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Dynamic Inhomogeneous Isoparametric Element with Coordinate Transformation

Published online by Cambridge University Press:  11 December 2015

Z.-L. Yang ,
J.-W. Zhang  and
Y. Wang
Z.-L. Yang
Affiliation:
College of Aerospace and Civil EngineeringHarbin Engineering UniversityHarbin, China
J.-W. Zhang
Affiliation:
College of Aerospace and Civil EngineeringHarbin Engineering UniversityHarbin, China
Y. Wang*
Affiliation:
College of Aerospace and Civil EngineeringHarbin Engineering UniversityHarbin, China
*
*Corresponding author ([email protected])
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Abstract

Based on the coordinate transformation method, the formula of the dynamic inhomogeneous isoparametric finite element method is presented for generating element stiffness, damping and mass matrices. First, the global coordinate form and simplified form of dynamic inhomogeneous finite element are given in this paper. Then, the discrete material parameter distributions under the isoparametric coordinate system are obtained by using the transformation relationship between the global coordinates and the isoparametric coordinates. The simplified form with the discrete material parameter distributions is obtained for generating the element stiffness and mass matrices of the dynamic inhomogeneous isoparametric element. The numerical examples show that the scheme proposed in present paper has high precision.

Keywords

Dynamic inhomogeneous finite elementInhomogeneous mediumCoordinate transformationIsoparametric coordinate
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 3 , June 2016 , pp. 289 - 296
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2016 

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References

1.Carta, G. and Brun, M., “A Dispersive Homogenization Model Based on Lattice Approximation for the Prediction o Wave Motion in Laminates,” Journal of Applied Mechanics, 79, pp. 021019-1–021019-8 (2012).CrossRefGoogle Scholar
2.Jocob, F., Vasilina, F. and Sergey, K., “Micro-Inertia Effects in Nonlinear Heterogeneous Media,” Journal of Numerical Methods in Engineering, 91, pp. 1406–1426 (2012).Google Scholar
3.Saeid, C., Alireza, M., Gilles, B., Emmanuel, B. and Mehrdad, B., “Scaling Behavior and the Effects of Heterogeneity on Shallow Seismic Imaging of Mineral Deposits: A Case Study from Brunswick No. 6 Mining area,” Journal of Applied Geophysics, 90, pp. 1–18 (2013).Google Scholar
4.Zhong, Z., Wu, L. and Chen, W., “Progress in the Study on Mechanics Problems of Functionally Graded Materials and Structures,” Journal of Advances in Mechanics, 40, pp. 528–541 (2010) (Text in Chinese).Google Scholar
5.Liu, J., Cao, X. S. and Wang, Z. K., “Propagation of Love Waves in a Smart Functionally Graded Piezoelectric Composite Structure,” Journal of Smart Materials & Structures, 16, pp. 13–24 (2007).CrossRefGoogle Scholar
6.Ding, S. and Li, X., “Mode-I Crack Problem for Functionally Graded Layered Structures,” Journal of Fracture, 168, pp. 209–226 (2011).CrossRefGoogle Scholar
7.Kucukcoban, S. and Kallivokas, L. F., “Mixed Perfectly-Matched-Layers for Direct Transient Analysis in 2D Elastic Heterogeneous Media,” Journal of Computer Methods in Applied Mechanics and Engineering, 200, pp. 57–76 (2011).CrossRefGoogle Scholar
8.Arash, J. and Hiroshi, T., “FDTD3C—A FORTRAN Program to Model Multi-Component Seismic Waves for Vertically Heterogeneous Attenuative Media,” Journal of Computers & Geosciences, 51, pp. 314–323 (2013).Google Scholar
9.Zhang, S. and Leech, C. M., “Use of Inhomogeneous Finite Elements for the Prediction of Stress in Rope Terminations,” Journal of Engineering Computations, 2, pp. 55–62 (1985).Google Scholar
10.Zhang, S. and Leech, C. M., “Inhomogeneous Isoparametric Elements for Stress Analysis of Composites,” Journal of Scientia Sinica, 8, pp. 832–845 (1987).Google Scholar
11.Kim, J. H. and Paulino, G. H., “Isoparametric Graded Finite Elements for Nonhomogeneous Isotropic and Orthotropic Materials,” Journal of Applied Mechanics, 69, pp. 502–514 (2002).CrossRefGoogle Scholar
12.Gao, Z., Zhou, Y. and Lee, K., “Graded Finite Element Simulation of Thermal Stress in Inhomogeneous High-Tc Superconductor,” Journal of Physica C, 470, pp. 2010–2015 (2010).CrossRefGoogle Scholar
13.Gao, Z., Lee, K. and Zhou, Y., “Coupled Thermo-Mechanical Analysis of Functionally Gradient Weak/Micro-Discontinues Interface with Graded Finite Element Method,” Journal of Acta Mechanica Solida Sinica, 25, pp. 331–340 (2012).CrossRefGoogle Scholar
14.Hassan, Z. and Mehran, K., “Three-Dimensional Static Analysis of Thick Functionally Graded Plates Using Graded Finite Element Method,” Journal of Mechanical Engineering Science, 228, pp. 1275–1285 (2014).Google Scholar
15.Kamran, A., Manouchehr, S. and Mehdi, A., “Transient Thermal Stresses in Functionally Graded Thick Truncated Cones by Graded Finite Element Method,” Journal of Pressure Vessels and Piping, 119, pp. 52–61 (2014).Google Scholar
16.Yang, Z., Wang, Y. and Hei, B., “Transient Analysis of 1D Inhomogeneous Media by Dynamic Inhomogeneous Finite Element Method,” Journal of Earth quake Engineering and Engineering Vibration, 12, pp. 569–576 (2013).CrossRefGoogle Scholar
17.Wang, Y., Yang, Z. and Hei, B., “An Investigation on the Displacement Response in One-Dimension Inhomogeneous Media Under Different Loading Speeds,” Journal of Northeastern University, 34, pp. 18–21 (2013) (Text in Chinese).Google Scholar
18.Zienkiewicz, O. C. and Taylor, R. L., The Finite Element Method (5th Edition) Volume 1: The Basis, Elsevier, Amsterdam (2000).Google Scholar
19.Reddy, J. N., An Introduction to the Finite Element Method, 2nd Ed., Mcgraw-Hill Inc., New York (1993).Google Scholar
20.Achenbach, J. D., Wave Propagation in Elastic Solids, North-Holland Publishing Company, Amsterdam (1973).Google Scholar