Finite Elements Based on Strong and Weak Formulations for Structural Mechanics: Stability, Accuracy and Reliability

Year 2017, Volume: 9 Issue: 2, 1 - 21, 14.04.2017

Francesco Tornabene , Nicholas Fantuzzi , Michele Bacciocchi

https://doi.org/10.24107/ijeas.304376

Cited By: 3

Abstract

The authors are presenting a novel
formulation based on the Differential Quadrature (DQ) method which is used to
approximate derivatives and integrals. The resulting scheme has been termed
strong and weak form finite elements (SFEM or WFEM), according to the numerical
scheme employed in the computation. Such numerical methods are applied to solve
some structural problems related to the mechanical behavior of plates and
shells, made of isotropic or composite materials.

The main differences
between these two approaches rely on the initial formulation – which is strong
or weak (variational) – and the implementation of the boundary conditions, that
for the former include the continuity of stresses and displacements, whereas in
the latter can consider the continuity of the displacements or both.

The two methodologies
consider also a mapping technique to transform an element of general shape
described in Cartesian coordinates into the same element in the computational
space. Such technique can be implemented by employing the classic
Lagrangian-shaped elements with a fixed number of nodes along the element edges
or blending functions which allow an “exact mapping” of the element. In
particular, the authors are employing NURBS (Not-Uniform Rational B-Splines)
for such nonlinear mapping in order to use the “exact” shape of CAD designs.

Keywords

Structural analysis, Numerical methods, Strong formulation finite element method, Weak formulation finite element method, Differential and integral quadrature

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