in this paper, two new quadrilateral elements are formulated to solve plane problems. low sensitivity to geometric distortion, no parasitic shear error, rotational invariance, and satisfying the felippa pure bending test are characteristics of these suggested elements. one proposed element is formulated by establishing equilibrium equations for the second-order strain field. the other suggested...

In this part of the work, a notion of generalized enrichment is proposed to construct the global partition polynomials or to enrich global partition polynomial basis with extra terms corresponding to the higher order derivatives of primary variable. This is accomplished by either multiplying enrichment functions with the original global partition polynomials, or increasing the order of global p...

A recent study [4] reveals that convergence of finite element methods usingH(div ,Ω)compatible finite element spaces deteriorates on non-affine quadrilateral grids. This phenomena is particularly troublesome for the lowest-order Raviart-Thomas elements, because it implies loss of convergence in some norms for finite element solutions of mixed and least-squares methods. In this paper we propose ...

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...

This paper introduces a new fixed mesh structural analysis technique based on isoparametric formulations from classic finite element analysis. Fixed mesh methods are popular in boundary based optimisation as they avoid mesh distortion problems and reanalysis is simple and efficient. The area ratio based fixed grid method is often employed due to its favourable simplicity in implementation. Howe...