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Study of Submodeling of a Small Component in a Structure

Errors can be minimized through careful consideration of sampling and response frequencies.

A study was performed to evaluate the accuracy achievable in the use of submodeling in finite-element modeling of the mechanical response of a structural system that includes components embedded in a larger structure that is subjected to a large transient load. The specific system studied was a simplified model of a “smart” projectile containing a substructure that supported an electronic-circuit board on which were mounted two capacitors and an eight-lead integrated circuit (see figure). The main body or shell of the projectile was represented as a cylindrical ring supporting the substructure. The dimensions of the various components were chosen to be typical of “smart” munitions. The transient load condition was represented by a velocity-versus-time boundary condition, typical of the velocity versus time of a projectile at launch, imposed at the lower surface of the cylindrical ring.

The Global Model includes the domain of interest represented by the submodel. The mesh of the global model is much coarser than that of the submodel.
In submodeling, the model of a structural system comprises a global model and local model denoted the submodel. The global model represents the entire structure and contains a coarse representation of a domain of interest (e.g., the integrated circuit, the capacitors, and the supporting substructure in this study). The global model is refined enough (that is, its computational mesh is fine enough) to enable accurate calculation of the displacement on the boundary of the local domain of interest. Subsequently, the solution obtained from the global model along the boundary of the domain of interest is applied as a displacement boundary condition on the submodel.

The submodel is a highly refined model of the domain of interest (that is, its computational mesh is much finer than that of the global model). The main motivation for submodeling is that it takes much less computation time than does modeling of the entire structure using a single mesh fine enough for the domain of interest. The primary assumption in submodeling is that the structural details of the submodel do not significantly affect the global model. In most practical applications, there are no known a priori methods for determining the validity of this assumption.

In the study, computational simulations to determine the deformations and stresses in the domain of interest during the first 1.4 ms of launch time were performed by use of (1) a fully refined baseline model of the entire structure, including the domain of interest; (2) a global-model/submodel combination utilizing the displacement boundary condition sampled at 1,000 subintervals of the 1.4-ms launch interval; and (3) a global-model/submodel combination utilizing the displacement boundary condition sampled at 100 subintervals of the 1.4-ms launch interval.

The two different time discretizations of the displacement boundary condition were used because time-dependent fidelity of boundary conditions had previously been found to affect results in submodeling and, hence, it was felt necessary to examine the effect in the system of this study. The results from the two submodel cases were found to be good approximations of those of the global model, but in the 100-point case, the stress peaks and valleys were found to overshoot and undershoot those of the baseline model. In the 1,000-point case, as expected, the stress peaks and valleys overshot and undershot by smaller amounts; that is, they approximated those of the baseline model more closely.

It was known a priori that submodeling might introduce spurious high-frequency content into the solution. The study included an examination of this effect, leading to the conclusion that through proper care in selection of the frequency of the global-model output, one can minimize adverse effects. It was shown that for the case studied, sufficient accuracy in the stress results of the submodel can be realized if one considers the desired frequency response range. If one subsequently samples the global loading finely enough, any high-frequency content introduced lies above the frequency range of interest.

This work was done by Brian M. Powers and David A. Hopkins of the Army Research Laboratory.

ARL-0042

Topics:
Capacitors Computer simulation Electrical systems Electronic equipment Energy storage systems Information Technology Integrated circuits Military vehicles and equipment Munitions Scale models Simulation and modeling Vehicles
This Brief includes a Technical Support Package (TSP).
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Study of Submodeling of a Small Component in a Structure

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    Defense Tech Briefs Magazine

    This article first appeared in the April, 2009 issue of Defense Tech Briefs Magazine (Vol. 3 No. 2).

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    Read more articles from the archives here.

    Overview

    The document titled "Evaluation of the Submodeling Technique for Analyzing Electronic Components" by Brian M. Powers and David A. Hopkins, published in October 2005, presents a comprehensive analysis of the submodeling technique, which is employed to enhance the evaluation of electronic components. The report is part of the Army Research Laboratory's efforts to improve methodologies in the field of electronic component analysis.

    The introduction outlines the significance of accurately analyzing electronic components, particularly in the context of military applications where reliability and performance are critical. The authors emphasize the need for advanced techniques that can provide detailed insights into component behavior under various conditions.

    The report includes a sample problem that illustrates the application of the submodeling technique. This section details the methodology used to implement the technique, including the selection of parameters and the computational processes involved. The sample problem serves as a practical example, demonstrating how submodeling can be utilized to break down complex systems into more manageable subcomponents, allowing for more precise analysis.

    Results from the application of the submodeling technique are presented, showcasing its effectiveness in improving the accuracy of simulations and analyses. The findings indicate that submodeling can significantly enhance the understanding of stress distributions and failure modes in electronic components, leading to better design and reliability assessments.

    In the conclusions section, the authors summarize the key benefits of the submodeling technique, highlighting its potential to streamline the analysis process and improve the overall reliability of electronic systems. They also discuss the implications of their findings for future research and development in the field, suggesting that further exploration of submodeling could lead to even more refined analytical tools.

    The report concludes with a list of references, providing sources for further reading and validation of the methodologies discussed. The distribution list indicates that the report is intended for a wide audience, reflecting its relevance to both military and civilian applications in electronic component analysis.

    Overall, this document serves as a valuable resource for researchers and engineers seeking to enhance their understanding of electronic component behavior through advanced analytical techniques.

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