Search results for "Line element"
showing 7 items of 7 documents
Arbitrarily shaped plates analysis via Line Element-Less Method (LEM)
2018
Abstract 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 appropri…
The Line Element-less Method Analysis of orthotropic beam for the De Saint Venant torsion problem
2010
Abstract This paper deals with the extension of a novel numerical technique, labelled line element-less method (LEM), in order to provide approximate solutions of the De Saint Venant torsion problem for orthotropic beams having simply and multiply connected cross-section. A suitable transformation of coordinates allows to take full advantage of the theory of analytic complex functions as in the isotropic case. A complex potential function analytic in all the transformed domain whose real and imaginary parts are related to the shear stress components and to the orthotropic ratio is introduced and expanded in the double-ended Laurent series involving harmonic polynomials. An element-free weak…
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…
Extension of the line element-less method to dynamic problems
2020
The line element-less method is an efficient approach for the approximate solution of the Laplace or biharmonic equation on a general bidimensional domain. Introducing generalized harmonic polynomials as approximation functions, we extend the line element-less method to the inhomogeneous Helmholtz equation and to the eigenvalue problem for the Helmholtz equation. The obtained approximate solutions are critically discussed and advantages as well as limitations of the approach are pointed out.
NOVEL TOOLS FOR THE MECHANICAL ANALYSIS OF THIN PLATES AND RELEVANCE ON MEMBRANE-BASED TECHNOLOGIES
2020
Innovative straight formulation for plate in bending
2017
In this paper it has been introduced an innovative formulation for evaluating the deflection function of a simply supported plate loaded by uniformly distributed edge moments. Framed into Line Element-less Method, this formulation allows the evaluation of solution in terms of deflection, through few lines of algorithm implemented by Mathematica software without resorting to any discretization neither in the domain nor in the boundary. Interesting savings in terms of time and computational costs are achieved. Results obtained by the proposed method are well contrasted by ones obtained by classical methods and Finite Element Method.
De Saint-Venant flexure-torsion problem handled by Line Element-less Method (LEM)
2010
In this paper, the De Saint-Venant flexure-torsion problem is developed via a technique by means of a novel complex potential function analytic in all the domain whose real and imaginary parts are related to the shear stresses. The latter feature makes the complex analysis enforceable for the shear problem. Taking full advantage of the double-ended Laurent series involving harmonic polynomials, a novel element-free weak form procedure, labelled Line Element-less Method (LEM), is introduced, imposing that the square of the net flux across the border is minimized with respect to expansion coefficients. Numerical implementation of the LEM results in systems of linear algebraic equations involv…