共查询到20条相似文献，搜索用时 0 毫秒
1.
Panayiotis Papadopoulos Reese E. Jones Jerome M. Solberg 《International journal for numerical methods in engineering》1995,38(15):2603-2617
This article advocates a new methodology for the finite element solution of contact problems involving bodies that may undergo finite motions and deformations. The analysis is based on a decomposition of the two-body contact problem into two simultaneous sub-problems, and results naturally in geometrically unbiased discretization of the contacting surfaces. A proposed two-dimensional contact element is specifically designed to unconditionally allow for exact transmission of constant normal traction through interacting surfaces. 相似文献
2.
P. WRIGGERS U. HUECK 《International journal for numerical methods in engineering》1996,39(9):1437-1454
The numerical simulation of processes undergoing finite deformations requires robust elements. For a broad range of applications these elements should have a good performance in bending dominated situations as well as in the case of incompressibility. The element should be insensitive against mesh distortions which frequently occurs during finite deformations. Furthermore, due to efficiency reasons a good coarse mesh accuracy in required in non-linear analysis. The QS6 element, developed in this paper, tries to fulfil the above-mentioned requirements. The performance is depicted by means of numerical examples. 相似文献
3.
P. Wriggers L. Krstulovic‐Opara J. Korelc 《International journal for numerical methods in engineering》2001,51(12):1469-1495
Finite deformation contact problems are associated with large sliding in the contact area. Thus, in the discrete problem a slave node can slide over several master segments. Standard contact formulations of surfaces discretized by low order finite elements leads to sudden changes in the surface normal field. This can cause loss of convergence properties in the solution procedure and furthermore may initiate jumps in the velocity field in dynamic solutions. Furthermore non‐smooth contact discretizations can lead to incorrect results in special cases where a good approximation of the contacting surfaces is needed. In this paper a smooth contact discretization is developed which circumvents most of the aformentioned problems. A smooth deformed surface with no slope discontinuities between segments is obtained by a C1‐continuous interpolation of the master surface. Different forms of discretizations are possible. Among these are Bézier, Hermitian or other types of spline interpolations. In this paper we compare two formulations which can be used to obtain smooth normal and tangent fields for frictional contact of deformable bodies. The formulation is developed for two‐dimensional applications and includes finite deformation behaviour. Examples show the performance of the new discretization technique for contact. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
4.
5.
T. Rumpel K. Schweizerhof 《International journal for numerical methods in engineering》2004,59(6):849-870
Deformation dependent pressure loading on solid structures is created by the interaction of fluids with the deformable surface of a structure. Such fairly simple load models are valid for static and quasi‐static analyses and they are a very efficient tool to represent the influence of a fluid on the behaviour of structures. Completing previous studies on the deformation dependence of the loading with the assumption of finite gas volumes, the current contribution focuses on the influence of modifications of the size and shape of a finite structure containing an incompressible fluid with a free surface. The linearization of the corresponding virtual work expression necessary for a Newton‐type solution leads to additional terms for the volume dependence. Investigating these terms the conservativeness of the problem can be proven by the symmetry of the linearized form. Similarly to gas loading, the discretization of the structure with finite elements leads to standard stiffness matrix forms plus the so‐called load stiffness matrices and a rank‐one update for each filled structure part, if the loaded surface segments are identical with element surfaces. Some numerical examples show the effectiveness of the approach and the necessity to take the corresponding terms in the variational expression and the following linearization into account. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
6.
Ismail Caylak Rolf Mahnken 《International journal for numerical methods in engineering》2012,90(2):218-242
This paper presents stabilized mixed finite element formulations for tetrahedral elements at large deformations using volume and area bubble functions. To this end, the corresponding weak formulations are derived for the standard two‐field method, the method of incompatible modes and the enhanced strain method. Then, the weak formulations will be linearized. Furthermore, the matrix formulations for the weak formulations and its linearizations are summarized. The numerical results for incompressible rubber‐like materials using a Neo‐Hookean material law show the locking‐free performance and the drastic damping of the stresses for the new stabilized tetrahedral elements in finite deformation problems. This paper is an extension of the works published by the authors regarding small deformation problems for linear elasticity and plasticity. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
7.
Tomoshi Miyamura Yoshihiro Kanno Makoto Ohsaki 《International journal for numerical methods in engineering》2010,81(6):701-727
In the present paper, a solution scheme is proposed for frictionless contact problems of linear elastic bodies, which are discretized using the finite element method with lower order elements. An approach combining the interior‐point method and the semismooth Newton method is proposed. In this method, an initial active set for the semismooth Newton method is obtained from the approximate optimal solution by the interior‐point method. The simplest node‐to‐node contact model is considered in the present paper, that is, pairs of matching nodes exist on the contact surfaces. However, the discussions can be easily extended to a node‐to‐segment or segment‐to‐segment contact model. In order to evaluate the proposed method, a number of illustrative examples of the frictionless contact problem are shown. The proposed combined method is compared with the interior‐point method and the semismooth Newton method. Two numerical examples that are difficult to solve using the semismooth Newton method are solved effectively using the proposed combined method. It is shown that the proposed method converges within far fewer iterations than the semismooth Newton methods or the interior‐point method. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
8.
Gustavo C. Buscaglia Ricardo Durn Eduardo A. Fancello Raúl A. Feijo Claudio Padra 《International journal for numerical methods in engineering》2001,50(2):395-418
The derivation of an a posteriori error estimator for frictionless contact problems under the hypotheses of linear elastic behaviour and infinitesimal deformation is presented. The approximated solution of this problem is obtained by using the finite element method. A penalization or augmented‐Lagrangian technique is used to deal with the unilateral boundary condition over the contact boundary. An a posteriori error estimator suitable for adaptive mesh refinement in this problem is proposed, together with its mathematical justification. Up to the present time, this mathematical proof is restricted to the penalization approach. Several numerical results are reported in order to corroborate the applicability of this estimator and to compare it with other a posteriori error estimators. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
9.
Michael A. Puso 《International journal for numerical methods in engineering》2004,59(3):315-336
A version of the mortar method is developed for tying arbitrary dissimilar 3D meshes with a focus on issues related to large deformation solid mechanics. Issues regarding momentum conservation, large deformations, computational efficiency and bending are considered. In particular, a mortar method formulation that is invariant to rigid body rotations is introduced. A scheme is presented for the numerical integration of the mortar surface projection integrals applicable to arbitrary 3D curved dissimilar interfaces. Here, integration need only be performed at problem initialization such that coefficients can be stored and used throughout a quasi‐static time stepping process even for large deformation problems. A degree of freedom reduction scheme exploiting the dual space interpolation method such that direct linear solution techniques can be applied without Lagrange multipliers is proposed. This provided a significant reduction in factorization times. Example problems which touch on the aforementioned solid mechanics related issues are presented. Published in 2003 by John Wiley & Sons, Ltd. 相似文献
10.
A new algorithm is presented for the boundary element analysis of the two-dimensional contact problem between elastic solids involving large displacements. The contact constraints are not applied node-on-node but node-on-element, using the element shape functions to distribute the geometry, displacements and tractions on each element in the contact zone. Thus, the discretizations performed along the two surfaces in contact need not necessarily be the same. The solution procedure is based on the updated Lagrangian approach and the resulting method is incremental. The algorithm guarantees equilibrium and compatibility at the nodes in the final deformed configuration and allows us to deal with problems undergoing large displacements without it being necessary to change the initial discretization of the boundary of the bodies. Only the frictionless static problem is dealt with, and the proposed algorithm is applied to the most representative receding contact problem: a layer pressed against an elastic foundation. The results obtained when the displacements are small are in good agreement with the analytical solution. When large displacements are considered, another nonlinearity appears and its influence will be shown in this paper. 相似文献
11.
S. Kweon A. A. Benzerga 《International journal for numerical methods in engineering》2013,94(10):895-919
This paper presents a time‐integration method for a viscoplastic physics‐based polymer model at finite strains. The macromolecular character of the model resides in (i) the viscoplastic law based on a double‐kink molecular mechanism, and (ii) a full chain network model inspired by rubber elasticity to describe the large‐strain orientation hardening. A back stress enters the constitutive model formulation. Essential aspects of a three‐dimensional finite‐element implementation are outlined, the main novelty being in the back stress formulation. The computational efficiency and accuracy of the algorithm are examined in a series of parameter studies. In addition, because a co‐rotational formulation of the constitutive equations is employed using the Jaumann rate in the hypoelastic equation and the back stress evolution equation a detailed analysis of stress oscillations is carried out up to very large strains in simple shear. Subsequently, three‐dimensional FE analyses of compression with friction and instability propagation in tension are used as a means to demonstrate the robustness of the implementation and the potential occurrence of stress oscillations and shear bands in large‐strain analyses. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
12.
13.
C. C. Celigoj 《International journal for numerical methods in engineering》2001,50(4):899-918
Analyzing axisymmetric solids under torsional loading the 3d(imensional) problem can always be reduced by one dimension, since the displacement field and the rotation field are independent of the cylindrical (angle) co‐ordinate Θ, respectively. For this purpose a four‐node ring‐element for finite deformation axisymmetric and torsional problems was recently developed and is now going to be up‐dated. The original assumption of the enhanced displacement gradient H̃ = α i⊗ G i is expanded in two steps according to Simo, Armero and Taylor and to Glaser and Armero, respectively: firstly in defining the additional unknowns (parameters) α i as objects in the material configuration and pushing forward H̃ by ( 1 + U ⊗ Grad ) ∣ξ=0—this provides ‘objectivity’—and secondly in replacing α i⊗ G i by G i⊗ α i. Numerical results of three classical benchmarks, the in‐plane torsion test, the copper rod impact and the thermomechanical localization of a rectangular strip are presented. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
14.
Jens Wackerfuß 《International journal for numerical methods in engineering》2009,77(7):969-997
In molecular mechanics, the formalism of the finite element method can be exploited in order to analyze the behavior of atomic structures in a computationally efficient way. Based on the atom‐related consideration of the atomic interactions, a direct correlation between the type of the underlying interatomic potential and the design of the related finite element is established. Each type of potential is represented by a specific finite element. A general formulation that unifies the various finite elements is proposed. Arbitrary diagonal‐ and cross‐terms dependent on bond length, valence angle, dihedral angle, improper dihedral angle and inversion angle can also be considered. The finite elements are formulated in a geometrically exact setting; the related formulas are stated in detail. The mesh generation can be performed using well‐known procedures typically used in molecular dynamics. Although adjacent elements overlap, a double counting of the element contributions (as a result of the assembly process) cannot occur a priori. As a consequence, the assembly process can be performed efficiently line by line. The presented formulation can easily be implemented in standard finite element codes; thus, already existing features (e.g. equation solver, visualization of the numerical results) can be employed. The formulation is applied to various interatomic potentials that are frequently used to describe the mechanical behavior of carbon nanotubes. The effectiveness and robustness of this method are demonstrated by means of several numerical examples. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
15.
İ Temizer 《International journal for numerical methods in engineering》2014,97(8):582-607
A computational homogenization framework is developed in the context of the thermomechanical contact of two boundary layers with microscopically rough surfaces. The major goal is to accurately capture the temperature jump across the macroscopic interface in the finite deformation regime with finite deviations from the equilibrium temperature. Motivated by the limit of scale separation, a two‐phase thermomechanically decoupled methodology is introduced, wherein a purely mechanical contact problem is followed by a purely thermal one. In order to correctly take into account finite size effects that are inherent to the problem, this algorithmically consistent two‐phase framework is cast within a self‐consistent iterative scheme that acts as a first‐order corrector. For a comparison with alternative coupled homogenization frameworks as well as for numerical validation, a mortar‐based thermomechanical contact algorithm is introduced. This algorithm is uniformly applicable to all orders of isogeometric discretizations through non‐uniform rational B‐spline basis functions. Overall, the two‐phase approach combined with the mortar contact algorithm delivers a computational framework of optimal efficiency that can accurately represent the geometry of smooth surface textures. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
16.
J. F. Molinari M. Ortiz 《International journal for numerical methods in engineering》2002,53(5):1101-1126
This paper is concerned with the development of a general framework for adaptive mesh refinement and coarsening in three‐dimensional finite‐deformation dynamic–plasticity problems. Mesh adaption is driven by a posteriori global error bounds derived on the basis of a variational formulation of the incremental problem. The particular mesh‐refinement strategy adopted is based on Rivara's longest‐edge propagation path (LEPP) bisection algorithm. Our strategy for mesh coarsening, or unrefinement, is based on the elimination of elements by edge‐collapse. The convergence characteristics of the method in the presence of strong elastic singularities are tested numerically. An application to the three‐dimensional simulation of adiabatic shear bands in dynamically loaded tantalum is also presented which demonstrates the robustness and versatility of the method. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
17.
C. C. Celigoj 《International journal for numerical methods in engineering》1998,43(8):1369-1382
When analyzing axisymmetric solids under torsion the possible reduction of the problem by one dimension, say the independence of the displacement- and rotation-field of the cylindrical (angle) co-ordinate Θ, should always be exploited. Whereas in the geometrically linear range the purely torsional problem, described by the rotational angle χ only, is always decoupled from the purely axisymmetric problem, described by the radial and axial displacements u and v only, this is not the case in finite deformation torsional problems. Thus, the finite deformation axisymmetric finite element with five enhanced gradient parameters can easily be extended to a finite deformation axisymmetric and torsional finite element with seven enhanced gradient parameters. Numerical results of two classical benchmarks, the in-plane torsion test and the necking of a circular bar, are presented. © 1998 John Wiley & Sons, Ltd. 相似文献
18.
19.
Piotr Kowalczyk 《International journal for numerical methods in engineering》2006,66(8):1234-1270
Implicit time integration algorithm derived by Simo for his large‐deformation elasto‐plastic constitutive model is generalized, for the case of isotropy and associative flow rule, towards viscoplastic material behaviour and consistently differentiated with respect to its input parameters. Combining it with the general formulation of design sensitivity analysis (DSA) for non‐linear finite element transient equilibrium problem, we come at a numerically efficient, closed‐form finite element formulation of DSA for large deformation elasto‐plastic and elasto‐viscoplastic problems, with various types of design variables (material constants, shape parameters). The paper handles several specific issues, like the use of a non‐algorithmic coefficient matrix or sensitivity discontinuities at points of instantaneous structural stiffness change. Computational examples demonstrate abilities of the formulation and quality of results. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
20.
Alexander Popp Markus Gitterle Michael W. Gee Wolfgang A. Wall 《International journal for numerical methods in engineering》2010,83(11):1428-1465
In this paper, an approach for three‐dimensional frictionless contact based on a dual mortar formulation and using a primal–dual active set strategy for direct constraint enforcement is presented. We focus on linear shape functions, but briefly address higher order interpolation as well. The study builds on previous work by the authors for two‐dimensional problems. First and foremost, the ideas of a consistently linearized dual mortar scheme and of an interpretation of the active set search as a semi‐smooth Newton method are extended to the 3D case. This allows for solving all types of nonlinearities (i.e. geometrical, material and contact) within one single Newton scheme. Owing to the dual Lagrange multiplier approach employed, this advantage is not accompanied by an undesirable increase in system size as the Lagrange multipliers can be condensed from the global system of equations. Moreover, it is pointed out that the presented method does not make use of any regularization of contact constraints. Numerical examples illustrate the efficiency of our method and the high quality of results in 3D finite deformation contact analysis. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献