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1.
Ryan Alberdi Guodong Zhang Kapil Khandelwal 《International journal for numerical methods in engineering》2018,114(9):1018-1051
This study presents an isogeometric framework for incorporating representative volume element–based multiscale models into computational homogenization. First‐order finite deformation homogenization theory is derived within the framework of the method of multiscale virtual power, and Lagrange multipliers are used to illustrate the effects of considering different kinematical constraints. Using a Lagrange multiplier approach in the numerical implementation of the discrete system naturally leads to a consolidated treatment of the commonly employed representative volume element boundary conditions. Implementation of finite deformation computational strain‐driven, stress‐driven, and mixed homogenization is detailed in the context of isogeometric analysis (IGA), and performance is compared to standard finite element analysis. As finite deformations are considered, a numerical multiscale stability analysis procedure is also detailed for use with IGA. Unique implementation aspects that arise when computational homogenization is performed using IGA are discussed, and the developed framework is applied to a complex curved microstructure representing an architectured material. 相似文献
2.
等几何分析是近年来在有限元法基础上发展起来的一种新的数值方法,它消除了有限元的几何误差,具有高阶连续性。该文研究了三维结构等几何分析中NURBS几何体的表示方式及载荷、约束的施加方法,分别从计算精度和仿真效率两个方面对比了等几何分析的计算结果与有限元法一阶单元和二阶单元的计算结果,展示了等几何分析相对于标准有限元法的优势,并以厚壁圆筒模型算例验证了等几何分析的实用性。将NURBS单元应用于几何形状精度要求高的齿轮和变截面圆筒,数值结果表明三维NURBS等几何分析方法在复杂三维结构的仿真计算中具有较好的灵活性和适用性,可得到连续的应力场,有望在工程中得到广泛应用。 相似文献
3.
Julien Vignollet Stefan May René de Borst 《International journal for numerical methods in engineering》2015,102(11):1733-1749
Zero‐thickness interface elements are commonly used in computational mechanics to model material interfaces or to introduce discontinuities. The latter class requires the existence of a non‐compliant interface prior to the onset of fracture initiation. This is accomplished by assigning a high dummy stiffness to the interface prior to cracking. This dummy stiffness is known to introduce oscillations in the traction profile when using Gauss quadrature for the interface elements, but these oscillations are removed when resorting to a Newton‐Cotes integration scheme 1. The traction oscillations are aggravated for interface elements that use B‐splines or non‐uniform rational B‐splines as basis functions (isogeometric interface elements), and worse, do not disappear when using Newton‐Cotes quadrature. An analysis is presented of this phenomenon, including eigenvalue analyses, and it appears that the use of lumped integration (at the control points) is the only way to avoid the oscillations in isogeometric interface elements. New findings have also been obtained for standard interface elements, for example that oscillations occur in the relative displacements at the interface irrespective of the value of the dummy stiffness. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
4.
Simon Bieber Bastian Oesterle Ekkehard Ramm Manfred Bischoff 《International journal for numerical methods in engineering》2018,114(8):801-827
We present a variational method for problems in solid and structural mechanics that is designed to be intrinsically free from locking when using equal‐order interpolation for all involved fields. The specific feature of the formulation is that it avoids all geometrical locking effects (as opposed to material locking effects, for instance Poisson locking) for any type of structural or solid model, independent of the underlying discretization scheme. The possibility of employing equal‐order interpolation for all involved fields circumvents the task of finding particular function spaces to remove locking and avoid artificial stress oscillations. This is particularly attractive, for instance, for isogeometric analysis using unstructured meshes or T‐splines. Comprehensive numerical tests underline the promising behavior of the proposed method for geometrically linear and nonlinear problems in terms of displacements and stress resultants using standard finite elements, isogeometric finite elements, and a meshless method. 相似文献
5.
Nhon Nguyen-Thanh Weidong Li Jiazhao Huang Narasimalu Srikanth Kun Zhou 《International journal for numerical methods in engineering》2019,120(2):209-230
A collocation method has been recently developed as a powerful alternative to Galerkin's method in the context of isogeometric analysis, characterized by significantly reduced computational cost, but still guaranteeing higher-order convergence rates. In this work, we propose a novel adaptive isogeometric analysis meshfree collocation (IGAM-C) for the two-dimensional (2D) elasticity and frictional contact problems. The concept of the IGAM-C method is based upon the correspondence between the isogeometric collocation and reproducing kernel meshfree approach, which facilitates the robust mesh adaptivity in isogeometric collocation. The proposed method reconciles collocation at the Greville points via the discretization of the strong form of the equilibrium equations. The adaptive refinement in collocation is guided by the gradient-based error estimator. Moreover, the resolution of the nonlinear equations governing the contact problem is derived from a strong form to avoid the disadvantages of numerical integration. Numerical examples are presented to demonstrate the effectiveness, robustness, and straightforward implementation of the present method for adaptive analysis. 相似文献
6.
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
7.
Michael A. Scott Michael J. Borden Clemens V. Verhoosel Thomas W. Sederberg Thomas J. R. Hughes 《International journal for numerical methods in engineering》2011,88(2):126-156
We develop finite element data structures for T‐splines based on Bézier extraction generalizing our previous work for NURBS. As in traditional finite element analysis, the extracted Bézier elements are defined in terms of a fixed set of polynomial basis functions, the so‐called Bernstein basis. The Bézier elements may be processed in the same way as in a standard finite element computer program, utilizing exactly the same data processing arrays. In fact, only the shape function subroutine needs to be modified while all other aspects of a finite element program remain the same. A byproduct of the extraction process is the element extraction operator. This operator localizes the topological and global smoothness information to the element level, and represents a canonical treatment of T‐junctions, referred to as ‘hanging nodes’ in finite element analysis and a fundamental feature of T‐splines. A detailed example is presented to illustrate the ideas. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
8.
D. J. Benson Y. Bazilevs E. De Luycker M.‐C. Hsu M. Scott T. J. R. Hughes T. Belytschko 《International journal for numerical methods in engineering》2010,83(6):765-785
Many of the formulations of current research interest, including iosogeometric methods and the extended finite element method, use nontraditional basis functions. Some, such as subdivision surfaces, may not have convenient analytical representations. The concept of an element, if appropriate at all, no longer coincides with the traditional definition. Developing a new software for each new class of basis functions is a large research burden, especially, if the problems involve large deformations, non‐linear materials, and contact. The objective of this paper is to present a method that separates as much as possible the generation and evaluation of the basis functions from the analysis, resulting in a formulation that can be implemented within the traditional structure of a finite element program but that permits the use of arbitrary sets of basis functions that are defined only through the input file. Elements ranging from a traditional linear four‐node tetrahedron through a higher‐order element combining XFEM and isogeometric analysis may be specified entirely through an input file without any additional programming. Examples of this framework to applications with Lagrange elements, isogeometric elements, and XFEM basis functions for fracture are presented. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
9.
J. Vignollet S. May R. de Borst 《International journal for numerical methods in engineering》2016,108(9):990-1006
An isogeometric model is developed for the analysis of fluid transport in pre‐existing faults or cracks that are embedded in a fluid‐saturated deformable porous medium. Flow of the interstitial fluid in the porous medium and fluid transport in the discontinuities are accounted for and are coupled. The modelling of a fluid‐saturated porous medium in general requires the interpolation of the displacements of the solid to be one order higher than that of the pressure of the interstitial fluid. Using order elevation and Bézier projection, a consistent procedure has been developed to accomplish this in an isogeometric framework. Particular attention has also been given to the spatial integration along the isogeometric interface element in order to suppress traction oscillations that can arise for certain integration rules when a relatively high dummy stiffness is used in a poromechanical model. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd. 相似文献
10.
D. Briassoulis 《International journal for numerical methods in engineering》2002,54(3):421-452
The asymptotic behaviour is considered to be one of the most demanding levels of benchmark testing for shell elements. In the present paper, the asymptotic behaviour of classical benchmark problems is analytically and numerically investigated. The aim is to examine the possibility of using the classical benchmark tests for testing the asymptotic behaviour of shell elements. Appropriate analytical approaches are introduced to investigate the asymptotic behaviour of the classical benchmark problems. The reformulated four‐node shell element (RFNS) is employed in the numerical analyses. It is shown that the classical benchmark tests, in addition to testing the reliability and robustness of shell elements, also represent strong challenging tests for the asymptotic behaviour of shell elements. In the course of the numerical investigation of the asymptotic behaviour of the classical benchmark problems, the reliability and efficiency of the RFNS element already established by means of the classical configuration of the benchmark tests is re‐confirmed in all cases of the corresponding asymptotic test configurations. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
11.
D. Briassoulis 《International journal for numerical methods in engineering》2002,54(5):631-670
The asymptotic behaviour of classical benchmark tests was investigated in the first part of this work. In the present second part, the behaviour of some new limit problems, recently proposed as being specifically applicable to benchmark testing of the asymptotic behaviour of shell elements, is analytically and numerically investigated. Exact analytical solutions are obtained based on Flugge's theory for cylindrical shells. These analytical solutions are used along with, and in comparison to, the corresponding solutions obtained earlier by symbolic calculus using the Reissner–Mindlin shell model. The reformulated four‐node shell (RFNS) element is employed in the numerical analyses in a parallel, supportive–comparative character, next to the analytical investigation of the asymptotic behaviour of the new limit tests. As with the case of the classical benchmark tests, in the course of the numerical investigation, the reliability and efficiency of the RFNS element is re‐confirmed in all cases of the new asymptotic tests. A good agreement with the boundary layers described analytically is obtained even in very thin shell element applications. The various load‐carrying mechanisms shown numerically to be active in the cases under investigation follow closely the analytical predictions. The energy components appear to be more sensitive to the modelling of boundary layers in cases of mixed mode problems. In several cases, the solutions obtained earlier by using symbolic calculus are shown to be inadequate. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
12.
Karel Matou&#x; Philippe H. Geubelle 《International journal for numerical methods in engineering》2006,65(2):190-223
Interfacial damage nucleation and evolution in reinforced elastomers subjected to finite strains is modelled using the mathematical theory of homogenization based on the asymptotic expansion of unknown variables. The microscale is characterized by a periodic unit cell, which contains particles dispersed in a blend and the particle matrix interface is characterized by a cohesive law. A novel numerical framework based on the perturbed Petrov–Galerkin method for the treatment of nearly incompressible behaviour is employed to solve the resulting boundary value problem on the microscale and the deformation path of a macroscale particle is predefined as in the micro‐history recovery procedure. A fully implicit and efficient finite element formulation, including consistent linearization, is presented. The proposed multiscale framework is capable of predicting the non‐homogeneous micro‐fields and damage nucleation and propagation along the particle matrix interface, as well as the macroscopic response and mechanical properties of the damaged continuum. Examples are considered involving simple unit cells in order to illustrate the multiscale algorithm and demonstrate the complexity of the underlying physical processes. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
13.
Herman C. J. Bruneel Igor De Rycke 《International journal for numerical methods in engineering》2002,54(2):299-316
QuickTrace is a new, fast contact detection algorithm. It searches for contact typically between a tool, modelled by some kind of geometrical surface facets, and deforming material. Contact is searched for at material surface points called contact nodes. A contact node is in contact with a facet when the contact node is inside of the tool and the negative outer normal on the material surface at the contact node ‘leaves’ the tool surface through that facet. When multiple facets are intersected, only the closest facet to the contact node should be considered. From this definition of contact, the penetration depth results automatically as a by‐product. In QuickTrace, the m facets of the tool are packaged in boxes that are hierarchically ordered in a search tree with an average depth of log4 m. The computational complexity for one contact search is proportional to this average depth. So, for n contact nodes the computational complexity is O(n log4 m). This places QuickTrace amongst the best performing contact detection algorithms. At the same time there are no approximations or tricks involved and the contact detection is absolutely correct. The algorithm can easily be extended to material–material or tool–tool contact. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
14.
The paper presents a self-contained and didactic approach to the stochastic collocation method. The method relies on the Lagrange polynomials and the Gauss quadrature rule. It is presented for large classes of mechanical problems, i.e. static problems, dynamic problems and spectral problems. After a general presentation of each of them, examples and results are provided. Numerical results show the high rate of convergence of the proposed method. 相似文献
15.
Peter Otto Laura De Lorenzis Jörg F. Unger 《International journal for numerical methods in engineering》2020,121(6):1248-1267
In this paper, the impact problem and the subsequent wave propagation are considered. For the contact discretization an intermediate non-uniform rational B-spline (NURBS) layer is added between the contacting finite element bodies, which allows a smooth contact formulation and efficient element-based integration. The impact event is ill-posed and requires a regularization to avoid propagating stress oscillations. A nonlinear mesh-dependent penalty regularization is used, where the stiffness of the penalty regularization increases upon mesh refinement. Explicit time integration methods are well suited for wave propagation problems, but are efficient only for diagonal mass matrices. Using a spectral element discretization in combination with a NURBS contact layer the bulk part of the mass matrix is diagonal. 相似文献
16.
Hugo Casquero Lei Liu Carles Bona‐Casas Yongjie Zhang Hector Gomez 《International journal for numerical methods in engineering》2016,105(11):855-880
We present a hybrid variational‐collocation, immersed, and fully‐implicit formulation for fluid‐structure interaction (FSI) using unstructured T‐splines. In our immersed methodology, we define an Eulerian mesh on the whole computational domain and a Lagrangian mesh on the solid domain, which moves arbitrarily on top of the Eulerian mesh. Mathematically, the problem reduces to solving three equations, namely, the linear momentum balance, mass conservation, and a condition of kinematic compatibility between the Lagrangian displacement and the Eulerian velocity. We use a weighted residual approach for the linear momentum and mass conservation equations, but we discretize directly the strong form of the kinematic relation, deriving a hybrid variational‐collocation method. We use T‐splines for both the spatial discretization and the information transfer between the Eulerian mesh and the Lagrangian mesh. T‐splines offer us two main advantages against non‐uniform rational B‐splines: they can be locally refined and they are unstructured. The generalized‐α method is used for the time discretization. We validate our formulation with a common FSI benchmark problem achieving excellent agreement with the theoretical solution. An example involving a partially immersed solid is also solved. The numerical examples show how the use of T‐junctions and extraordinary nodes results in an accurate, efficient, and flexible method. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
17.
《International journal for numerical methods in engineering》2018,114(12):1310-1330
In this paper, we propose a novel approach to combine two complementary numerical models of the dynamical behaviour of mechanical systems: primal (compatible) and dual (equilibrated). This combined model provides an improved estimate of the eigenfrequencies of the system by feeding each model with information from the other. Numerical solutions obtained from both the fundamental models and from the proposed approach are presented and studied. This approach will be applicable to any eigenvalue problem associated with a PDE that can be expressed by complementary numerical models. 相似文献
18.
Hongguan Zhang Tadahiro Shibutani 《International journal for numerical methods in engineering》2019,118(1):18-37
In this paper, a new method is proposed that extend the classical deterministic isogeometric analysis (IGA) into a probabilistic analytical framework in order to evaluate the uncertainty in shape and aim to investigate a possible extension of IGA in the field of computational stochastic mechanics. Stochastic IGA (SIGA) method for uncertainty in shape is developed by employing the geometric characteristics of the non-uniform rational basis spline and the probability characteristics of polynomial chaos expansions (PCE). The proposed method can accurately and freely evaluate problems of uncertainty in shape caused by deformation of the structural model. Additionally, we use the intrusive formulation approach to incorporate PCE into the IGA framework, and the C++ programming language to implement this analysis procedure. To verify the validity and applicability of the proposed method, two numerical examples are presented. The validity and accuracy of the results are assessed by comparing them to the results obtained by Monte Carlo simulation based on the IGA algorithm. 相似文献
19.
Klaus‐Jürgen Bathe Dominique Chapelle Phill‐Seung Lee 《International journal for numerical methods in engineering》2003,57(8):1039-1052
In general, shell structural problems can be identified to fall into one of the categories of membrane‐dominated, bending‐dominated and mixed shell problems. The asymptotic behaviour with a well‐defined load‐scaling factor shows distinctly into which category a given shell problem falls. The objective of this paper is to present a shell problem and its solution for which there is no convergence to a well‐defined load‐scaling factor as the thickness of the shell decreases. Such shells are unduly sensitive in their behaviour because the ratio of membrane to bending energy stored changes significantly and indeed can fluctuate with changes in shell thickness. We briefly review the different asymptotic behaviours that shell problems can display, and then present the specific problem considered and its numerical solution using finite element analysis. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
20.
Hideaki Kaneko Peter A. Padilla 《International journal for numerical methods in engineering》1999,45(4):491-495
In this note, we make a few comments concerning the paper of Hughes and Akin (Int. J. Numer. Meth. Engng., 15 , 733–751 (1980)). Our primary goal is to demonstrate that the rate of convergence of numerical solutions of the finite element method with singular basis functions depends upon the location of additional collocation points associated with the singular elements. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献