Model verification and validation (V&V) is an enabling methodology for the development of computational models that can be used to make engineering predictions with quantified confidence. Model V&V procedures are needed by government and industry to reduce the time, cost, and risk associated with full-scale testing of products, materials, and weapon systems. Quantifying the confidence and predictive accuracy of model calculations provides the decision-maker with the information necessary for making high-consequence decisions. The development of guidelines and procedures for conducting a model V&V program are currently being defined by a broad spectrum of researchers. This report reviews the concepts involved in such a program.Model V&V is a current topic of great interest to both government and industry. In response to a ban on the production of new strategic weapons and nuclear testing, the Department of Energy (DOE) initiated the ScienceBased Stockpile Stewardship Program (SSP). An objective of the SSP is to maintain a high level of confidence in the safety, reliability, and performance of the existing nuclear weapons stockpile in the absence of nuclear testing.This objective has challenged the national laboratories to develop high-confidence tools and methods that can be used to provide credible models needed for stockpile certification via numerical simulation.There has been a significant increase in activity recently to define V&V methods and procedures. The U.S. Model V&V is fundamentally different from software V&V. Code developers developing computer programs perform software V&V to ensure code correctness, reliability, and robustness. In model V&V, the end product is a predictive model based on fundamental physics of the problem being solved. In all applications of practical interest, the calculations involved in obtaining solutions with the model require a computer code, e.g., finite element or finite difference analysis. Therefore, engineers seeking to develop credible predictive models critically need model V&V guidelines and procedures.The expected outcome of the model V&V process is the quantified level of agreement between experimental data and model prediction, as well as the predictive accuracy of the model. This report attempts to describe the general philosophy, definitions, concepts, and processes for conducting a successful V&V program. This objective is motivated by the need for highly accurate numerical models for making predictions to support the SSP, and also by the lack of guidelines, standards and procedures for performing V&V for complex numerical models.

Numerous theoretical investigations on the natural frequencies for complete spherical shells have been reported over the past four decades. However, attempts at correlating the theoretical results with either experimental or simulated results (both for axisymmetric and nonaxisymmetric modes of vibration) are almost completely lacking. In this paper, natural frequencies and mode shapes obtained from axisymmetric and nonaxisymmetric theories of vibration of complete spherical shells and from finite element computer simulations of the vibrations, with and without geometrical imperfections, are presented. Modal tests reported elsewhere on commercially available, thin spherical marine floats (with imperfections) are then utilized as a basis for comparison of frequencies to both the theoretical and numerical results. Because of the imperfections present, “splitting” of frequencies of nonaxisymmetric modes is anticipated. The presence of this frequency splitting phenomenon is demonstrated. In addition, results of a “whole field” measurement on one of the imperfect shells using dynamic holography are presented.

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