In this paper, we analyze the supercloseness property of the streamline diffusion finite element method (SDFEM) on Shishkin triangular meshes, which is different from one in the case of rectangular meshes. The analysis depends on integral inequalities for the part related to the diffusion in the bilinear form. Moreover, our result allows the construction of a simple postprocessing that yields a more accurate solution. Finally, numerical experiments support these theoretical results.
This paper presents a study of a hybrid grid shell, which is made of quadrangular meshes diagonally stiffened by pre-tensioned thin cables. The construction of the hybrid structure by translating a spatial curve against another spatial curve is firstly described. Then the elasto-plastic buckling analyses of the perfect hybrid structure and the corresponding single-layer lattice shell are carried out, and the influence of the asymmetric load on the failure loads is discussed based on a finite element model. Furthermore, the different shapes and sizes of imperfections are considered in this study. Two schemes of imposing imperfections are chosen: the first several eigenvalue buckling modes and the deformed shape of the loaded structure obtained from a geometrical non-linear analysis are chosen as the imperfection shape. Finally, the effects of different structural parameters, such as the rise-to-span ratio, beam section dimension, area and pre-stress of cables and boundary conditions, on the failure loads are investigated.
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