and a finite element model, the dynamic stresses are computed at the root region of the blades. Such work can only estimate the local stress, but the full-field information is not available. The next section will describe the relevant theory required for understanding the proposed technique introduced for estimating dynamic stress-strain. THEORY The traditional design process relies on the general development of a finite element model, the assembly of the system matrices, the application of loads and the boundary conditions followed by the solution of the set of equations and the recovery of the stress-strain solution as shown in Figure 1. Along with being challenging to accurately depict the transient events, the traditional design process also has other issues, such as the actual loading is not known and the actual boundary conditions are not well understood. Component Discretize Assemble Apply BC & Loads Solve for Displacements Dynamic Stress-Strain Figure 1: Schematic Showing Normal Finite Element Model Development For the approach considered in this work, the difference is that the actual application of the loads and the boundary conditions is not specifically performed. Rather, the sparse set of displacements, measured from an actual operating event, is used with a set of orthogonal expansion functions to obtain the full field displacement solution. This displacement solution is then used with the normal back substitution and recovery of the stress-strain solution in the finite element modeling process. This procedure is shown schematically in Figure 2 where the limited set of measurement DOFs are used with the expansion processes to obtain the full field displacement for the system. Figure 2: Schematic Showing Alternation Expansion/Solution Sequence The full field displacement data is obtained from the limited sets of measured data using an expansion technique. Hence the expansion forms the basis of the proposed approach. A review of the model reduction/expansion techniques is presented in the next section. 203
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