The present paper is made up of two parts. In the first part, we study the mathematical stability and convergence of the quadrilateral MITC elements for the Reissner-Mindlin plate problem in an abstract setting. We generalize the Brezzi-Bathe-Fortin conditions to the quadrilateral MITC elements by weakening the second and fourth conditions. Under these conditions, we show the well-posedness of ...

We will prove two conditions for a tangential quadrilateral to be cyclic. According to one of these, a tangential quadrilateral is cyclic if and only if its Newton line is perpendicular to the Newton line of its contact quadrilateral.

Polynomials suffice as finite element basis functions for triangles, parallelograms, and some other elements of little practical importance. Rational basis functions extend the range of allowed elements to the much wider class of well-set algebraic elements, where well-set is a convexity type constraint. The extension field from R(x, y) to R(x, y, √ x2 + y2) removes this quadrilateral constrain...

A flux recovery technique is introduced and analyzed for the computed solution of the primal hybrid finite element method for second-order elliptic problems. The recovery is carried out over a single element at a time while ensuring the continuity of the flux across the interelement edges and the validity of the discrete conservation law at the element level. Our construction is general enough ...

The purpose of this study was to compare the results of different hierarchical models in engineering analysis applied to dentistry with 2D and 3D models of a tooth and its supporting structures under 100 N occlusal loading at 45° and examine the reliability of simplified 2D models in dental research. Five models were built from computed-tomography scans: four 2D models with Plane Strain and Pla...

We introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element analysis. A gradientbased shape optimisation technique is implemented to minimise compliance, i.e. to maximise stiffness. Different control meshes describing the sam...

We consider a nonconforming streamline-diiusion nite element method for solving convection-diiusion problems. The theoretical and numerical investigation for triangular and tetrahedral meshes recently given by John, Maubach and Tobiska has shown that the usual application of the SDFEM gives not a suucient stabilization. Additional parameter dependent jump terms have been proposed which preserve...