Principal Investigator: Vinod K. Tewary

Objective: Develop an interactive tool available over the world wide web (WWW) for using Green's function and boundary element methods to facilitate the design, inspection, and manufacture of components made with advanced materials.

Background:

In August, 1994, the Center for Computational and Theoretical Materials Science (CTCMS) of NIST sponsored a workshop organized by the PI and Prof. J. R. Berger (Colorado School of Mines) in Boulder, Colorado, on Green's functions and boundary element analysis for the mechanical properties of advanced materials. A number of university/industry/national laboratory partnerships developed as a direct outcome of the workshop. With the cooperation of NIST and the National Science Foundation, several of these partnerships formed a consortium which then received support for research related to the theme of the workshop. This support was primarily for graduate students working with the academic participants, and the goals of this one-year effort have largely been attained.

Based on the past year of the consortium's research activities, the idea of a Library of Green's functions, introduced at the workshop by Prof. F. J. Rizzo (Iowa State Univ.), has grown and has come to the forefront as an outstanding example of the type of modern computational tool the CTCMS is striving to develop. Emphasis has been on constructing Library entries with a discretized or numerical form. While such entries would form the bulk of a future working library, analytical and semi-analytical Green's functions will play a significant role - especially for the characterization of material properties.

The idea of the library is simple: with today's capability for massive amounts of storage and rapid transfer of data, it is possible to identify, (pre)compute, and save generic, repeatedly-useful items, called discretized region-dependent Green's functions, when modeling difficult physical problems by computer. With a library of such functions, the designer need not have the expertise of the computational engineer and need not wait for lengthy computations, often done on very large computers by specialists. Such computations are usually based on resources and modeling effort a designer either cannot or would rather not expend. In short, with the library and today's technology, the fruits of modeling effort and heavy computation by computational experts may be stored and speedily used repeatedly by non-experts.

Conversations the PI and collaborators have had with industrial designers and computational engineers have highlighted the need for the proposed library. At present the design process involves a series of iterations between the designers (and their solid-modeling software) and the analysts (and their finite-element or boundary-element software). If a complicated component is involved, even relatively small changes in design can result in days or a week or more of re-analysis. Reduction of this time-cycle is critical for engineering firms to remain competitive in today's marketplace. This is precisely where the proposed library would have its greatest impact.

Conceptually how the library would work in the design process is straightforward. For example, say a landing-gear strut for a commercial aircraft is being re-designed where certain new features such as elliptical holes must now be introduced. The designer would be able to call up from a menu of shapes available in the library the region-dependent Green's function associated with the strut minus the holes. At this point the designer could play endless "what if" scenarios involving holes of various shapes, in different positions, involving various loads and imposed displacements. With the library, the designer would be able to place new holes or other geometric details, on the strut. The entire strut-plus-holes would not have to be remodeled in each scenario, and most importantly, the time and effort for each new computation would be a function of the small changes only. The designers would then have an almost immediate answer as to the consequences of introducing the new shapes into the overall strut design. There would be no need to wait for a full analysis from the finite element support group.

As we enter the era of advanced materials, the Green's functions library will be even more useful. The advanced materials are anisotropic in contrast to traditional materials which are largely isotropic. The conventional mathematical techniques of analysis are computationally inefficient for anisotropic materials. Powerful mathematical techniques have been developed at NIST for calculating the anisotropic Green's functions. The computed values of the Green's functions using these special techniques will be available to industrial users through the library. This will avoid the need for the industry to get sidetracked into learning specialized techniques for calculation of anisotropic Green's functions.

The proposed library is widely applicable to a variety of problems in stress analysis, ultrasonics, and acoustics. As such, the library would be a valuable tool in the hands of engineers responsible for inspection or design and manufacturing. The library would allow the engineer responsible for inspection to play endless "what if" scenarios with different input waves and sensor locations. The design or manufacturing engineer could also play "what if" games as to the effects of changing relatively small details on the overall stress distribution in a complex part. With the main library tool available at an internet web site, and specialized depositories of pre-computed Green's functions developed for industry-specific components, the library would be a continuously developing tool.

Industrial Partnerships:

An industrial partner is to be identified. The investigators have had initial conversations with engineers at Ball aerospace, Lockheed-Martin, Motorola, Automated Analysis Corp., Structural Dynamics Research Corporation, Ford, Caterpillar, and others. One of our main goals initially is to identify an appropriate industrial partner where we would develop significant library entities specifically for the identified company.

A workshop is organized at NIST, Gaithersburg on Oct. 15 and 16, 1998, that will help identifying an Industrial partner.

References:

"Boundary elements and a Green's function library " paper by F.J. Rizzo, P.A. Martin, and R.A. Roberts; Proceedings of the NIST workshop on Green’s functions and boundary element analysis, NIST Special Publication SP 910 (1996). (Download, in pdf)

"Boundary element analysis of bimaterials using anisotropic elastic Green's functions" paper by John Berger; Proceedings of the NIST workshop on Green’s functions and boundary element analysis, NIST Special Publication SP 910 (1996). (Download, in pdf)

"Elastic Green’s functions for anisotropic solids (review)," paper by V.K. Tewary; Proceedings of the NIST workshop on Green’s functions and boundary element analysis, NIST Special Publication SP 910 (1996). (Download, in pdf)