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1.
Heng Hu Salim Belouettar Michel Potier-Ferry El Mostafa Daya Ahmed Makradi 《Composite Structures》2010,92(2):515-522
The paper presents a combination of the Arlequin Method (AM) and the Asymptotic Numerical Method (ANM) for studying nonlinear problems related to the mechanical behavior of sandwich composite structures. The Arlequin Method is a multi-scale method in which different models are crossed and glued to each other. The ANM is an alternative method which falls into the category of numerical perturbation techniques. By introducing the power series expansions into the equilibrium equation, the nonlinear problem is transformed into a sequence of linear problems and solved by the standard finite element method. Compared to other classical solvers (Newton–Raphson Method, Modified Newton–Raphson Method), ANM offers a considerable interest in the computation time and reliability. To validate this method, the AM is combined with the ANM to simulate the local damage of 2D–2D and 2D–2D-coupled sandwich beams. The simulation results are compared to a reference solution calculated from a 2D beam without any coupling. In case of the 2D–2D-coupled sandwich beam, the simulation shows a good agreement with the reference solution for both the local damage and the deformation at the loaded point. However, in case of 2D–1D-coupled sandwich beam, the simulation deviate from the reference solution due to the constant thickness of the 1D zig-zag element used to model the 1D zone of the sandwich beam. 相似文献
2.
This work deals with the convergence acceleration of iterative nonlinear methods. Two convergence accelerating techniques
are evaluated: the Modified Mininal Polynomial Extrapolation Method (MMPE) and the Padé approximants. The algorithms studied
in this work are iterative correctors: Newton’s modified method, a high-order iterative corrector presented in Damil et al.
(Commun Numer Methods Eng 15:701–708, 1999) and an original algorithm for vibration of viscoelastic structures. We first describe
the iterative algorithms for the considered nonlinear problems. Secondly, the two accelerating techniques are presented. Finally,
through several numerical tests from the thin shell theory, Navier–Stokes equations and vibration of viscoelastic shells,
the advantages and drawbacks of each accelerating technique is discussed. 相似文献
3.
In this paper, the linearly conforming radial point interpolation method is extended for geometric nonlinear analysis of plates
and cylindrical shells. The Sander’s nonlinear shell theory is utilized and the arc-length technique is implemented in conjunction
with the modified Newton–Raphson method to solve the nonlinear equilibrium equations. The radial and polynomial basis functions
are employed to construct the shape functions with Delta function property using a set of arbitrarily distributed nodes in
local support domains. Besides the conventional nodal integration, a stabilized conforming nodal integration is applied to
restore the conformability and to improve the accuracy of solutions. Small rotations and deformations, as well as finite strains,
are assumed for the present formulation. Comparisons of present solutions are made with the results reported in the literature
and good agreements are obtained. The numerical examples have demonstrated that the present approach, combined with arc-length
method, is quite effective in tracing the load-deflection paths of snap-through and snap-back phenomena in shell problems. 相似文献
4.
To study the vibrations of a tank partially filled with a liquid in low-gravity environment, we first have to find the static
position of the liquid. In this paper, we present a three-dimensional finite element approach to find this equilibrium configuration
for any tank geometry. Both gravity and capillary effects are taken into account. The nonlinear equations of this problem
are derived from the differentiation of the total potential energy of the system, then the problem is transformed into a liquid
free surface form-finding. The well-known singularity of this kind of problems is regularized using the updated reference
strategy. The equations of the regularized problem are discretized using the finite element method and solved by the Newton–Raphson
algorithm. Several examples illustrate the effectiveness of this method, even for complex cases, and two validation tests
are presented. The linear sloshing vibrations of the liquid are finally studied near this equilibrium position and two validation
cases are proposed for the eigenvalue dynamic problem. 相似文献
5.
The computational efficiencies of the continuum and consistent (algorithmic) tangent moduli tensors in rate-independent crystal
elastoplasticity are examined in conjunction with the available implicit state update algorithms. It is, in this context,
shown that the consistent tangent moduli associated with the state update algorithm with the exponential mapping coincide
with the continuum tangent moduli. After verifying the reported performance of the exponential mapping algorithm in preserving
the incompressibility of plastic deformation in a single crystal grain, we carry out numerical experiments to understand the
convergence trends of the global Newton–Raphson iterative procedure with different kinds of tangent moduli tensors. Having
done this, we are concerned with the performance of those tangent moduli tensors for the micro-scale analysis of a polycrystalline
aggregate, which is regarded as a representative volume element, subjected to macro-scale uniform deformation in the context
of the two-scale homogenization method. 相似文献
6.
Nonlinear forced vibration of damped plates coupling asymptotic numerical method and reduction models 总被引:1,自引:1,他引:0
F. Boumediene L. Duigou E. H. Boutyour A. Miloudi J. M. Cadou 《Computational Mechanics》2011,47(4):359-377
This work concerns the computation of the nonlinear solutions of forced vibration of damped plates. In a recent work (Boumediene
et al. in Comput Struct 87:1508–1515, 2009), a numerical method coupling an asymptotic numerical method (ANM), harmonic balance method and Finite Element method was
proposed to resolve this type of problem. The harmonic balance method transforms the dynamic equations to equivalent static
ones which are solved by using a perturbation method (ANM) and the finite element method. The numerical results presented
in reference (Boumediene et al. in Comput Struct 87:1508–1515, 2009) show that the ANM is very efficient and permits one to obtain the nonlinear solutions with few matrix triangulation numbers
compared to a classical incremental iterative method. However, putting a great number of harmonics (6 or greater) into the
load vector leads to tangent matrices with a great size. The computational time necessary for the triangulation of such matrices
can then be large. In this paper, reduced order models are proposed to decrease the size of these matrices and consequently
the computational time. We consider two reduced bases. In the first one, the reduced basis is obtained by the resolution of
a classical eigenvalue problem. The second one is obtained by using the nonlinear solutions computed during the first step
of the calculus which is realized with the ANM. Several classical benchmarks of nonlinear damped plates are presented to show
the efficiency of the proposed numerical methods. 相似文献
7.
Adisorn Owatsiriwong Bupavech Phansri Jung-Sik Kong Kyung-Ho Park 《Computational Mechanics》2009,44(2):161-172
This study deals with the particular integral formulation for purely axisymmetric elastoplastic analysis. The axisymmetric
elastostatic equation is used for the complementary solution. The axisymmetric particular integrals for displacement and strain
rates are derived by integrating three-dimensional formulation along the circumferential direction leading to elliptic integrals.
The particular integrals for stress and traction rates are obtained by using the stress–strain and traction–stress relations.
The Newton–Raphson algorithm for the plastic multiplier is used to solve the system equation. The numerical results for four
example problems are given and compared with their analytical solutions or those by other BEM and FEM programs to demonstrate
the accuracy of the present formulation. Generally, agreement among all of those results is satisfactory. 相似文献
8.
Influence of neutral surface position on the nonlinear stability behavior of functionally graded plates 总被引:1,自引:0,他引:1
Nonlinear behavior of functionally graded material (FGM) skew plates under in-plane load is investigated here using a shear
deformable finite element method. The material is graded in the thickness direction and a simple power law based on the rule
of mixture is used to estimate the effective material properties. The neutral surface position for such FGM plates is determined
and the first order shear deformation theory based on exact neutral surface position is employed here. The present model is
compared with the conventional mid-surface based formulation, which uses extension-bending coupling matrix to include the
noncoincidence of neutral surface with the geometric mid-surface for unsymmetric plates. The nonlinear governing equations
are solved through Newton–Raphson technique. The nonlinear behavior of FGM skew plates under compressive and tensile in-plane
load are examined considering different system parameters such as constituent gradient index, boundary condition, thickness-to-span
ratio and skew angle.
An erratum to this article can be found at 相似文献
9.
Hesham Hamed Ibrahim Hong Hee Yoo Mohammad Tawfik Kwan-Soo Lee 《Computational Mechanics》2010,46(3):377-386
A nonlinear finite element model is provided for the nonlinear random response of functionally graded material panels subject
to combined thermal and random acoustic loads. Material properties are assumed to be temperature-dependent, and graded in
the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents.
The governing equations are derived using the first-order shear-deformable plate theory with von Karman geometric nonlinearity
and the principle of virtual work. The thermal load is assumed to be steady state constant temperature distribution, and the
acoustic excitation is considered to be a stationary white-Gaussian random pressure with zero mean and uniform magnitude over
the plate surface. The governing equations are transformed to modal coordinates to reduce the computational efforts. Newton–Raphson
iteration method is employed to obtain the dynamic response at each time step of the Newmark implicit scheme for numerical
integration. Finally, numerical results are provided to study the effects of volume fraction exponent, temperature rise, and
the sound pressure level on the panel response. 相似文献
10.
Michael Müller 《Computational Mechanics》2007,40(4):683-705
In the vicinity of limit and bifurcation points the global stiffness matrix of a finite element formulation becomes ill-conditioned
and at the critical point singular. This disturbs the convergence behavior of the standard Newton–Raphson scheme as well as
the arc-length method. The stabilization procedure suggested solves the numerical defects and is thus able to pass critical
points. Bifurcation points are passed on the primary path. Branch switching to the secondary path is done automatically. The
stabilization procedure and the imperfection force are derived based on the eigenvalues and -vectors of the structure. 相似文献
11.
12.
J. M. Cadou M. Potier‐Ferry B. Cochelin N. Damil 《International journal for numerical methods in engineering》2001,50(4):825-845
This paper deals with the use of the asymptotic numerical method (ANM) for solving non‐linear problems, with particular emphasis on the stationary Navier–Stokes equation and the Petrov–Galerkin formulation. ANM is a combination of a perturbation technique and a finite element method allowing to transform a non‐linear problem into a succession of linear ones that admit the same tangent matrix. This method has been applied with success in non‐linear elasticity and fluid mechanics. In this paper, we apply the same kind of technique for solving Navier–Stokes equation with the so‐called Petrov–Galerkin weighting. The main difficulty comes from the fact that the non‐linearity is no more quadratic and it is not evident, in this case, to be able to compute a large number of terms of the perturbation series. Several examples of fluid mechanic are presented to demonstrate the performance of such a method. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
13.
The non-linear flutter and thermal buckling of an FGM panel under the combined effect of elevated temperature conditions and
aerodynamic loading is investigated using a finite element model based on the thin plate theory and von Karman strain-displacement
relations to account for moderately large deflection. The aerodynamic pressure is modeled using the quasi-steady first order
piston theory. The governing non-linear equations are obtained using the principal of virtual work adopting an approach based
on the thermal strain being a cumulative physical quantity to account for temperature dependent material properties. This
system of non-linear equations is solved by Newton–Raphson numerical technique. It is found that the temperature increase
has an adverse effect on the FGM panel flutter characteristics through decreasing the critical dynamic pressure. Decreasing
the volume fraction enhances flutter characteristics but this is limited by structural integrity aspect. The presence of aerodynamic
flow results in postponing the buckling temperature and in suppressing the post buckling deflection while the temperature
increase gives way for higher limit cycle amplitude. 相似文献
14.
This work presents an improved predictor/multi-corrector algorithm for linear structural dynamics problems, based on the
time-discontinuous Galerkin finite element method. The improved algorithm employs the Gauss–Seidel method to calculate iteratively
the solutions that exist in the phase of the predictor/multi-corrector of the numerical implementation. Stability analyses
of iterative algorithms reveal that such an improved scheme retains the unconditionally stable behavior with greater efficiency
than another iterative algorithm. Also, numerical examples are presented, demonstrating that the proposed method is more stable
and accurate than several commonly used algorithms in structural dynamic applications.
Received 18 June 1999 相似文献
15.
The study of tri-phasic interactions in nano-hydroxyapatite/konjac glucomannan/chitosan composite 总被引:3,自引:0,他引:3
Zhou Gang Li Yubao Zhang Li Li Hong Wang Mingbo Cheng Lin Wang Yuanyuan Wang Huanan Shi Pujiang 《Journal of Materials Science》2007,42(8):2591-2597
The interactions among the three phases of nano-hydroxyapatite (n-HA), Konjac glucomannan (KGM) and Chitosan (CS) in n-HA/KGM/CS
composite were investigated using TEM, IR, XRD, XPS and TGA methods. The crystalline structure of n-HA was studied by means
of Rietveld method. A series of structure parameters, such as, cell lattice parameters (a or c), bonding lengths and a numerical index of distortion for PO4 tetrahedron, were calculated by Newton–Raphson calculating method to characterize the crystalline structure of HA at atom
level. The results showed that n-HA was mainly linked with KGM and CS by hydrogen bonding between OH−–PO43− of n-HA and –C=O, –NH of KGM-CS copolymer, and there was a stable interface formed between the three phases in the composite.
Besides, orientation of this hydrogen bonding resulted in the decrease of the relative crystallization degree of KGM-CS copolymer. 相似文献
16.
We show in this work that the Asymptotic Numerical Method (ANM) combined with the Method of Fundamental Solution (MFS) can be a robust algorithm to solve the nonlinear Poisson problem. The ANM transforms the nonlinear problem into a sequence of linear ones which can be solved by MFS. This last method consists of approximating the solution of the linear Poisson problem by a linear combination of fundamental solutions. Some examples are presented to show the efficiency of the proposed method. 相似文献
17.
The importance of a suitable temporal integrator for fully nonlinear simulations of surface gravity waves is emphasized. Via
numerical examples, it is demonstrated that constant-step procedures are inefficient. This relates to the practice of energy-conserving
symplectic integration, assuming constant time steps, and is compared to direct numerical simulations using Runge–Kutta integrators
with variable time-step control. It is concluded that the latter with automatic variable time-step control is the more efficient,
and should be applied. The practice and efficiency of a stabilization procedure for the time-step selection is described and
illustrated. An important point of the method is that the linear part of the prognostic equations is integrated analytically,
which means that this part is obtained to machine presicion for any (large) time step (time interval). The evolution and instabilities
of highly nonlinear water waves in three dimensions are exemplified through an accurate and efficient time-integration procedure.
We are grateful to Professor J. N. Newman for his longstanding and pioneering contributions to the research field of marine
hydrodynamics. His analytical and numerical works on fundamental and industrial problems in relation to water waves and their
interaction with floating bodies have inspired us and many fellow scientist world wide over long time. 相似文献
18.
E. H. Boutyour H. Zahrouni M. Potier‐Ferry M. Boudi 《International journal for numerical methods in engineering》2004,60(12):1987-2012
The aim of this work is to develop a reliable and fast algorithm to compute bifurcation points and bifurcated branches. It is based upon the asymptotic numerical method (ANM) and Padé approximants. The bifurcation point is detected by analysing the poles of Padé approximants or by evaluating, along the computed solution branch, a bifurcation indicator well adapted to ANM. Several examples are presented to assess the effectiveness of the proposed method, that emanate from buckling problems of thin elastic shells. Especially problems involving large rotations are discussed. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
19.
Luis Távara Vladislav Mantič Alberto Salvadori Leonard J. Gray Federico París 《Computational Mechanics》2013,51(4):535-551
A new symmetric boundary integral formulation for cohesive cracks growing in the interior of homogeneous linear elastic isotropic media with a known crack path is developed and implemented in a numerical code. A crack path can be known due to some symmetry implications or the presence of a weak or bonded surface between two solids. The use of a two-dimensional exponential cohesive law and of a special technique for its inclusion in the symmetric Galerkin boundary element method allows us to develop a simple and efficient formulation and implementation of a cohesive zone model. This formulation is dependent on only one variable in the cohesive zone (relative displacement). The corresponding constitutive cohesive equations present a softening branch which induces to the problem a potential instability. The development and implementation of a suitable solution algorithm capable of following the growth of the cohesive zone and subsequent crack growth becomes an important issue. An arc-length control combined with a Newton–Raphson algorithm for iterative solution of nonlinear equations is developed. The boundary element method is very attractive for modeling cohesive crack problems as all nonlinearities are located along the boundaries (including the crack boundaries) of linear elastic domains. A Galerkin approximation scheme, applied to a suitable symmetric integral formulation, ensures an easy treatment of cracks in homogeneous media and excellent convergence behavior of the numerical solution. Numerical results for the wedge split and mixed-mode flexure tests are presented. 相似文献
20.
Siamak Niroomandi Icíar Alfaro Elías Cueto Francisco Chinesta 《International journal for numerical methods in engineering》2010,81(9):1180-1206
In this paper, we develop a novel algorithm for the dimensional reduction of the models of hyperelastic solids undergoing large strains. Unlike standard proper orthogonal decomposition methods, the proposed algorithm minimizes the use of the Newton algorithms in the search of non‐linear equilibrium paths of elastic bodies. The proposed technique is based upon two main ingredients. On one side, the use of classic proper orthogonal decomposition techniques, that extract the most valuable information from pre‐computed, complete models. This information is used to build global shape functions in a Ritz‐like framework. On the other hand, to reduce the use of Newton procedures, an asymptotic expansion is made for some variables of interest. This expansion shows the interesting feature of possessing one unique tangent operator for all the terms of the expansion, thus minimizing the updating of the tangent stiffness matrix of the problem. The paper is completed with some numerical examples in order to show the performance of the technique in the framework of hyperelastic (Kirchhoff–Saint Venant and neo‐Hookean) solids. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献