Computational Continuum Mechanics: Computational Geometry and Finite Element Analysis

This book presents the nonlinear theory of continuum mechanics and demonstrates its use in developing nonlinear computer formulations for large displacement dynamic analysis. Basic concepts used in continuum mechanics are presented and used to develop nonlinear general finite element formulations that can be effectively used in large displacement analysis. The book considers two nonlinear finite element dynamic formulations: a general large-deformation finite element formulation and then a formulation that can efficiently solve small deformation problems that characterize very and moderately stiff structures. The book presents material clearly and systematically, assuming the reader has only basic knowledge in matrix and vector algebra and dynamics. The book is designed for use by advanced undergraduates and first-year graduate students. It is also a reference for researchers, practicing engineers, and scientists working in computational mechanics, bio-mechanics, computational biology, multibody system dynamics, and other fields of science and engineering using the general continuum mechanics theory.

[1]  Thomas J. R. Hughes,et al.  Improved numerical dissipation for time integration algorithms in structural dynamics , 1977 .

[2]  H. R. Milner,et al.  Accurate finite element analysis of large displacements in skeletal frames , 1981 .

[3]  E. P. Popov,et al.  Accuracy and stability of integration algorithms for elastoplastic constitutive relations , 1985 .

[4]  A. Shabana,et al.  Dynamic analysis of multibody systems using component modes , 1985 .

[5]  A. A. Shabana.  Automated Analysis of Constrained Systems of Rigid and Flexible Bodies , 1985 .

[6]  S. S. Kim,et al.  QR Decomposition for State Space Representation of Constrained Mechanical Dynamic Systems , 1986 .

[7]  J. C. Simo,et al.  A return mapping algorithm for plane stress elastoplasticity , 1986 .

[8]  J. G. Jalón,et al.  Dynamic Analysis of Three-Dimensional Mechanisms in “Natural” Coordinates , 1987 .

[9]  Charbel Farhat,et al.  A parallel active column equation solver , 1988 .

[10]  M. A. Serna,et al.  A modified Lagrangian formulation for the dynamic analysis of constrained mechanical systems , 1988 .

[11]  M. Géradin,et al.  A beam finite element non‐linear theory with finite rotations , 1988 .

[12]  C. Farhat,et al.  A method of finite element tearing and interconnecting and its parallel solution algorithm , 1991 .

[13]  Michel Géradin,et al.  A superelement formulation for mechanism analysis , 1992 .

[14]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

[15]  A. Shabana.  Finite Element Incremental Approach and Exact Rigid Body Inertia , 1995 .

[16]  O. Bauchau,et al.  Numerical integration of non‐linear elastic multi‐body systems , 1995 .

[17]  Charbel Farhat,et al.  Implicit time integration of a class of constrained hybrid formulations—Part I: Spectral stability theory , 1995 .

[18]  D. Hodges,et al.  Cross-sectional analysis of composite beams including large initial twist and curvature effects , 1996 .

[19]  Ahmed A. Shabana.  RESONANCE CONDITIONS AND DEFORMABLE BODY CO-ORDINATE SYSTEMS , 1996 .

[20]  Carlo L. Bottasso,et al.  Energy preserving/decaying schemes for non-linear beam dynamics using the helicoidal approximation , 1997 .

[21]  A. Shabana.  Computer Implementation of the Absolute Nodal Coordinate Formulation for Flexible Multibody Dynamics , 1998 .

[22]  O. Bauchau.  Computational Schemes for Flexible, Nonlinear Multi-Body Systems , 1998 .

[23]  M. Crisfield,et al.  Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[24]  A. Shabana,et al.  Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems , 2000 .

[25]  A. J. Chen,et al.  Finite Element Method in Dynamics of Flexible Multibody Systems: Modeling of Holonomic Constraints and Energy Conserving Integration Schemes , 2000 .

[26]  A. Shabana,et al.  DEVELOPMENT OF SIMPLE MODELS FOR THE ELASTIC FORCES IN THE ABSOLUTE NODAL CO-ORDINATE FORMULATION , 2000 .

[27]  Gregory M. Hulbert,et al.  A Gluing Algorithm for Network-Distributed Multibody Dynamics Simulation , 2001 .

[28]  Mohamed A. Omar,et al.  A TWO-DIMENSIONAL SHEAR DEFORMABLE BEAM FOR LARGE ROTATION AND DEFORMATION PROBLEMS , 2001 .

[29]  M. A. Crisfield,et al.  Dynamic analysis of 3D beams with joints in presence of large rotations , 2001 .

[30]  R. Y. Yakoub,et al.  Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Applications , 2001 .

[31]  R. Y. Yakoub,et al.  Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory , 2001 .

[32]  Peter Betsch,et al.  Constrained integration of rigid body dynamics , 2001 .

[33]  M. Borri,et al.  Integration of elastic multibody systems by invariant conserving/dissipating algorithms. II. Numerical schemes and applications , 2001 .

[34]  A. Shabana,et al.  Study of the Centrifugal Stiffening Effect Using the Finite Element Absolute Nodal Coordinate Formulation , 2002 .

[35]  Stefan von Dombrowski,et al.  Analysis of Large Flexible Body Deformation in Multibody Systems Using Absolute Coordinates , 2002 .

[36]  P. Betsch,et al.  A DAE Approach to Flexible Multibody Dynamics , 2002 .

[37]  P. Betsch,et al.  Frame‐indifferent beam finite elements based upon the geometrically exact beam theory , 2002 .

[38]  Ignacio Romero,et al.  Numerical integration of the stiff dynamics of geometrically exact shells: an energy‐dissipative momentum‐conserving scheme , 2002 .

[39]  Ignacio Romero,et al.  An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy–momentum conserving scheme in dynamics , 2002 .

[40]  Olivier A. Bauchau,et al.  Robust integration schemes for flexible multibody systems , 2003 .

[41]  G. Hulbert,et al.  Efficient numerical solution of constrained multibody dynamics systems , 2003 .

[42]  Oleg Dmitrochenko,et al.  Generalization of Plate Finite Elements for Absolute Nodal Coordinate Formulation , 2003 .

[43]  Aki Mikkola,et al.  A Non-Incremental Finite Element Procedure for the Analysis of Large Deformation of Plates and Shells in Mechanical System Applications , 2003 .

[44]  A. Mikkola,et al.  Description of Elastic Forces in Absolute Nodal Coordinate Formulation , 2003 .

[45]  A. Shabana,et al.  Use of the Finite Element Absolute Nodal Coordinate Formulation in Modeling Slope Discontinuity , 2003 .

[46]  Zheng-Dong Ma,et al.  A Gluing Algorithm for Distributed Simulation of Multibody Systems , 2003 .

[47]  Aki Mikkola,et al.  A Non-Incremental Nonlinear Finite Element Solution for Cable Problems , 2003 .

[48]  J. Mayo,et al.  Describing Rigid-Flexible Multibody Systems Using Absolute Coordinates , 2003 .

[49]  J. Mayo,et al.  Efficient Evaluation of the Elastic Forces and the Jacobian in the Absolute Nodal Coordinate Formulation , 2004 .

[50]  S. Leyendecker,et al.  Energy-conserving integration of constrained Hamiltonian systems – a comparison of approaches , 2004 .

[51]  Jeong-Hyun Sohn,et al.  Large Deflection Analysis of a Thin Plate: Computer Simulations and Experiments , 2004 .

[52]  J. Domínguez,et al.  An Internal Damping Model for the Absolute Nodal Coordinate Formulation , 2005 .

[53]  Johannes Gerstmayr,et al.  Deformation modes in the finite element absolute nodal coordinate formulation , 2006 .

[54]  Aki Mikkola,et al.  Development of elastic forces for a large deformation plate element based on the absolute nodal coordinate formulation , 2006 .

[55]  Johannes Gerstmayr,et al.  Analysis of Thin Beams and Cables Using the Absolute Nodal Co-ordinate Formulation , 2006 .

[56]  S. Leyendecker,et al.  Objective energy-momentum conserving integration for the constrained dynamics of geometrically exact beams , 2006 .

[57]  Hiroyuki Sugiyama,et al.  Coupled Deformation Modes in the Large Deformation Finite-Element Analysis: Problem Definition , 2007 .