The Experts below are selected from a list of 57 Experts worldwide ranked by ideXlab platform
Ahmed A. Shabana - One of the best experts on this subject based on the ideXlab platform.
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computer implementation of the absolute nodal coordinate formulation for flexible multibody dynamics
Nonlinear Dynamics, 1998Co-Authors: Ahmed A. ShabanaAbstract:Deformable components in multibody systems are subject to kinematic constraints that represent mechanical joints and specified motion trajectories. These constraints can, in general, be described using a set of nonlinear algebraic equations that depend on the system generalized coordinates and time. When the kinematic constraints are augmented to the differential equations of motion of the system, it is desirable to have a formulation that leads to a minimum number of non-zero coefficients for the unknown accelerations and constraint forces in order to be able to exploit efficient sparse Matrix algorithms. This paper describes procedures for the computer implementation of the absolute nodal coordinate formulation' for flexible multibody applications. In the absolute nodal coordinate formulation, no infinitesimal or finite rotations are used as nodal coordinates. The configuration of the finite Element is defined using global displacement coordinates and slopes. By using this mixed set of coordinates, beam and plate Elements can be treated as isoparametric Elements. As a consequence, the dynamic formulation of these widely used Elements using the absolute nodal coordinate formulation leads to a constant Mass Matrix. It is the objective of this study to develop computational procedures that exploit this feature. In one of these procedures, an optimum sparse Matrix structure is obtained for the deformable bodies using the QR decomposition. Using the fact that the Element Mass Matrix is constant, a QR decomposition of a modified constant connectivity Jacobian Matrix is obtained for the deformable body. A constant velocity transformation is used to obtain an identity generalized inertia Matrix associated with the second derivatives of the generalized coordinates, thereby minimizing the number of non-zero entries of the coefficient Matrix that appears in the augmented Lagrangian formulation of the equations of motion of the flexible multibody systems. An alternate computational procedure based on Cholesky decomposition is also presented in this paper. This alternate procedure, which has the same computational advantages as the one based on the QR decomposition, leads to a square velocity transformation Matrix. The computational procedures proposed in this investigation can be used for the treatment of large deformation problems in flexible multibody systems. They have also the advantages of the algorithms based on the floating frame of reference formulations since they allow for easy addition of general nonlinear constraint and force functions.
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A computer implementation of the absolute nodal coordinate formulation for flexible multibody dynamics,” Nonlinear Dynamics
1998Co-Authors: Ahmed A. ShabanaAbstract:Abstract. Deformable components in multibody systems are subject to kinematic constraints that represent mechanical joints and specified motion trajectories. These constraints can, in general, be described using a set of nonlinear algebraic equations that depend on the system generalized coordinates and time. When the kinematic constraints are augmented to the differential equations of motion of the system, it is desirable to have a formulation that leads to a minimum number of non-zero coefficients for the unknown accelerations and constraint forces in order to be able to exploit efficient sparse Matrix algorithms. This paper describes procedures for the computer implementation of the absolute nodal coordinate formulation for flexible multibody applications. In the absolute nodal coordinate formulation, no infinitesimal or finite rotations are used as nodal coordinates. The configuration of the finite Element is defined using global displacement coordinates and slopes. By using this mixed set of coordinates, beam and plate Elements can be treated as isoparametric Elements. As a consequence, the dynamic formulation of these widely used Elements using the absolute nodal coordinate formulation leads to a constant Mass Matrix. It is the objective of this study to develop computational procedures that exploit this feature. In one of these procedures, an optimum sparse Matrix structure is obtained for the deformable bodies using the QR decomposition. Using the fact that the Element Mass Matrix is constant, a QR decomposition of a modified constant connectivity Jacobian Matrix is obtained for the deformable body. A constant velocity transformation is used to obtain a
M L L Wijerathne - One of the best experts on this subject based on the ideXlab platform.
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linear finite Elements with orthogonal discontinuous basis functions for explicit earthquake ground motion modeling
International Journal for Numerical Methods in Engineering, 2011Co-Authors: Tsuyoshi Ichimura, Muneo Hori, M L L WijerathneAbstract:The dynamic explicit finite Element method is commonly used in earthquake ground motion modeling. In this method, the Element Mass Matrix is approximately lumped, which may lead to numerical dispersion. On the other hand, the orthogonal finite Element method, based on orthogonal polynomial basis functions, naturally derives a lumped diagonal Mass Matrix and can be applied to dynamic explicit finite Element analysis. In this paper, we propose finite Elements based on orthogonal discontinuous basis functions, the Element Mass matrices of which are lumped without approximation. Orthogonal discontinuous basis functions are used to improve the accuracy and reduce the numerical dispersion in earthquake ground motion modeling. We present a detailed formulation of the 4-node tetrahedral and 8-node hexahedral Elements. The relationship between the proposed finite Elements and conventional finite Elements is investigated, and the solutions obtained from the conventional explicit finite Element method are compared with analytical solutions to verify the numerical dispersion caused by the lumping approximation. Comparison of solutions obtained with the proposed finite Elements to analytical solutions demonstrates the usefulness of the technique. Examples are also presented to illustrate the effectiveness of the proposed method in earthquake ground motion modeling in the actual three-dimensional crust structure.
Daniel A. White - One of the best experts on this subject based on the ideXlab platform.
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A generalized Mass lumping technique for vector finite-Element solutions of the time-dependent Maxwell equations
IEEE Transactions on Antennas and Propagation, 2005Co-Authors: Aaron Fisher, R.n. Rieben, G.h. Rodrigue, Daniel A. WhiteAbstract:Time-domain finite-Element solutions of Maxwell's equations require the solution of a sparse linear system involving the Mass Matrix at every time step. This process represents the bulk of the computational effort in time-dependent simulations. As such, Mass lumping techniques in which the Mass Matrix is reduced to a diagonal or block-diagonal Matrix are very desirable. In this paper, we present a special set of high order 1-form (also known as curl-conforming) basis functions and reduced order integration rules that, together, allow for a dramatic reduction in the number of nonzero entries in a vector finite Element Mass Matrix. The method is derived from the Nedelec curl-conforming polynomial spaces and is valid for arbitrary order hexahedral basis functions for finite-Element solutions to the second-order wave equation for the electric (or magnetic) field intensity. We present a numerical eigenvalue convergence analysis of the method and quantify its accuracy and performance via a series of computational experiments.
Tsuyoshi Ichimura - One of the best experts on this subject based on the ideXlab platform.
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linear finite Elements with orthogonal discontinuous basis functions for explicit earthquake ground motion modeling
International Journal for Numerical Methods in Engineering, 2011Co-Authors: Tsuyoshi Ichimura, Muneo Hori, M L L WijerathneAbstract:The dynamic explicit finite Element method is commonly used in earthquake ground motion modeling. In this method, the Element Mass Matrix is approximately lumped, which may lead to numerical dispersion. On the other hand, the orthogonal finite Element method, based on orthogonal polynomial basis functions, naturally derives a lumped diagonal Mass Matrix and can be applied to dynamic explicit finite Element analysis. In this paper, we propose finite Elements based on orthogonal discontinuous basis functions, the Element Mass matrices of which are lumped without approximation. Orthogonal discontinuous basis functions are used to improve the accuracy and reduce the numerical dispersion in earthquake ground motion modeling. We present a detailed formulation of the 4-node tetrahedral and 8-node hexahedral Elements. The relationship between the proposed finite Elements and conventional finite Elements is investigated, and the solutions obtained from the conventional explicit finite Element method are compared with analytical solutions to verify the numerical dispersion caused by the lumping approximation. Comparison of solutions obtained with the proposed finite Elements to analytical solutions demonstrates the usefulness of the technique. Examples are also presented to illustrate the effectiveness of the proposed method in earthquake ground motion modeling in the actual three-dimensional crust structure.
Aaron Fisher - One of the best experts on this subject based on the ideXlab platform.
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A generalized Mass lumping technique for vector finite-Element solutions of the time-dependent Maxwell equations
IEEE Transactions on Antennas and Propagation, 2005Co-Authors: Aaron Fisher, R.n. Rieben, G.h. Rodrigue, Daniel A. WhiteAbstract:Time-domain finite-Element solutions of Maxwell's equations require the solution of a sparse linear system involving the Mass Matrix at every time step. This process represents the bulk of the computational effort in time-dependent simulations. As such, Mass lumping techniques in which the Mass Matrix is reduced to a diagonal or block-diagonal Matrix are very desirable. In this paper, we present a special set of high order 1-form (also known as curl-conforming) basis functions and reduced order integration rules that, together, allow for a dramatic reduction in the number of nonzero entries in a vector finite Element Mass Matrix. The method is derived from the Nedelec curl-conforming polynomial spaces and is valid for arbitrary order hexahedral basis functions for finite-Element solutions to the second-order wave equation for the electric (or magnetic) field intensity. We present a numerical eigenvalue convergence analysis of the method and quantify its accuracy and performance via a series of computational experiments.