In this work, a new method for mesh simpliication and surface reconstruction speciically designed for the needs of CAD/CAM engineering design and analysis is introduced. The method simpliies the original free-form face model by rst constructing restricted curvature deviation regions, generating a boundary conforming nite element quadrilateral mesh of the regions, and then tting a smooth surface...

This chapter explains techniques for the generation of quadrilateral and hexahedral element meshes. Since structured meshes are discussed in detail in other parts of this volume, we focus on the generation of unstructured meshes, with special attention paid to the 3D case. Quadrilateral or hexahedral element meshes are the meshes of choice for many applications, a fact that can be explained emp...

In this paper, the finite element analysis of two-dimensional linear viscoelastic problems is performed using quadrilateral complex Fourier elements and, the results are compared with those obtained by quadrilateral classic Lagrange elements. Complex Fourier shape functions contain a shape parameter which is a constant unknown parameter adopted to enhance approximation’s accuracy. Since the iso...

The recently developed consecutive-interpolation procedure (CIP) based 4-node quadrilateral element (CQ4) is used to study free and forced 2-dimensional vibrations of elastic and piezoelectric structures of complex geometries. For some of these problems results have also been computed with the standard quadrilateral element under the constraint that the two approaches have the same number of de...

In this paper, double integrals over an arbitrary quadrilateral are evaluated exploiting finite element method. The physical region is transformed into a standard quadrilateral finite element using the basis functions in local space. Then the standard quadrilateral is subdivided into two triangles, and each triangle is further discretized into 4 n right isosceles triangles, with area 1 2n2, and...

Subelement patterns using bisection of edges and schemes for selecting edges to be split are described for the local refinement of elements in all-quadrilateral and quadrilateral-dominant planar meshes. Subelement patterns using trisection of edges are also described for the local refinement of elements in all-quadrilateral planar meshes. These patterns and schemes are easily extendible to quad...

A multilevel adaptive refinement technique is presented for unstructured quadrilateral meshes in which the mesh is kept conformal at all times. This means that the refined mesh, like the original, is formed of only quadrilateral elements that intersect strictly along edges or at vertices, i.e., vertices of one quadrilateral element do not lie in an edge of another quadrilateral. Elements are re...

In this paper, we introduce a new family of mixed finite element spaces of higher order (k ≥ 1) on general quadrilateral grids. A typical element has two fewer degrees of freedom than the well-known RaviartThomas finite element RT[k], yet enjoys an optimal-order approximation for the velocity in L 2-norm. The order of approximation in the divergence norm is one less than the velocity, as is com...

Stiffness matrix of the four-node quadrilateral plane stress element is decomposed into normal and shear components. A computer program is developed to obtain the straining modes using adequate and reduced integration. Then a solution for the problem of mixing straining modes is found. Accuracy of the computer program is validated by a closed-form stiffness matrix, derived for the plane rectang...