A new fe approach for adaptive reliability assurance

Abstract

The existing adaptive approaches developed for and used with the conventional finite elements are comparatively inefficient in dealing with problems with multiple right-hand sides due to a substantially different adjustment needed for each of them. This problem can be bypassed if the adaptive approach is based on p-extension of the so-called Hybrid-Trefftz (HT) finite elements whereby the interelement continuity is enforced on a non-conforming internal displacement field which satisfies the governing non-homogeneous differential equations of the problem. As in the standard hybrid-stress methods, the HT elements make use of an auxiliary conforming frame function field, independently defined at the element boundary in terms of the conventional nodal freedoms which are the final unknowns of the problem. In the HT p-extension the frame functions involve an optional number of hierarchic modes and the number of internal displacement modes is a function of the number of frame function degrees of freedom. A typical HT FE subroutine is associated with a library of optional sets of internal displacement functions including local solutions in the vicinity of various singularities. This makes it possible to efficiently handle difficult singularity problems without mesh refinement. The presented adaptive approach enables the specified accuracy to be reached, simultaneously for all right-hand sides, in a single trial by suitably uniformly adjusting the number of the hierarchic degrees of freedom of the elements.