Study on Singular Elements with HRR Singularities (One-dimensional Singular Elements)

摘要

In analyzing a cracked solid by using the finite element method, the singularity of the tip of crack must be taken into consideration and for this purpose the so-called singular element which has either O(r{sup}(-1/2) singularity or O(r{sup}(-1) singularity have been developed so far. The order of singularity of the tip of a crack in a strain-hardening solid is different from that in a linear-elastic solid and it becomes O(r{sup}(-1/2)～O(r{sup}(-1) according to the work hardening exponent of the solid. This singularity is called as the HRR singularity. In our series of researches, the HRR singular elements will be examined from the one-dimensional case to the three-dimensional one by using the super-parametric elements. One-dimensional HRR singular elements will be focused in the present research. Consequently, the singular elements with O(r{sup}(-(l-1)/l) singularity can be developed successfully by using the super-parametric element defined by the linear shape function and l-th. order of the polynomial function defining the geometry and moving its mid-side nodes to the appropriate site on the edge of element.