The orthogonal meshless finite volume method for solving Euler–Bernoulli beam and thin plate problems

In this paper a new method untitled “orthogonal meshless finite volume method” (OMFVM) is developed for solving elastostatic problems in Euler–Bernoulli beam and thin plate. In this method, the weak formulation of a conservation law is discretized by restricting it to a discrete set of test functions. In contrast to the usual finite volume approach, the test functions are not taken as characteristic functions of the control volumes in a spatial grid, but are chosen from a Heaviside step function. The present approach eliminates the expensive process of directly differentiating the OMLS interpolations in the entire domain. This method was evaluated by applying the formulation to a variety of patch test and thin beam problems. The formulation successfully reproduced exact solutions. Numerical examples demonstrate the advantages of the present methods: (i) lower-order polynomial basis can be used in the OMLS interpolations; (ii) smaller support sizes can be used in the OMFVM approach; and (iii) higher accuracies and computational efficiencies are obtained.