Inverse Problems in Structural Mechanics

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Virginia Tech


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.



unitized structures, finite element models, fiber optic sensors, load updating, genetic algorithms, placement optimization, panel optimization, inverse problems