Discrete singular convolution and its application to the analysis of plates with internal supports. II: Applications.

*(English)*Zbl 1058.74644Summary: Part II of this series of two papers [for part I see the preceding review Zbl 1058.74643)] presents the applications of the discrete singular convolution (DSC) algorithm. The main purpose is to explore the utility, to test the accuracy and examine the convergence of the proposed approach for vibration analysis of rectangular plates with internal supports. Both partial internal line supports and complex internal supports are considered for 21 square plates of various combinations of edge support conditions. The effects of different size, shape and topology of the internal supports and different boundary conditions on the vibration response of plates are investigated. The partial internal line supports may vary from a central point support to a full range of cross or diagonal line supports. Several closed-loop supports, such as ring, square and rhombus, and their combinations are studied for complex internal supports. Convergence and comparison studies are carried out to establish the correctness and accuracy of the DSC algorithm. The DSC results are compared with those in the available literature obtained by using other methods. Numerical results indicate that the DSC algorithm exhibits controllable accuracy for plate analysis and shows excellent flexibility in handling complex geometries, boundary conditions and support conditions.

##### MSC:

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74K20 | Plates |

74H45 | Vibrations in dynamical problems in solid mechanics |

PDF
BibTeX
XML
Cite

\textit{Y. Xiang} et al., Int. J. Numer. Methods Eng. 55, No. 8, 947--971 (2002; Zbl 1058.74644)

Full Text:
DOI

##### References:

[1] | Wei, Journal of Chemical Physics 110 pp 8930– (1999) |

[2] | Wei, Journal of Physics A: Mathematics and General 33 pp 4935– (2000) |

[3] | Wei, Journal of Physics A: Mathematics and General 33 pp 8577– (2000) |

[4] | Wei, Computer Methods in Applied Mechanics and Engineering 190 pp 2017– (2001) |

[5] | Wei, Journal of Physics B 33 pp 343– (2000) |

[6] | Wei, Physica D 137 pp 247– (2000) |

[7] | A unified method for computational mechanics. In Computational Mechanics for the Next Millennium, (eds). Elsevier: Amsterdam, 1999; 1049-1054. · Zbl 0937.60101 |

[8] | Veletsos, Journal of Applied Mechanics 23 pp 97– (1956) · Zbl 0071.18901 |

[9] | Ungar, Journal of Engineering for Industry 83 pp 434– (1961) · doi:10.1115/1.3664551 |

[10] | Bolotin, Inzhenernyi Zhurnal 3 pp 86– (1961) |

[11] | Moskalenko, Prikladnaya Mekhanika 1 pp 59– (1965) |

[12] | Cheung, Journal of the Engineering Mechanics Division, ASCE 97 pp 391– (1971) |

[13] | Elishakoff, Journal of Applied Mechanics 46 pp 656– (1979) · Zbl 0418.73062 · doi:10.1115/1.3424622 |

[14] | Azimi, Journal of Sound and Vibration 93 pp 9– (1984) |

[15] | Mizusawa, Earthquake Engineering and Structural Dynamics 12 pp 847– (1984) |

[16] | Takahashi, Journal of Sound and Vibration 62 pp 455– (1979) |

[17] | Wu, Earthquake Engineering and Structural Dynamics 3 pp 3– (1974) |

[18] | Kim, Journal of Sound and Vibration 114 pp 129– (1987) |

[19] | Liew, Journal of Sound and Vibration 147 pp 255– (1991) |

[20] | Liew, Computers and Structures 49 pp 31– (1993) |

[21] | Zhou, International Journal of Solids and Structures 31 pp 347– (1994) |

[22] | Zhou, Computers and Structures 57 pp 731– (1995) |

[23] | Zhou, International Journal of Solids and Structures 38 pp 5565– (2001) |

[24] | Kong, Journal of Sound and Vibration 184 pp 639– (1995) |

[25] | Cheung, Thin-Walled Structures 37 pp 305– (2000) |

[26] | Liew, Journal of Sound and Vibration 172 pp 527– (1994) |

[27] | Liew, Computers and Structures 49 pp 59– (1993) |

[28] | Zhou, Journal of Sound and Vibration 223 pp 231– (1999) |

[29] | Leissa, Journal of Sound and Vibration 31 pp 257– (1973) · Zbl 0268.73033 |

[30] | Dynamics of Elastic Systems. John Wiley and Sons, Inc.: New York, 1963. |

[31] | Nowacki, Archiwum Mechaniki Stosowanej 5 pp 437– (1953) |

[32] | Johns, Journal of Sound and Vibration 25 pp 75– (1972) |

[33] | Kim, Journal of Sound and Vibration 117 pp 249– (1987) |

[34] | Bapat, Journal of Sound and Vibration 155 pp 325– (1992) |

[35] | Bapat, Journal of Sound and Vibration 134 pp 291– (1989) |

[36] | Liew, Journal of Engineering Mechanics, ASCE 120 pp 499– (1994) |

[37] | Vibration of Mindlin Plates-Programming the p-Version Ritz Method. Elsevier Science: Oxford, 1998. · Zbl 0940.74002 |

[38] | Nagaya, Journal of Sound and Vibration 94 pp 71– (1984) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.