SBIR-STTR Award

This project will develop an integrated, computer graphical design tool for the numerical solution of boundary value problems over domains containing geometric features with widely varying scales. Many hours are presently spent in modeling such problems. The proposed Structural Zooming System (SZS) will significantly reduce the cost and increase the accuracy of such analyses. The central concept, as introduced here, is simple, and is coined ''structural zooming." This concept approaches the problem of modeling a large complex object (the "parent" object) by recursively analyzing smaller portions ("child" objects) of the parent. Geometrical and mesh refinements may be introduced for each successive analysis. After an analysis of the parent, a child is extracted. Boundary conditions derived from the parent analysis are applied to the child at the parenUchild interface, and the child is analyzed. Overall accuracy is improved using an iterative algorithm involving reanalysis of both the parent and child objects to reduce disequilibrium at the interface (caused by "back-coupling" effects). Finally, the method is recursive a grandchild, greatgrandchild objects, etc., can be defined if responses on more refined geometrical scales are required. Phase I research will address the feasibility of structural zooming. A two-dimensional prototype, consisting of a number of distinct software modules, will be developed. Phase II will develop a completely integrated Structural Zooming System for two and three dimensional objects, utilizing software designs and recommendations developed during Phase I. Anticipated Results and

Potential Commercial Applications:
The Structural Zooming System will improve the accuracy and reduce the cost of analyses of problems containing geometric features of widely varying scales in a number of areas of research. These include structural mechanics, aerospace engineering, earthquake engineering, geotechnical engineering and geotectonics, computational electromagnetics, automotive engineering, structure survivability under blast loading, and transient dynamics.

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.