn 《Operations Research Letters》1982,1(3):117-120
This paper presents a simple yet practically useful Gauss-Seidel iterative method for solving a class of nonlinear variational inequality problems over rectangles and of nonlinear complementarity problems. This scheme is a nonlinear generalization of a robust iterative method for linear complementarity problems developed by Mangasarian. Global convergence is presented for problems with Z-functions. It is noted that the suggested method can be viewed as a specific case of a class of linear approximation methods studied by Pang and others. 相似文献
16.
A variational approach to stochastic nonlinear diffusion problems with dynamical boundary conditions
We study a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise; we allow stochastic boundary conditions that depend on the time derivative of the solution on the boundary. This work provides the existence and uniqueness of the solution and it shows the existence of an ergodic invariant measure for the corresponding transition semigroup; furthermore, under suitable additional assumptions, uniqueness and strong asymptotic stability of the invariant measure are proved. 相似文献
17.
We prove existence and uniqueness results for weak solutions of
nonlinear degenerate problems arising in various physical models. The main
novelty in the article concerns the uniqueness, which employs a technique
based in showing that weak solutions are also entropy solutions, for which
uniqueness follows from a straightforward adaptation of known results. We
treat equations with lower order terms that have a particular structure and
show with a counterexample that for general lower order terms the uniqueness
does not hold.AMS Subject Classification: 35D99, 35K65, 35R35. 相似文献
18.
Relaxation control for a class of semilinear impulsive controlled systems is investigated. Existence of mild solutions for semilinear impulsive controlled systems is proved. By introducing a regular countably additive measure, we convexify the original control systems and obtain the corresponding relaxed control systems. The existence of optimal relaxed controls and relaxation results is also proved. 相似文献
19.
N. Zirakashvili 《Journal of Mathematical Sciences》2009,157(1):79-84
Using the method of boundary elements, we obtain numerical solutions of two-dimensional (plane deformation) boundary-value
problems on the elastic equilibrium of infinite and finite homogeneous isotropic bodies having elliptic holes with cracks
and cuts of finite length.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 51, Differential
Equations and Their Applications, 2008. 相似文献
20.
Ying-Xiong Xiao Ping Zhang Shi Shu 《Journal of Computational and Applied Mathematics》2007,200(2):637-652
Based on the geometric grid information as geometric coordinates, an algebraic multigrid (AMG) method with the interpolation reproducing the rigid body modes (namely the kernel elements of semi-definite operator arising from linear elasticity) is constructed, and such method is applied to the linear elasticity problems with a traction free boundary condition and crystal problems with free boundary conditions as well. The results of various numerical experiments in two dimensions are presented. It is shown from the numerical results that the constructed AMG method is robust and efficient for such semi-definite problems, and the convergence is uniformly bounded away from one independent of the problem size. Furthermore, the AMG method proposed in this paper has better convergence rate than the commonly used AMG methods. Simultaneously, an AMG method that can preserve the quotient space, which means that if the exact solution of original problem belongs to the quotient space of discrete operator considered, then the numerical solution of AMG method is convergent in the same quotient space, is obtained using the technique of orthogonal decomposition. 相似文献