Numerical implementation of hybrid-{T}refftz displacement elements

Freitas, J. A. T., and C. Cismaşiu. "Numerical implementation of hybrid-{T}refftz displacement elements." Computers & Structures. 73 (1999): 207-225.


The numerical implementation of the displacement model of the hybrid-{T}refftz finite element formulation is presented. The geometry of the supporting element is not constrained a priori. Unbounded, non-convex and multiply connected elements can be used. The approximation basis is naturally hierarchical and very rich. It is constructed on polynomial solutions of the governing differential equation, and extended to include the particular terms known to model accurately important local effects, namely the singular stress patterns due to cracks or point loads. Numerical and semi-analytical methods are used to compute the finite element matrices and vectors, all of which present boundary integral expressions. Appropriate procedures to store, manipulate and solve symmetric highly sparse systems are used. The characteristics of the finite element solving system in terms of sparsity and conditioning are analysed, as well as its sensitivity to the effects of mesh distortion, incompressibility and rotation of the local reference systems. Benchmark tests are used also to illustrate the performance of the element in the estimation of displacements, stresses and stress intensity factors.