## Discrete singular convolution and its application to the analysis of plates with internal supports. I: Theory and algorithm.(English)Zbl 1058.74643

Summary: This paper presents a novel computational approach, the discrete singular convolution (DSC) algorithm, for analysing plate structures. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied. Approximations to the delta distribution are constructed as either band-limited reproducing kernels or approximate reproducing kernels. Unified features of the DSC algorithm for solving differential equations are explored. It is demonstrated that different methods of implementation for the present algorithm, such as global, local, Galerkin, collocation, and finite difference, can be deduced from a single starting point. The use of the algorithm for the vibration analysis of plates with internal supports is discussed. Detailed formulation is given to the treatment of different plate boundary conditions, including simply supported, elastically supported and clamped edges. This work paves the way for applying the DSC approach in part II of the present paper [see the following review Zbl 1058.74644)] to plates with complex support conditions, which have not been fully addressed in the literature yet.

### MSC:

 74S30 Other numerical methods in solid mechanics (MSC2010) 74K20 Plates 74H45 Vibrations in dynamical problems in solid mechanics

### Keywords:

square plates; vibration analysis; wavelets

Zbl 1058.74644
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### References:

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