Special elements for discontinuous concentrated forces in plane elastic solids

摘要

Emphasis in the paper is placed on the treatment of discontinuous concentrated forces applied in the two-dimensional elastic solids by special elements constructed in the context of hybrid finite element method, in which two independent fields are respectively assumed inside the element or along the element boundary. According to the physical definitions of fundamental solutions, the element interior homogeneous and particular displacement and stress solutions are separately approximated by the combination of fundamental solutions to give true representation of local effect caused by point loads, while the element boundary displacement solutions are approximated by the conventional shape functions. The stationary condition of the hybrid functional produces the relationship of these two fields and the element stiffness equation. The advantage of special elements established is that a large element independent of location of discontinuous point loads can be used to avoid the requirement of mesh refinement in the vicinity of the area with local concentrated loads. Finally, numerical experiment is carried out to verify the present special elements and investigate the effectiveness of them in aspect of mesh reduction.