A Thefftz patch recovery method for smooth stress resultants and applications to Reissner-Mindlin equilibrium plate models - Maunder, Edward A.W. (Computer Assisted Methods in Engineering and Science, 2023)
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.