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A Trefftz patch recovery method for smooth stress resultants and applications to Reissner--Mindlin equilibrium plate models

Maunder E. W. A.

Computer Assisted Mechanics and Engineering Sciences

2001

Vol. 8, No. 2-3

409-424

A method is proposed for smoothing approximate fields of stress-resultants in patches of finite elements. The method is based on combining Trefftz fields of stress-resultants in a p-version so as to obtain a closest fit using the strain energy norm as a measure. The local systems of equations are formulated from boundary integrals. The method is applied to a problem of a square plate modelled by hybrid equilibrium plate elements using Reissner--Mindlin theory. Results for the problem indicate that the smooth solution for stresses can be in close agreement with the analytic solution in the interior of a patch. Proposals are also included to aid the visualization of tensor and vector continuous fields as stress trajectories.