Static and free vibration analyses of rectangular plates by the new version of the differential quadrature element method.

*(English)*Zbl 1041.74563Summary: A new version of the differential quadrature method is presented in this paper to overcome the difficulty existing in the ordinary differential quadrature method for applying multi-boundary conditions in two-dimensional problems. Since the weighting coefficients of the first derivative are the same as for the ordinary differential quadrature method even with the introduction of multi-degree-of-freedom at the boundary points, the method is easier to extend to two- or three-dimensional problems. A new version of the differential quadrature plate element has been established for demonstration. The essential difference from the existing old version of the differential quadrature plate element is the way the weighting coefficients are determined. The methodology is worked out in detail and some numerical examples are given to show the efficiency of the present method.

##### MSC:

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

74H45 | Vibrations in dynamical problems in solid mechanics |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |