The coordinate transformation for quadrilateral isoparametric elements is well-defined in the finite element literature. However, a corresponding inverse transformation is not found. In fact, it has been commonly believed that no explicit solutions to the inverse transformation problem exist. This paper shows that if geometric considerations are used, a complete set of general solutions to the ...

Four quadrilateral elements for the Reissner-Mindlin plate model are considered. The elements are the stabilized MITC4 element of Lyly, Stenberg and Vihinen [27], the MIN4 element of Tessler and Hughes [35], the Q4BL element of Zienkiewicz et al [39] and the FMIN4 element of Kikuchi and Ishii [21]. For all elements except the Q4BL element, a unifying variational formulation is introduced, and o...

This note studies the approximation error of a local projection operator on polynomials of total degree k defined on quadrilaterals. Among other applications, this projection operator permits to derive easily error estimates for quadrature formulas.

We present stable mixed finite elements for planar linear elasticity on general quadrilateral meshes. The symmetry of the stress tensor is imposed weakly and so there are three primary variables, the stress tensor, the displacement vector field, and the scalar rotation. We develop and analyze a stable family of methods, indexed by an integer r ≥ 2 and with rate of convergence in the L2 norm of ...

Thanks to recent improvements, computational methods can now be used to convert triangular meshes into quadrilateral meshes so that the quadrilateral elements capture well the principal curvature directional fields of surfaces and intrinsically have surface parametric values. In this study, a quadrilateral mesh generated using the mixed integer quadrangulation technique of Bommes et al. is used...

General strategy for developing finite elements of general geometric shape explained on quadrilateral folded plate structure element ensuring invariance properties is presented in this paper. The basic idea of this strategy consists in using the natural coordinate system only for defining the element geometry and performing the element integration in a mapped biunit square. For defining the app...

In this work, some nonconforming elements on arbitrary quadrilateral meshes in solving incompressible elastic equations are analyzed. A uniform optimal convergence rate is established at the incompressible limit ν = 0.5 for both displacement and stresses (or pressure in the case of incompressible flow).

This paper investigates the use of a steady state genetic algorithm (GA) to perform quadrilateral finite element mesh smoothing. GAS short for genetic algorithm smoother moves one to 64 nodes at the same time. GAs smooth as well as untangle (removing twisted and inverted elements), which has been a separate operation in the past.