A mesh is said to be dendritic if it contains elements with mid-side (edge) nodes when the predominant element topology has only corner nodes. A dendritic mesh is illustrated in Figure 1 where the predominant element is a four-node quadrilateral, but has also several five-node quadrilateral elements each with one mid-edge node plus four corner nodes. Such meshes arise when an approximately unif...

The purpose of this paper is to investigate the use of a genetic algorithm (GA) to perform the finite element analysis mesh smoothing process. It is the goal of this paper to take a simple quadrilateral mesh and smooth it using a GA into a useful model that will provide a correct solution. The GA smoothing technique is demonstrated on two simple quadrilateral mesh examples. Only one node is mov...

This work presents a study on the performance of nodal bases on triangles and on quadrilaterals for discontinuous Galerkin solutions of hyperbolic conservation laws. A nodal basis on triangles and two tensor product nodal bases on quadrilaterals are considered. The quadrilateral element bases are constructed from the Lagrange interpolating polynomials associated with the Legendre–Gauss–Lobatto ...

We consider the approximation properties of finite element spaces on quadrilateral meshes. The finite element spaces are constructed starting with a given finite dimensional space of functions on a square reference element, which is then transformed to a space of functions on each convex quadrilateral element via a bilinear isomorphism of the square onto the element. It is known that for affine...

Certain difficulties with the use of quadrilateral or hexahedral finite elements are related to mesh refinement and to element compatibility and quality after refinement. In this paper, special refinement elements are presented that make possible connecting two special elements to one edge of an 8-node quadrilateral element (2D). The main idea in refinement elements is to place some midside nod...

This paper reports numerical analyses of free vibration of laminated composite plate/ shell structures of various shapes, span-to-thickness ratios, boundary conditions and lay-up sequences. The method is based on a novel four-node quadrilateral element, namely MISQ20, within the framework of the first-order shear deformation theory (FSDT). The element is built by incorporating a strain smoothin...

A general 2D-hp-adaptive Finite Element FE implementation in Fortran 90 is described. The implementation is based on an abstract data structure, which allows to incorporate the full hp-adaptivity of triangular and quadrilateral nite elements. The h-reenement strategies are based on h2-reenement of quadrilaterals and h4-reenement of triangles. For p-reenement we allow the approximation order to ...

Schneiders and Debye (1995) present two algorithms for quadrilateral mesh refinement. These algorithms refine quadrilateral meshes while maintaining mesh conformity. The first algorithm maintains conformity by introducing triangles. The second algorithm maintains conformity without triangles, but requires a larger degree of refinement. Both algorithms introduce nodes with non-optimal valences. ...