Goal-Oriented Error Estimation Applied to Direct Solution of Steady-State Analysis With Frequency Domain Finite Element Method
-
摘要: 研究了针对频域有限元直接动态分析的面向目标误差估计以及误差范围估计计算方法.面向目标的误差估计方法就是专门针对如何准确和经济地估算特定值误差的一种方法,利用原问题的共轭偶问题进行计算.频域有限元的直接动态分析是模拟频域扫描实验的一种计算方法,专门针对谐振激励的线性动态响应问题,利用将原自由度分解为实部和虚部描述频率的变化,从而计算变形体的动态响应.利用扩展针对有限元的面向目标误差估计的自由度,将该方法应用到直接动态分析中进行误差估计.通过建立同时包含实部和虚部自由度的能量弱形式及偶问题,并将其数值实现,估算频域直接动态分析有限元解的误差及误差范围,并通过悬臂梁的激振算例进行了验证.Abstract: Based on the concept of constitutive relation error along with residual of both origin and dual problems, a goal-oriented error estimation method with extended degrees of freedom was developed. It leads to the high quality local error bounds in the problem of direct-solution steady-state dynamic analysis with frequency domain finite element, which involves enrichments with plural variable basis functions. The solution of steadystate dynamic procedure calculated the harmonic response directly in terms of the physical degrees of freedom in the model, which used mass, damping, and stiffness matrices of the system. An enriched form of goal-oriented error estimation aiming at this frequency calculation was formed and implemented. A three dimensional finite element example was carried out to illustrate the computational procedures.
-
[1] Zhang R, Zhang C, Jiang J. A new approach to direct solution of 2D heat transfer problem with non-linear source-terms in frequency domain[J].International Journal of Nonlinear Sciences and Numerical Simulation, 2006, 7(3):295-298. [2] Ainsworth M, Oden J T. A posteriori error estimation in finite element analysis[J].Comput Methods Appl Mech Engrg, 1997, 142(1/2):1-88. [3] Oden J T, Prudhomme S. Estimation of modeling error in computational mechanics[J].Journal of Computational Physics, 2002, 182(2): 496-515. [4] Ladeveze P, Rougeota Ph, Blanchardb P, Moreaub J P. Local error estimators for finite element linear analysis[J].Comput Methods Appl Mech Engrg, 1999, 176(1/4):231-246. [5] Grtsch T, Bathe K J. A posteriori error estimation techniques in practical finite element analysis[J].Computers and Structures, 2005, 83(4/5):235-265. [6] Schleupen A, Ramm E. Local and global error estimations in linear structural dynamics[J].Computers and Structures, 2000, 76(6):741-756. [7] Larsson F, Hansbo P, Runesson K. Strategies for computing goal-oriented a posteriori error measures in non-linear elasticity[J].Int J Numer Meth Engng, 2002, 55(8):879-894. [8] van der Zee K G, Verhoosel C V. Isogeometric analysis-based goal-oriented error estimation for free-boundary problems[J].Finite Elements in Analysis and Design, 2011, 47(6):600-609. [9] van der Zee K G, Oden J T, Prudhomme S, Hawkins-Daarud A. Goal-oriented error estimation for Cahn-Hilliard models of binary phase transition[J].Numerical Methods for Partial Differential Equations, 2011, 27(1):160-196. [10] Ni Y Q, Zheng G, Ko J M. Nonlinear periodically forced vibration of stay cables[J].Transactions of the ASME. Journal of Vibration and Acoustics, 2004, 126(2):245-252. [11] Challamel N. On the comparison of Timoshenko and shear models in beam dynamics[J].Journal of Engineering Mechanics, ASCE, 2006,132(10): 1141- 1146. [12] Han S M, Benaoya H, Wei T. Dynamics of transversely vibration beams using four engineering theories[J].Journal of Sound and Vibration, 1999, 225(5): 935- 988. [13] Oden J T, Prudhomme S, Bauman P. On the extension of goal-oriented error estimation and hierarchical modeling to discrete lattice models[J].Comput Methods Appl Mech Engrg, 2005,194(34/35):3668-3688. [14] Fuentes D, Littlefield D, Oden J T, Prudhomme S. Extensions of goal-oriented error estimation methods to simulations of highly-nonlinear response of shock-loaded elastomer-reinforced structures[J]. Comput Methods Appl Mech Engrg, 2006, 195(37/40): 4659-4680. [15] Prudhomme S, Oden J T. On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors[J]. Comput Methods Appl Mech Engrg, 1999, 176(1/4):313-331. [16] Oden J T, Prudhomme S. Goal-oriented error estimation and adaptivity for the finite element method[J]. Computers and Mathematics With Applications, 2001, 41(5/6): 735-756. [17] Rüter M, Stein E. Goal-oriented a posteriori error estimates in linear elastic fracture mechanics[J].Computer Methods in Applied Mechanics and Engineering, 2006, 195(4/6):251-278. [18] Chamoina L, Ladevèze P. Strict and practical bounds through a non-intrusive and goal-oriented error estimation method for linear viscoelasticity problems[J].Finite Elements in Analysis and Design, 2009, 45(4): 251-262. [19] Fang F, Pain C C, Navon I M, Gorman G J, Piggott M D, Allison P A, Goddard A J H. A POD goal-oriented error measure for mesh optimization[J]. Int J Numer Meth Fluids, 2010, 63(2):185-206. [20] Pannachet T, Díez P, Askes H, Sluys L J. Error assessment and mesh adaptivity for regularized continuous failure models[J]. Comput Methods Appl Mech Engrg, 2010, 199(17/20): 961-978. [21] Panetier J, Ladeveze P, Chamoin L. Strict and effective bounds in goal-oriented error estimation applied to fracture mechanics problems solved with XFEM[J]. Int J Numer Meth Engng, 2010, 81(6):671-700. [22] Pardo D. multigoal-oriented adaptivity for hp-finite element methods[J]. Procedia Computer Science, 2010, 1(1):1953-1961.
点击查看大图
计量
- 文章访问数: 1494
- HTML全文浏览量: 122
- PDF下载量: 804
- 被引次数: 0