Automatic finite element mesh generation techniques have become commonly used tools for the analysis of complex, real-world models. All of these methods can, however, create distorted and even unusable elements. Fortunately, several techniques exist which can take an existing mesh and improve its quality. Smoothing (also referred to as mesh relaxation) is one such method, which repositions noda...

The effects of selected membrane, plate and flat shell finite element formulations on optimal topologies are numerically investigated. Two different membrane components are considered. The first is a standard 4-node bilinear quadrilateral, and the other is a 4-node element accounting for in-plane (drilling) rotations. Plate elements selected for evaluation include discrete Kirchhoff quadrilater...

In this paper, we explore three different ways of developing T-Trefftz finite elements of quadrilateral as well as polygonal shapes. In all of these three approaches, in addition to assuming an inter-element compatible displacement field along the element boundary, an interior displacement field for each element is independently assumed as a linear combination of T-Trefftz trial functions. In a...

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...

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...

We present an extension of the original progressive mesh algorithm for large dynamic meshes that contain a mix of triangle and quadrilateral elements. The demand for this extension comes from the visualisation of dynamic finite element simulations, such as car crashes or metal sheet punch operations. These methods use meshes, which consist mainly of quadrilaterals, due to their increased numeri...

Intra-ply shear locking results in unrealistic fibre stresses and spurious wrinkling in composite forming simulations. Three remedies are investigated: aligning the mesh, applying reduced integration and using multi-field elements. The bias extension simulation is used to test several triangular and quadrilateral elements on their capability to avoid locking. Their performance under large defor...