A new simple and accurate four-node quadrilateral element is developed for linear static and dynamic analysis of thin to moderately thick laminated, anisotropic plate/shell structures within the first-order shear deformation theory (FSDT). The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the conventional bilinear four-node quadrila...

We study the approximation properties of some finite element subspaces of H(div; Ω) andH(curl ; Ω) defined on hexahedral meshes in three dimensions. This work extends results previously obtained for quadrilateral H(div; Ω) finite elements and for quadrilateral scalar finite element spaces. The finite element spaces we consider are constructed starting from a given finite dimensional space of ve...

This paper presents a triangular-to-quadrilateral mesh conversion method that can control the directionality of the output quadrilateral mesh according to a user-specified vector field. Given a triangular mesh and a vector field, the method first scores all possible quadrilaterals that can be formed by pairs of adjacent triangles, according to their shape and directionality. It then converts th...

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...

A uniform finite element mesh rarely provides the best discretization of a domain to accommodate a solution with both optimal efficiency and minimal error. Mesh adaptation can approach a more optimal solution by accommodating regions of the mesh with higher or lower element density. Extensive attention has been given to mesh adaptation in both computational mechanics and computer graphics to pr...

This paper presents a simple method based on strain energy density criterion to study the crack initiation angle by finite element method under biaxial loading condition. The crack surface relative displacement method is used to eliminate the calculation of the stress intensity factors which are normally required. The analysis is performed using higher order four node quadrilateral element. The...

For the nonconforming rotated Q1 element over a mildly distorted quadrilateral mesh, we propose a superconvergence property at the element center, the vertices and the midpoints of four edges. Numerics are presented to confirm this observation.

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...