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Finite Rotations (finite + rotation)
Selected AbstractsA geometrically and materially non-linear piezoelectric three-dimensional-beam finite element formulation including warping effectsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008A. Butz Abstract This paper is concerned with a three-dimensional piezoelectric beam formulation and its finite element implementation. The developed model considers geometrically and materially non-linear effects. An eccentric beam formulation is derived based on the Timoshenko kinematics. The kinematic assumptions are extended by three additional warping functions of the cross section. These functions follow from torsion and piezoelectrically induced shear deformations. The presented beam formulation incorporates large displacements and finite rotations and allows the investigation of stability problems. The finite element model has two nodes with nine mechanical and five electrical degrees of freedom. It provides an accurate approximation of the electric potential, which is assumed to be linear in the direction of the beam axis and quadratic within the cross section. The mechanical degrees of freedom are three displacements, three rotations and three scaling factors for the warping functions. The latter are computed in a preprocess by solving a two-dimensional in-plane equilibrium condition with the finite element method. The gained warping patterns are considered within the integration through the cross section of the beam formulation. With respect to material non-linearities, which arise in ferroelectric materials, the scalar Preisach model is embedded in the formulation. This model is a mathematical model for the general description of hysteresis phenomena. Its application to piezoelectric materials leads to a phenomenological model for ferroelectric hysteresis effects. Here, the polarization direction is assumed to be constant, which leads to unidirectional constitutive equations. Some examples demonstrate the capability of the proposed model. Copyright © 2008 John Wiley & Sons, Ltd. [source] Optimal design and optimal control of structures undergoing finite rotations and elastic deformationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004A. Ibrahimbegovic Abstract In this work, we deal with the optimal design and optimal control of structures undergoing large rotations and large elastic deformations. In other words, we show how to find the corresponding initial configuration through optimal design or the corresponding set of multiple load parameters through optimal control, in order to recover a desired deformed configuration or some desirable features of the deformed configuration as specified more precisely by the objective or cost function. The model problem chosen to illustrate the proposed optimal design and optimal control methodologies is the one of geometrically exact beam. First, we present a non-standard formulation of the optimal design and optimal control problems, relying on the method of Lagrange multipliers in order to make the mechanics state variables independent from either design or control variables and thus provide the most general basis for developing the best possible solution procedure. Two different solution procedures are then explored, one based on the diffuse approximation of response function and gradient method and the other one based on genetic algorithm. A number of numerical examples are given in order to illustrate both the advantages and potential drawbacks of each of the presented procedures. Copyright © 2004 John Wiley & Sons, Ltd. [source] A general high-order finite element formulation for shells at large strains and finite rotationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2003Y. Ba Abstract For hyperelastic shells with finite rotations and large strains a p -finite element formulation is presented accommodating general kinematic assumptions, interpolation polynomials and particularly general three-dimensional hyperelastic constitutive laws. This goal is achieved by hierarchical, high-order shell models. The tangent stiffness matrices for the hierarchical shell models are derived by computer algebra. Both non-hierarchical, nodal as well as hierarchical element shape functions are admissible. Numerical experiments show the high-order formulation to be less prone to locking effects. Copyright © 2003 John Wiley & Sons, Ltd. [source] 3D dynamics of discrete element systems comprising irregular discrete elements,integration solution for finite rotations in 3DINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2003A. Munjiza Abstract An algorithm for transient dynamics of discrete element systems comprising a large number of irregular discrete elements in 3D is presented. The algorithm is a natural extension of contact detection, contact interaction and transient dynamics algorithms developed in recent years in the context of discrete element methods and also the combined finite-discrete element method. It complements the existing algorithmic procedures enabling transient motion including finite rotations of irregular discrete elements in 3D space to be accurately integrated. Copyright © 2002 John Wiley & Sons, Ltd. [source] 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 dynamicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2002I. Romero Abstract We present in this paper a new finite element formulation of geometrically exact rod models in the three-dimensional dynamic elastic range. The proposed formulation leads to an objective (or frame-indifferent under superposed rigid body motions) approximation of the strain measures of the rod involving finite rotations of the director frame, in contrast with some existing formulations. This goal is accomplished through a direct finite element interpolation of the director fields defining the motion of the rod's cross-section. Furthermore, the proposed framework allows the development of time-stepping algorithms that preserve the conservation laws of the underlying continuum Hamiltonian system. The conservation laws of linear and angular momenta are inherited by construction, leading to an improved approximation of the rod's dynamics. Several numerical simulations are presented illustrating these properties. Copyright © 2002 John Wiley & Sons, Ltd. [source] Energy consistent time integration of planar multibody systemsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006Stefan Uhlar The planar motion of rigid bodies and multibody systems can be easily described by coordinates belonging to a linear vector space. This is due to the fact that in the planar case finite rotations commute. Accordingly, using this type of generalized coordinates can be considered as canonical description of planar multibody systems. However, the extension to the three-dimensional case is not straightforward. In contrast to that, employing the elements of the direction cosine matrix as redundant coordinates makes possible a straightforward treatment of both planar and three-dimensional multibody systems. This alternative approach leads in general to differential-algebraic equations (DAEs) governing the dynamics of rigid body systems. The main purpose of the present paper is to present a comparison of the two alternative descriptions. In both cases energy-consistent time integration schemes are applied. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||