Arbitrarily shaped plates analysis via Line Element-Less Method (LEM)

An innovative procedure is introduced for the analysis of arbitrarily shaped thin plates with various boundary conditions and under generic transverse loading conditions. Framed into Line Element-less Method, a truly meshfree method, this novel approach yields the solution in terms of the deflection function in a straightforward manner, without resorting to any discretization, neither in the domain nor on the boundary. Specifically, expressing the deflection function through a series expansion in terms of harmonic polynomials, it is shown that the proposed method requires only the evaluation of line integrals along the boundary parametric equation. Further, minimization of appropriately introduced novel functionals directly leads to simple systems of linear algebraic equations for the unknown expansion coefficients. Notably, the proposed procedure yields exact solutions, when available, for different plate geometries. Additionally, several numerical applications are presented to show the reliability and simplicity of the approach, and comparisons with pertinent Finite Element method data demonstrate the efficiency and accuracy of the proposed procedure.