检索结果-内蒙古大学图书馆

Energy-dissipative momentum-conserving time-stepping algorithms for finite strain multiplicative plasticity

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2006年第37-40期195卷 4862-4889页

作者： Armero, F. Univ Calif Berkeley Dept Civil & Environm Engn Berkeley CA 94720 USA

This paper presents a new energy-dissipative momentum-conserving algorithm for multiplicative models of finite strain plasticity. The proposed scheme preserves exactly the conservation laws of linear and angular momenta, and leads to the exact energy dissipation between the two computed solutions in a given time step. In particular, the energy is exactly conserved if the step is elastic, thus recovering existing energy-momentum-conserving schemes in the purely elastic range. Extensions accommodating a strictly non-negative numerical energy dissipation in the high-frequency to handle the numerical stiffness of the problem are also discussed briefly. These conservation/dissipation properties are proven rigorously in the very nonlinear setting of multiplicative finite strain plasticity. In fact, the analysis drives the design of the new return mapping algorithm proposed to integrate the plastic evolution equations so the above dissipation/conservation properties hold. These analyses account for the spatial discretization of the problem in the context of the finite element method. Several representative numerical simulations are presented to illustrate the performance of the new algorithm. (c) 2005 Elsevier B.V. All rights reserved.

关键词： finite strain plasticity multiplicative plasticity nonlinear dynamics time-stepping algorithms energy-momentum schemes finite elements

来源：评论

学校读者我要写书评

暂无评论

On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part I: low-order methods for two model problems and nonlinear elastodynamics

引用

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2001年第20-21期190卷 2603-2649页

作者： Armero, F Romero, I Univ Calif Berkeley Dept Civil & Environm Engn Berkeley CA 94720 USA

We present in this paper the development of a class of time-stepping algorithms for nonlinear elastodynamics that exhibits the controllable numerical dissipation in the high-frequency range required for the robust solution of the resulting numerically stiff systems. To motivate and illustrate better the developments in this general case, we present first the formulation and analysis of these methods for two simple model problems. Namely, we consider a nonlinear elastic spring/mass system and a simplified model of thin elastic beams. As it is discussed in detail in this paper, the conservation by the numerical algorithm of the momenta and corresponding relative equilibria of these characteristic Hamiltonian systems with symmetry is of the main importance. These conservation properties lead for a fixed and finite time step to a correct qualitative picture of the phase space where the discrete dynamics takes place, even in the presence of the desired and controlled numerical dissipation of the energy. This situation is contrasted with traditional "dissipative" numerical schemes, which are shown through rigorous analyses to not only lose their dissipative character in the general nonlinear range, but also the aforementioned conservation properties, thus leading to a qualitatively distorted approximation of the phase dynamics. The key for a successful algorithm in this context is the incorporation of the numerical dissipation in the internal modes of the motion while not affecting the group motions of the systems. The algorithms presented in this work accomplish these goals. The focus in this first part is given to first-order methods. Representative numerical simulations, ranging from applications in nonlinear structural dynamics to nonlinear continuum three-dimensional elastodynamics, are presented in the context of the finite element method to illustrate these ideas and results. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： nonlinear elastodynamics time-stepping algorithms high-frequency dissipation relative equilibria finite element method

来源：评论

学校读者我要写书评

暂无评论

The iterative group implicit algorithm for parallel transient finite element analysis

引用

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2000年第4期47卷 869-885页

作者： Modak, S Sotelino, ED Purdue Univ Sch Civil Engn W Lafayette IN 47907 USA Comp & Struct Inc Berkeley CA USA

The Iterative Group Implicit (IGI) algorithm is developed for the parallel solution of general structural dynamic problems. In this method the original structure is partitioned into a number of a subdomains. Each subdomain is solved independently and therefore concurrently, using any traditional direct solution method. The IGI algorithm is an extension of the Group Implicit (GI) algorithm, and similarly to that method compatibility of the interface degrees of freedom is restored using a mass averaging rule. However, unlike the GI algorithm, in the IGI algorithm an iterative procedure is devised to restore equilibrium at the interface degrees of freedom. The IGI method has the same algorithmic characteristics as the underlying solution method used to solve each subdomain. Furthermore, the solution obtained by this method, once the iteration converges, is the same as the one obtained if the subdomain solution method is used to solve the whole structure. Numerical studies are carried out which demonstrate that the performance of the IGI algorithm is superior to that of the GI algorithm both in terms of accuracy and efficiency. Finally, the IGI method is highly modular and scalable, and therefore very well suited for distributed and parallel computing. Copyright (C) 2000 John Wiley & Sons, Ltd.

关键词： parallel processing distributed computing structural dynamics transient finite element analysis time-stepping algorithms

来源：评论

学校读者我要写书评

暂无评论

A new dissipative time-stepping algorithm for frictional contact problems:: formulation and analysis

引用

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 1999年第1-2期179卷 151-178页

作者： Armero, F Petöcz, E Univ Calif Berkeley Dept Civil & Environm Engn Berkeley CA 94720 USA

This paper presents a new time-stepping algorithm for frictional contact problems that exhibits unconditional positive energy dissipation. More specifically, the proposed scheme preserves a priori stability estimates of the continuum problem for both frictionless and frictional contact, leading to improved numerical stability properties in particular. For the normal contact component, the algorithm exhibits full energy conservation between released stales, while the energy does not increase over its initial value due to the enforcement of the normal contact constraint during persistent contact. A penalty regularization is considered to this purpose. A new regularization of the stick conditions is considered for the frictional part. The new scheme is shown rigorously to exhibit positive energy dissipation like the continuum physical problem in this frictional case. Coulomb friction is assumed. Complete analyses of these considerations, as well as a detailed description of their finite element implementation are included in the general finite deformation range. Representative numerical simulations are presented to assess the performance of the newly proposed methods. (C) 1999 Elsevier Science S.A. All rights reserved.

关键词： frictional contact/impact of solids time-stepping algorithms finite element method

来源：评论

学校读者我要写书评

暂无评论

Energy-momentum consistent finite element discretization of dynamic finite viscoelasticity

引用

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2010年第11期81卷 1341-1386页

作者： Gross, M. Betsch, P. Univ Siegen Dept Mech Engn Chair Computat Mech D-57068 Siegen NRW Germany

This paper is concerned with energy-momentum consistent time discretizations of dynamic finite viscoelasticity. Energy consistency means that the total energy is conserved or dissipated by the fully discretized system in agreement with the laws of thermodynamics. The discretization is energy-momentum consistent if also momentum maps are conserved when group motions are superimposed to deformations. The performed approximation is based on a three-field formulation, in which the deformation field. the velocity field and a strain-like viscous internal variable field are treated as independent quantities. The new nonlinear viscous evolution equation satisfies a non-negative viscous dissipation not only in the continuous case, but also in the fully discretized system. The initial boundary value problem is discretized by using finite elements in space and time. Thereby, the temporal approximation is performed prior to the spatial approximation in order to preserve the stress objectivity for finite rotation increments (incremental objectivity). Although the present approach makes possible to design schemes of arbitrary order, the focus is on finite elements relying on linear Lagrange polynomials for the sake of clearness. The discrete energy-momentum consistency is based on the collocation property and an enhanced second Piola-Kirchhoff stress tensor. The obtained coupled non-linear algebraic equations are consistently linearized. The corresponding iterative solution procedure is associated with newly proposed convergence criteria, which take the discrete energy consistency into account. The iterative solution procedure is therefore not complicated by different scalings in the independent variables, since the motion of the element is taken into account for solving the viscous evolution equation. Representative numerical simulations with various boundary conditions show the superior stability of the new time-integration algorithm in comparison with the ordinary midpoint rul

关键词： finite viscoelasticity space-time finite element methods time-stepping algorithms energy-momentum consistency consistent linearization scaling-free convergence criteria

来源：评论

学校读者我要写书评

暂无评论

Volume-preserving energy-momentum schemes for isochoric multiplicative plasticity

引用

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2007年第41-44期196卷 4130-4159页

作者： Armero, F. Zambrana-Rojas, C. Univ Calif Berkeley Dept Civil & Environm Engn Berkeley CA 94720 USA

This paper presents a new energy-dissipative momentum-conserving algorithm for multiplicative finite strain plasticity (F = (FFp)-F-e )that also preserves exactly the plastic volume for isochoric plastic models. The new algorithm exhibits exactly the conservation laws of linear and angular momentum of the underlying physical problem as well as its energy evolution. A strictly positive energy dissipation, in fact the exact energy dissipation, is obtained by design during plastic steps while enforcing the plastic consistency (i.e. the yield condition) on the final stress appearing in the equations of motion. Exact energy conservation is attained, in particular, during elastic steps. The aforementioned preservation of the plastic volume is obtained by a new treatment of the geometric structure behind the considered multiplicative models of finite strain plasticity. Namely, we present a new approximation of the reference and elastic metrics whose contractions with the incremental total and elastic strains lead exactly to the increment of the total and elastic natural volumetric strains, respectively. The elastic metric is defined in the intermediate configuration, defined itself by the proper discrete approximation in time of the plastic deformation gradient F-p. The new algorithm extends to the plastic range existing energy-momentum-conserving schemes for nonlinear elastic problems, but incorporating a new modified elastic stress formula consistent with this new geometric setting. The inherited conservation laws of momenta and, especially, the non-negative character of the energy dissipation leads to an improved performance over existing, more classical schemes showing numerical instabilities in the considered highly nonlinear geometric setting of large deformations and strains. Several numerical simulations are presented illustrating these properties. (c) 2007 Elsevier B.V. All rights reserved.

关键词： finite strain multiplicative plasticity nonlinear dynamics time-stepping algorithms energy-momentum schemes return mapping algorithms

来源：评论

学校读者我要写书评

暂无评论

An object-oriented programming framework for the parallel dynamic analysis of structures

引用

COMPUTERS & STRUCTURES 2002年第1期80卷 77-84页

作者： Modak, S Sotelino, ED Purdue Univ Sch Civil Engn W Lafayette IN 47907 USA Comp & Struct Inc Berkeley CA 94704 USA

This work addresses the time history analysis of structures subjected to dynamic loads using high performance computing environments. Structural mechanics, parallel computing, and object-oriented programming methodologies are integrated to design and implement frameworks for parallel and sequential transient finite element analysis (TFE++ and PTFE++). The object-oriented approach is employed to facilitate extensibility, reusability, maintainability and simplicity of the resulting software. Parallel processing concepts and algorithms are used in the design of PTFE++. An application has been developed to demonstrate the developed frameworks. It has been found that PTFE++ provides an efficient way to analyze large structural systems. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： parallel processing distributed computing object-oriented programming structural dynamics transient finite element analysis time-stepping algorithms

来源：评论

学校读者我要写书评

暂无评论

time-discretized variational formulation of non-smooth frictional contact

引用

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2002年第8期53卷 1801-1829页

作者： Pandolfi, A Kane, C Marsden, JE Ortiz, M CALTECH Grad Aeronaut Labs Firestone Flight Sci Lab Pasadena CA 91125 USA Politecn Milan Dipartimento Ingn Strutturale I-20133 Milan Italy

The present work extends the non-smooth contact class of algorithms introduced by Kane et al. to the case of friction. The formulation specifically addresses contact geometries, e.g. involving multiple collisions between tightly packed non-smooth bodies, for which neither normals nor gap functions can be properly defined. A key aspect of the approach is that the incremental displacements follow from a minimum principle. The objective function comprises terms which account for inertia, strain energy, contact, friction and external forcing. The Euler-Lagrange equations corresponding to this extended variational principle are shown to be consistent with the equations of motion of solids in frictional contact. In addition to its value as a basis for formulating numerical algorithms, the variational framework offers theoretical advantages as regards the selection of trajectories in cases of non-uniqueness. We present numerical and analytical examples which demonstrate the good momentum and energy conservation characteristics of the numerical algorithms, as well as the ability of the approach to account for stick and slip conditions. Copyright (C) 2001 John Wiley Sons, Ltd.

关键词： non-smooth frictional contact incremental variational formulation time-stepping algorithms closest point projection non-smooth analysis

来源：评论

学校读者我要写书评

暂无评论

The generalized method for structural dynamics applications

引用

ADVANCES IN ENGINEERING SOFTWARE 2002年第7-10期33卷 565-575页

作者： Modak, S Sotelino, ED Purdue Univ Sch Civil Engn W Lafayette IN 47907 USA Comp & Struct Inc R&D Berkeley CA USA

A new single-step time-integration method for solving structural dynamics problems, termed generalized method, has been developed. Most of the existing single-step solution algorithms are special cases of this method. The derivation of the generalized method starts with the Taylor series approximations of the displacement, velocity, and acceleration between two time-stations. Equilibrium is satisfied in a weighted-average sense over the time-step by means of a weak form of the Galerkin procedure. The displacement, velocity, and acceleration are updated using the truncated Taylor series expressions. Numerical tests have been carried out to demonstrate the validity of the developed method. (C) 2002 Civil-Comp Ltd and Elsevier Science Ltd. All rights reserved.

关键词： implicit time-integration time-stepping algorithms structural dynamics transient finite element analysis

来源：评论

学校读者我要写书评

暂无评论

The generalized method for structural dynamics applications

The generalized method for structural dynamics applications

引用

2nd International Conference on Engineering Computational Technology/5th International Conference on Computational Structures Technology

作者： Modak, S Sotelino, ED Purdue Univ Sch Civil Engn W Lafayette IN 47907 USA Comp & Struct Inc R&D Berkeley CA USA

关键词： implicit time-integration time-stepping algorithms structural dynamics transient finite element analysis

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：