This thesis presents a novel method for the correlation of FEM results to experimental test results known as the "Load updating method." Specifically, the load updating method uses the math model from the FEM and the strains measured from experimental or flight test data as inputs and then predicts the loads in the FEM which would result in strains that would correlate best to the measured strains in the least squared sense. In this research, the load updating method is applied to the analysis of a complex frame structure whose validation is challenging due to the complex nature of its structural behavior, load distributions, and error derived from residual strains. A FEM created for this structure is used to generate strain data for thirty-two different load cases. These same thirty-two load cases are replicated in an experimental setup consisting of the frame, supporting structure, and thirty actuators which are used to load the frame according to the specifications for each of the thirty-two load conditions. A force-strain matrix is created from the math model in NASTRAN using unit loads which are separately applied to each load point in order to extract strain results for each of the locations of the seventy-four strain gages. The strain data from the structural test and the force-strain matrix is then input into a Matlab code which is created to perform the load updating method. This algorithm delivers a set of coefficients which in turn gives the updated loads. These loads are applied to the FEM and the strain values extracted for correlation to the strains from test data. It is found that the load updating method applied to this structure produces strains which correlate well to the experimental strain data. Although the loads found using the load updating method do not perfectly match those which are applied during the test, this error is primarily attributed to residual strains within the structure. In summary, the load updating method provides a way to predict loads which, when applied to the FEM, would result in strains that correlate best to the experimental strains. Ultimately, this method could prove especially useful for predicting loads in experimental and flight test structures and could aid greatly in the Federal Aviation Administration (FAA) certification process. / Master of Science / The research presented in this thesis provides a new way for correlating data obtained during structural testing with results obtained from computer analysis known as the finite element method (FEM). During the process of certifying an aircraft structure with the FAA, it is important to be able to demonstrate that the results obtained for a given structure with a computer model matches the results produced by a real world experiment within a reasonable tolerance. Traditionally, differences between these two results have been accounted for by adjusting the model within the computer until its results match those from the test. However, in this research the loads which are applied on the computer model are changed instead until loads are found which produce results in the computer models that match those from testing. This method, known as the load updating method, therefore provides a way to predict loads on a structure where the loads are unknown such as a flight test article. Here, the ability of the load updating method to predict loads on a complex three dimensional frame structure is explored and the accuracy of the results studied by comparing the results to those from a structural test whose loads are known. It was found that the load updating method does indeed predict unknown loads to a reasonable accuracy and could aid future design efforts immensely.

This dissertation deals with the solution of three inverse problems in structural mechanics. The first one is load updating for finite element models (FEMs). A least squares fitting is used to identify the load parameters. The basic studies are made for geometrically linear and nonlinear FEMs of beams or frames by using a four-noded curved beam element, which, for a given precision, may significantly solve the ill-posed problem by reducing the overall number of degrees of freedom (DOF) of the system, especially the number of the unknown variables to obtain an overdetermined system. For the basic studies, the unknown applied load within an element is represented by a linear combination of integrated Legendre polynomials, the coefficients of which are the parameters to be extracted using measured displacements or strains. The optimizer L-BFGS-B is used to solve the least squares problem. The second problem is the placement optimization of a distributed sensing fiber optic sensor for a smart bed using Genetic Algorithms (GA), where the sensor performance is maximized. The sensing fiber optic cable is represented by a Non-uniform Rational B-Splines (NURBS) curve, which changes the placement of a set of infinite number of the infinitesimal sensors to the placement of a set of finite number of the control points. The sensor performance is simplified as the integration of the absolute curvature change of the fiber optic cable with respect to a perturbation due to the body movement of a patient. The smart bed is modeled as an elastic mattress core, which supports a fiber optic sensor cable. The initial and deformed geometries of the bed due to the body weight of the patient are calculated using MSC/NASTRAN for a given body pressure. The deformation of the fiber optic cable can be extracted from the deformation of the mattress. The performance of the fiber optic sensor for any given placement is further calculated for any given perturbation. The third application is stiffened panel optimization, including the size and placement optimization for the blade stiffeners, subject to buckling and stress constraints. The present work uses NURBS for the panel and stiffener representation. The mesh for the panel is generated using DistMesh, a triangulation algorithm in MATLAB. A NASTRAN/MATLAB interface is developed to automatically transfer the data between the analysis and optimization processes respectively. The optimization consists of minimizing the weight of the stiffened panel with design variables being the thickness of the plate and height and width of the stiffener as well as the placement of the stiffeners subjected to buckling and stress constraints under in-plane normal/shear and out-plane pressure loading conditions. / Ph. D.