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Discrete singular convolution methodology for free vibration and stability analyses of arbitrary straight-sided quadrilateral plates. (English) Zbl 1153.74022
Summary: 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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