The present study proposes a dynamic numerical solution for deflections of curved beam structures. In order to extract characteristic equations of an arch under an in-plane constant moving load, an analysis procedure based on the Euler–Bernoulli beam theory considering polar system is conducted. A prismatic semicircular arch with uniform cross section, in various boundary conditions, is assumed. Radial and tangential displacements, as well as bending moments are obtained using differential quadrature method as a well-known numerical method. In addition to parametric studies, a curved steel bridge as an actual application is analyzed by the mentioned method. By using this differential quadrature technique, the function values and some partial derivatives are approximated by weighting coefficients. Convergence study is carried out to demonstrate the stability of the present method. In order to confirm the high level of accuracy of this approach, some comparisons are made between the results obtained by selected methods such as differential quadrature method, Galerkin method, and finite element method. The results show that in the structural problems with specific geometry, using differential quadrature method, which is independent of domain discretization, is proven to be efficient.
In this paper, a new numerical technique, the differential quadrature method (DQM) has been developed for dynamic analysis of the nanobeams in the polar coordinate system. DQ approximation of the required partial derivatives is given by a weighted linear sum of the function values at all grid points. A semicircular arch with small-scale effects is investigated by the nonlocal continuum theory with simply supported boundary conditions. The governing equations for Euler-Bernoulli nonlocal beam models are derived. The expressions of the bending displacement are presented analytically. The convergence properties and the accuracy of the DQM for bending of curved nanobeams are investigated through a number of numerical computations. It can be observed that use of DQM, which is independent of domain discretization to be efficient.
In this study, static analysis of the two-dimensional rectangular nanoplates are investigated by the Differential Quadrature Method (DQM). Numerical solution procedures are proposed for deflection of an embedded nanoplate under distributed nanoparticles based on the DQM within the framework of Kirchhoff and Mindlin plate theories. The governing equations and the related boundary conditions are derived by using nonlocal elasticity theory. The difference between the two models is discussed and bending properties of the nanoplate are illustrated. Consequently, the DQM has been successfully applied to analyze nanoplates with discontinuous loading and various boundary conditions for solving Kirchhoff and Mindlin plates with small-scale effect, which are not solvable directly. The results show that the above mentioned effects play an important role on the static behavior of the nanoplates.
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