An accurate differential quadrature procedure for the numerical solution of the moving load problem

In moving load-type problems, the moving point load is modeled mathematically by a time-dependent Dirac-delta function. A key and difficult step in solving this type of problems using a point discrete method such as the differential quadrature method is the discretization of the Dirac-delta function in a simple and accurate manner. This paper is conducted to facilitate this step and to present a new way to do this task. In this way, the Dirac-delta function is approximated by orthogonal polynomials such as the Legendre and Chebyshev polynomials. Unlike the original Dirac-delta function, which is a generalized singularity function, the resulting approximation function is a non-singular function which can be discretized simply and efficiently. The proposed procedure is applied herein to solve the moving load problem in beams and rectangular plates. Comparisons with available analytical and numerical solutions prove that the proposed approach is highly accurate and efficient.