Full Field Dynamic Stress/Strain from Limited Sets of Measured Data Pawan Pingle, Peter Avitabile Structural Dynamics and Acoustic Systems Laboratory University of Massachusetts Lowell One University Avenue Lowell, Massachusetts 01854 ABSTRACT Often times occasional events may cause significant displacement and corresponding stress strain damage to a structure. Using limited sets of measured data, expansion of real time data has been shown to provide accurate full field displacement results. This displacement data can be used in conjunction with the finite element model to identify full field dynamic stress-strain results. This approach is demonstrated for an analytical model to show the methodology proposed. Examples illustrating different configurations of measured data sets along with simulated noise are presented to illustrate the technique. NOMENCLATURE Symbols: ^ nX ` ` @ @ @ @ @ full set displacement vector ^ aX reduced set displacement vector > aM reduced mass matrix > nM expanded mass matrix > aK reduced stiffness matrix > nK expanded stiffness matrix > aU reduced shape matrix > @g aU generalized inverse of reduced shape matrix > @ nU expanded shape matrix > @T transformation matrix. > @ UT SEREP transformation matrix. > @ n REF reference data at all degrees of freedom (dofs) > @ a RTO real time operating data at measured dofs > @ n ERTO expanded real time operating data at all dofs INTRODUCTION Failure of a structure due to dynamic loading invariably involves occurrence of dynamic stresses and strains in the structure. The induced dynamic stresses and strains may be higher than the maximum permissible limit. Periodic estimation of such induced dynamic stresses and strains is extremely crucial for averting any dangerous accidents. Different loading conditions will impact the structure’s health differently. General design processes use a factor of safety to counter the problem of keeping the induced stresses and strains within the permissible limits. However, there is no accurate way to estimate the remaining fatigue life of the structure especially when occasional, unexpected locating conditions occur. To accurately predict the remaining useful life of a structure, correct estimation of dynamic stresses and strains induced in the structure is of prime importance. There are primarily two approaches traditionally used to evaluate such transient stresses in structures. The first approach would be to collect the transient response information at limited locations. Such a process, although predicts the real-time response of the structure under severe dynamic loadings, but does so at only limited locations. Massive structures such as T. Proulx (ed.), Linking Models and Experiments, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series 5, 187 DOI 10.1007/978-1-4419-9305-2_13, © The Society for Experimental Mechanics, Inc. 2011
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