bridges, ships, wind-turbines would need thousands of sensors to get the required data, which is highly improbable and unfeasible. The second approach would be to predict the transient forces that the structure experiences and then using the analytical model find the dynamic stresses the structure experiences. The problem herein lies with the force estimation process which is highly sensitive to the number of chosen degrees of freedom and their distribution on the structure. Apart from this, the other issues such as approximations while developing a finite element model invariably induce errors in estimation of dynamic stresses on the structure. The approach used in this paper has been introduced in [1] where full-field real-time displacements were obtained successfully from limited sets of displacement data using a real time operating data expansion technique recently studied by Chipman [2]. The limited set of sensors would provide displacement data and the expansion algorithm would expand the limited data set to a full-field displacement solution thereby completely eliminating the force estimation step required in the previous approach. In this paper, the full-field displacements are used to obtain full-field dynamic stress strain information. The estimated dynamic stress-strains using this approach are then compared with reference stress-strain solutions to validate the proposed approach. THEORY The approach presented in this work is conceptually explained in the schematic shown in Figure 1. Traditional finite element design process involves discretization of the component into elements, assembling the system matrices and applying appropriate approximations of boundary conditions and loading to estimate the dynamic stress-strain that the component sees throughout the designed life of the component/structure. The approach presented in this work involves collecting experimental displacement data at limited measurable locations, then a real-time operating data expansion technique is used to expand the limited displacement data set to full-field displacements. The expansion technique uses mode shape information which is obtained from the analytical model of the structure. Figure 1: Schematic showing various design approaches to estimate dynamic stress-strain Finally the full-field displacement data set is used to recover the dynamic stress-strain information by using backsubstitution process shown in Figure 2. The finite element process is interrupted to incorporate the expanded full-field displacement solution in order to obtain the full-field dynamic stress-strain solution. In Figure 2, the full-field strain solution is shown at one time step; however, the full-field strain solution is obtained for all the required time steps through the recovery process. 188
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