Engineering problems sometimes involve the numerical solution of boundary value problems over domains containing geometric features with widely varying scales. Often, a detailed solution is required at one or more of these features. Small details (for example, cracks and flaws) in large structures may have profound effects upon global structural performance. Conversely, large-scale conditions may have effect on local performance (for example, tectonic stresses may cause rock failures near tunnels). Many man-hours and CPU-hours are currently spent in modeling such problems. With the proposed structural zooming technique, it is now possible to design an integrated program which allows the analyst to interactively focus upon a small region of interest, to modify the local geometry, and then to obtain highly accurate responses in that region which reflect both the properties of the overall structure and the local detail. The structural zooming technique is a general technique that can be applied to the numerical solution of a set of partial differential equations. It can be applied to problems in computational structural mechanics (for example, in automobile and aerospace engineering), fluid mechanics, geomechanics and geotectonics, fracture mechanics, and electromagnetics. Problems with widely varying geometric scales of interest exist in each of these areas. The use of the structural zooming technique could result in more accurate analysis at specific regions of interest at a lower cost. During Phase II of this project, the Principal Investigator proposes to concentrate the research in the area of structural mechanics.
