Discrete singular convolution methodology for free vibration and stability analyses of arbitrary straight-sided quadrilateral plates.

*(English)*Zbl 1153.74022Summary: A new discrete singular convolution (DSC) method is developed for vibration, buckling and static analyses of arbitrary straight-sided quadrilateral plates. The straight-sided quadrilateral domain is mapped into a square domain in the computational space using a four-node element. By using the geometric transformation, the governing equations and boundary conditions of the plate are transformed from the physical domain into a square computational domain. Numerical examples illustrate the accuracy and convergence of DSC method for straight-sided quadrilateral thin plates such as rectangular, skew, trapezoidal and rhombic plates. The results obtained by DSC method are compared with those obtained by other numerical and analytical methods.

##### MSC:

74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |

74H45 | Vibrations in dynamical problems in solid mechanics |

74K20 | Plates |

74G60 | Bifurcation and buckling |

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

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\textit{Ö. Civalek}, Commun. Numer. Methods Eng. 24, No. 11, 1475--1495 (2008; Zbl 1153.74022)

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