J. A. Teixeira de Freitas, C. Tiago, E. M. B. R. Pereira
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Modelling the effect of point forces and moments in plate bending with hybrid-Trefftz stress elements
The formulation of the hybrid-Trefftz stress element for plate bending is extended to the modelling of concentrated forces and moments, either as prescribed loads or as reactions at point supports. As the bending, torsion and shear fields are hypersingular, the flexibility matrix of the element involves the use of the finite part integration concept. In addition, it requires the confirmation of the positive-definiteness of the flexibility under gross shape distortion. The tests illustrate the modelling of applied concentrated forces and moments and also the combination of boundary layer and point reaction effects. The results obtained are validated using converged solutions obtained with a stress-based hybrid-mixed element (HMS) and a displacement-based mixed element (MITC).
期刊介绍：
The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems.
The Journal is known for welcoming contributions in a wide range of areas in computational engineering, including computational issues in model reduction, uncertainty quantification, verification and validation, inverse analysis and stochastic methods, optimisation, element technology, solution techniques and parallel computing, damage and fracture, mechanics at micro and nano-scales, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, and error estimation and mesh generation. It is emphasized that this is by no means an exhaustive list, and particularly papers on multi-scale, multi-physics or multi-disciplinary problems, and on new, emerging topics are welcome.
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