Time discontinuous Galerkin methods with energy decaying correction for non‐linear elastodynamics

In this paper a new time discontinuous Galerkin (TDG) formulation for non‐linear elastodynamics is presented. The new formulation embeds an energy correction which ensures truly energy decaying, thus allowing to achieve unconditional stability that, as shown in the paper, is not guaranteed by the classical TDG formulation. The resulting method is simple and easily implementable into existing finite element codes. Moreover, it inherits the desirable higher‐order accuracy and high‐frequency dissipation properties of the classical formulation. Numerical results illustrate the very good performance of the proposed formulation. Copyright © 2010 John Wiley & Sons, Ltd.     

任意荷载作用下结构动力响应的并行算法

介绍计算任意荷载作用下线性结构动力响应的精细时程积分及其并行算法。离散化结构的动力响应方程通过变量变换可以转换为一阶线性常微分方程组，该方程组的解由表示初值影响的齐次方程解和反映荷载作用的积分之和构成。上述第一项用矩阵指数函数计算，第二项在本文中用数值积分计算。这种算法很适应并行计算，已在ＴＲＡＮＳＰＵＴＥＲ并行机上实现。     

结构随机响应的并行计算

本文对结构在地震载荷下的非平稳随机响应作了研究，把地震载荷用不同频率虚拟激励替代，采用精细时程积分进行分析，着重研究了这一算法的并行性，设计了高效并行算法，并在ＴＲＡＮＳＰＵＴＥＲ并行机上实现了该算法。     

Multi‐time‐step and two‐scale domain decomposition method for non‐linear structural dynamics

In this paper we propose a method to improve the means of taking into account the specific time‐scale and space‐scale characteristics in time‐dependent non‐linear problems. This method enables the use of arbitrary time steps in each subdomain: these can be coupled by prescribing continuous velocities at the interfaces, which are modelled using a dual Schur formulation. For certain subdomains, in space, we adopt a two‐scale resolution technique inspired by the multigrid methods in order to obtain the part of the solution related to small variation lengths on a refined scale and the part corresponding to large variation lengths on a coarse scale. For non‐linear problems, we propose an algorithm with a single iteration level to deal with both the non‐linear equilibrium and the two space scales thanks to a two‐grid method in which the relaxation steps are performed using a non‐linear, preconditioned conjugate gradient algorithm. Finally, we present an example which demonstrates the feasibility of the method. Copyright © 2003 John Wiley & Sons, Ltd.     

An effective data parallel self-starting explicit methodology for computational structural dynamics on the connection machine CM-5

This paper discusses the implementation aspects and our experiences towards a data parallel explicit self-starting finite element transient methodology with emphasis on the Connection Machine (CM-5) for linear and non-linear computational structural dynamic applications involving structured and unstructured grids. The parallel implementation criteria that influence the efficiency of an algorithm include the amount of communication, communication routing, and load balancing. To provide simplicity, high level of accuracy, and to retain the generality of the finite element implementation for both linear and non-linear transient explicit problems on a data parallel computer which permit optimum amount of communications, we implemented the present self-starting dynamic formulations (in comparison to the traditional approaches) based on nodal displacements, nodal velocities, and elemental stresses on the CM-5. Data parallel language CMFortran is employed with virtual processor constructs and with:SERIAL and:PARALLEL layout directives for arrays. The communications via the present approach involve only one gather operation (extraction of element nodal displacements or velocities from global displacement vector) and one scatter operation (dispersion of element forces onto global force vector) for each time step. These gather and scatter operations are implemented using the Connection Machine Scientific Software Library communication primitives for both structured and unstructured finite element meshes. The implementation aspects of the present self-starting formulations for linear and elastoplastic applications on serial and data parallel machines are discussed. Numerical test models for linear and non-linear one-dimensional applications and a two-dimensional unstructured finite element mesh are then illustrated and their performance studies are discussed.     

Local modal reduction in explicit dynamics with domain decomposition. Part 1: extension to subdomains undergoing finite rigid rotations

We present an extension of the dual Schur multidomain method with local linear modal reduction previously introduced by Gravouil, Combescure, Herry and Faucher to the case of modal reduction on geometrically non‐linear vibrating subdomains. This first part of a two‐part paper describes a new formalism, based on an original set of parameters, to represent a subdomain's finite rigid‐body motion. Special attention is paid to the stability issues with time integration using the central difference scheme. The method is validated on an academic example and its efficiency is demonstrated on a large‐scale example. Copyright © 2004 John Wiley & Sons, Ltd.