The Experts below are selected from a list of 15474 Experts worldwide ranked by ideXlab platform
Albert C To - One of the best experts on this subject based on the ideXlab platform.
-
multiresolution molecular mechanics a unified and consistent framework for general finite Element Shape Functions
Computer Methods in Applied Mechanics and Engineering, 2015Co-Authors: Qingcheng Yang, Albert C ToAbstract:We present a general mathematical framework for the newly proposed energy-based concurrent atomistic/continuum method Multiresolution Molecular Mechanics (MMM) (Yang et al., 2013). The main features of the generalized framework are: (1) Consistency with the atomistic framework by directly employing the interatomic potential to calculate force and energy; (2) Simple procedure for analytically deriving the optimal summation rule for any given finite Element Shape Function employed in the coarse-grained region. The procedure for obtaining the optimal summation rule is developed based on deriving and then fitting the atomic energy distribution within an Element under the constraint of a given Shape Function. To validate the generalized framework, test problems including non-local harmonic and anharmonic models undergoing tensile, shear and bending deformations will be solved using linear, bilinear and quadratic Elements, respectively. Results obtained using the proposed optimal summation rules for the different Element types will be compared with Gauss quadrature for accuracy. Through error structure analyses, it is found that the proposed summation rule always outperforms Gauss quadrature, even when the latter employs more quadrature points than the former. It is argued that widely-used numerical quadrature techniques such as Gauss quadrature are not optimal for coarse-grained atomic energy approximation because they do not account for the discrete nature of the atoms. In contrast, the present summation rule is derived consistently from the underlying atomic energy distribution, and thus has better accuracy and smaller computational cost.
Qingcheng Yang - One of the best experts on this subject based on the ideXlab platform.
-
multiresolution molecular mechanics a unified and consistent framework for general finite Element Shape Functions
Computer Methods in Applied Mechanics and Engineering, 2015Co-Authors: Qingcheng Yang, Albert C ToAbstract:We present a general mathematical framework for the newly proposed energy-based concurrent atomistic/continuum method Multiresolution Molecular Mechanics (MMM) (Yang et al., 2013). The main features of the generalized framework are: (1) Consistency with the atomistic framework by directly employing the interatomic potential to calculate force and energy; (2) Simple procedure for analytically deriving the optimal summation rule for any given finite Element Shape Function employed in the coarse-grained region. The procedure for obtaining the optimal summation rule is developed based on deriving and then fitting the atomic energy distribution within an Element under the constraint of a given Shape Function. To validate the generalized framework, test problems including non-local harmonic and anharmonic models undergoing tensile, shear and bending deformations will be solved using linear, bilinear and quadratic Elements, respectively. Results obtained using the proposed optimal summation rules for the different Element types will be compared with Gauss quadrature for accuracy. Through error structure analyses, it is found that the proposed summation rule always outperforms Gauss quadrature, even when the latter employs more quadrature points than the former. It is argued that widely-used numerical quadrature techniques such as Gauss quadrature are not optimal for coarse-grained atomic energy approximation because they do not account for the discrete nature of the atoms. In contrast, the present summation rule is derived consistently from the underlying atomic energy distribution, and thus has better accuracy and smaller computational cost.
S Gopalakrishnan - One of the best experts on this subject based on the ideXlab platform.
-
a spectral finite Element model for analysis of axial flexural shear coupled wave propagation in laminated composite beams
Composite Structures, 2003Co-Authors: Roy D Mahapatra, S GopalakrishnanAbstract:A spectral finite Element model (SFEM) for analysis of axial–flexural–shear coupled wave propagation in thick laminated composite beams is presented. Range of validity of the first order shear deformation in the context of higher order Lamb wave modes is discussed. Concept of spectral Element Shape Function, dynamic strain–displacement matrix and dynamically consistent force vector are derived. An exact dynamic stiffness matrix is derived, which is used in finite Element (FE) analysis. Computation is performed in the Fourier domain at FFT sampling points over broad frequency band. Post-processing of the response is performed in both the frequency domain as well as in the time domain, which is suitable for structural diagnostics and broad-band wave propagation problems. To extend the range of engineering applications of SFEM, linear damping models are formulated. Effect of viscous damping on group speeds and wave amplitudes are studied for graphite–epoxy composite beams. Response under impact type loading is compared with time domain FE results. Numerical examples are presented, where the effect of axial–flexural–shear coupling is characterized. Efficient application of the model is shown considering laminated beam with ply-drops. Also a global/local model for estimation of Mode-II crack tip field in a delaminated thick composite beam is presented.
Roy D Mahapatra - One of the best experts on this subject based on the ideXlab platform.
-
a spectral finite Element model for analysis of axial flexural shear coupled wave propagation in laminated composite beams
Composite Structures, 2003Co-Authors: Roy D Mahapatra, S GopalakrishnanAbstract:A spectral finite Element model (SFEM) for analysis of axial–flexural–shear coupled wave propagation in thick laminated composite beams is presented. Range of validity of the first order shear deformation in the context of higher order Lamb wave modes is discussed. Concept of spectral Element Shape Function, dynamic strain–displacement matrix and dynamically consistent force vector are derived. An exact dynamic stiffness matrix is derived, which is used in finite Element (FE) analysis. Computation is performed in the Fourier domain at FFT sampling points over broad frequency band. Post-processing of the response is performed in both the frequency domain as well as in the time domain, which is suitable for structural diagnostics and broad-band wave propagation problems. To extend the range of engineering applications of SFEM, linear damping models are formulated. Effect of viscous damping on group speeds and wave amplitudes are studied for graphite–epoxy composite beams. Response under impact type loading is compared with time domain FE results. Numerical examples are presented, where the effect of axial–flexural–shear coupling is characterized. Efficient application of the model is shown considering laminated beam with ply-drops. Also a global/local model for estimation of Mode-II crack tip field in a delaminated thick composite beam is presented.
H F Nied - One of the best experts on this subject based on the ideXlab platform.
-
stress intensity factors for three dimensional surface cracks using enriched finite Elements
International Journal for Numerical Methods in Engineering, 2002Co-Authors: Ali Ayhan, H F NiedAbstract:The analysis of three-dimensional crack problems using enriched crack tip Elements is examined in this paper. It is demonstrated that the enriched finite Element approach is a very effective technique for obtaining stress intensity factors for general three-dimensional crack problems. The influence of compatibility, integration, Element Shape Function order, and mesh refinement on solution convergence is investigated to ascertain the accuracy of the numerical results. It is shown that integration order has the greatest impact on solution accuracy. Sample results are presented for semi-circular surface cracks and compared with previously obtained solutions available in the literature. Good agreement is obtained between the different numerical solutions, except in the small zone near the free surface where previously published results have often neglected the change in the stress singularity at the free surface. The enriched crack tip Element appears to be particularly effective in this region, since boundary conditions can be easily imposed on the stress intensity factors to accurately represent the correct free surface condition. Copyright © 2002 John Wiley & Sons, Ltd.