This investigation presents a method of extraction of the built-in stress in films grown by thin-film deposition or growing in microplate structures. Although thin-film deposition processes are well controlled, the stress values might significantly vary, reaching ±40% of the projected value. The assumption of variance yields more accurate solutions for the deflection than the values obtained by assuming the exact interlaminar stress yielded by the deposition process. The extraction method was used in conjunction with a gradient-based optimization method to evaluate the effective stress based on the response of the microplate to distributed load. The estimation of the deflection in the model versus the experimental method is based on static deflection matching. The estimation of root-mean-square error based on the proposed model was reduced to 0.38% versus the experimental evaluation, while the deflection resulting from the assumption of the nominal interlaminar stress yield errors of up to 40% versus experiments.[2014-0220]Index Terms-Finite element methods, measurement errors, nonlinear differential equations, optimization methods, pressure measurement, Stone equation.

Presented herein is a mathematical model employing differential equations formulation for brush seals used in gas turbine engines. These components are used to seal the bearing chamber from the environment and reduce the loss of lubricant in the atmosphere, ensuring a MTBR long enough to have required the change the seals only during the engine overhaul operation. The model assumes a single curved bristle loop in the form of a curved-bridge beam subjected to the influences of complex external loads (static and dynamic). Further, a model for clustered bristles is proposed. Specifically, the static forces acting on the curved-bridge beam include the weight of the oil capillary attached to the beam, the weight of the beam itself, the capillary force developed between the surfaces of the bristles in the brush and the temperature gradient. The dynamic forces include the leakage oil pressure and the rotation of the shaft. This complex loading induces a nonlinear large deflection on the curved-bridge beam. Also, the temperature gradient present on the bristles during the gas turbine engine operation generates a change in the geometry of the beam and in the magnitude of the forces acting on the bristles modeled as beams. In the present model, the weights are assumed as uniformly distributed forces on the surface of the beam while the capillary forces and the force generated by the rotating shaft are considered to be non-uniform. The equation expressing the curvature of the beam under general loading force is developed and one can choose the appropriate method of solving the generated differential equation after the expression of the general force is defined. Hence, the ordinary differential equation describing the nonlinear large deflection of the curved-bridge beam will be derived using general nonlinear elasticity theory.