Search results for "Harmonic polynomials"
showing 2 items of 2 documents
Line element-less method (LEM) for beam torsion solution (truly no-mesh method)
2008
In this paper a new numerical method for finding approximate solutions of the torsion problem is proposed. The method takes full advantage of the theory of analytic complex function. A new potential function directly in terms of shear stresses is proposed and expanded in the double-ended Laurent series involving harmonic polynomials. A novel element-free weak form procedure, labelled Line Element-Less Method (LEM), has been developed imposing that the square of the net flux across the border is minimum with respect to coefficients expansion. Numerical implementation of the LEM results in systems of linear algebraic equations involving symmetric and positive-definite matrices without resorti…
Exact and approximate analytical solutions for nonlocal nanoplates of arbitrary shapes in bending using the line element-less method
2021
AbstractIn this study, an innovative procedure is presented for the analysis of the static behavior of plates at the micro and nano scale, with arbitrary shape and various boundary conditions. In this regard, the well-known Eringen’s nonlocal elasticity theory is used to appropriately model small length scale effects. The proposed mesh-free procedure, namely the Line Element-Less Method (LEM), only requires the evaluation of simple line integrals along the plate boundary parametric equation. Further, variations of appropriately introduced functionals eventually lead to a linear system of algebraic equations in terms of the expansion coefficients of the deflection function. Notably, the prop…