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This study compares energy minimization with direct stiffness for linear structural analysis. The energy minimization approach locates the generalized displacement vector by minimizing the total potential energy of the structure being analyzed. From the survey of variable metric and conjugate gradient algorithms included in this study, the Davidon-Fletcher-Powell variable metric algorithm and the FletcherReeves conjugate gradient algorithm were chosen to minimize the total potential energy. A description of both algorithms is presented. The direct stiffness method assembles the equilibrium equations of the structure being analyzed. These equations are solved by Gaussian elimination to determine the generalized displacement vector. Computer codes have been written for the energy minimization and direct stiffness methods. The comparison was based on computational effort, in terms of computer time, required for analysis. The results of this study show energy minimization is not competitive with direct stiffness for linear structural analysis. As the problem size increases by degree of freedom the direct stiffness method rapidly increases in superiority over the energy minimization method. / Master of Science

Poisson's ratio for aluminum is estimated from velocity profile measurements of a free-free beam under dynamic loading conditions A weighted least-squares method is used to select a beam model which is subsequently used to determine the transverse and anticlastic radii of curvature. The model of the beam velocity profile is selected using forward regression with the possible regressor set formed by products of Legendre polynomials in x and y, the two-dimensional coordinates of the beam. The resulting model is manipulated to extract the transverse and anticlastic radii of curvature of the beam which are then used to find local and global estimates of Poisson's ratio. Estimates for Poisson's ratio are found for three different forcing frequencies and three force amplitudes at each frequency. The frequencies selected correspond to the frequencies of the operating shapes dominated by the first, second, and third bending modes. A statistical analysis is performed to assess the quality of the estimates of Poisson's ratio. Results show that the estimates of Poisson fs ratio are dependent on the forcing frequency and forcing amplitude. All estimates are below the accepted value of .33 for aluminum. Contributions of plate modes adversely affect the estimates. Estimates based on the first and third operating shapes exhibit a lower variance than the estimate based on the second operating shapes. / Master of Science

Composite diaphragm strength and behavior were studied using non-linear finite element analysis. A total of 57 three panel diaphragm models were analyzed to failure. Parameters studied included beam size and orientation, panel dimension, connector type and distance, slab opening, yield plateau, and beam connection flexibility. Shear connector, deck-to-concrete interface, and beam connection were the components modeled non-linearly. Orthotropic behavior was used for the deck elements. 2-D and 3-D contours of concrete slab, steel deck and deck-to-concrete interfacial stresses and connector forces are presented to clearly show the behavior of the diaphragm in relation with the component behavior. Complete and incomplete connector force redistributions were observed and an expression of yield plateau length required to develop a complete connector force redistribution was developed. Expressions for diaphragm strength based on beam, beam connection and connector strength for both the complete and incomplete connector force redistribution cases were presented. The diaphragm strength predicted by the expression compared favorably with the finite element results. / Master of Science

The main objective of this study is to develop an analytical model to explain the behavior of a hybrid structure under different loading conditions. The model developed for a simply supported beam on moment capacity, stiffness, and deflection can be generalized to deal with any type of material combination. The dependence of moment capacity of the hybrid beam on the thickness of the composite sheet was investigated. The inherent property of a high Young's modulus and strain-to-failure properties of the composite material increased the moment capacity of the RC beam dramatically. The moment model showed a percentage increase of 284% for KFRP while on the other hand the percentage increases for CFRP and GFRP were 191% and 174% respectively when using a FRP sheet of thickness 0.025 mm. KFRP showed the highest increase in moment capacity because of its high strain-to-failure. CFRP on the other hand has a high Young's modulus, but its strain to failure is low, causing it to lie in the middle range. The analytical model is that the ability of a beam to handle moment is strongly dependent on the strength characteristics and the thickness of the FRP sheet. / Master of Science

Experimental evaluations of impact damage resistance and residual compression strengths after impact are presented for nine laminated fiber reinforced composite material systems. The experiments employ a small scale specimen for assessing the impact damage resistance and impact damage tolerance of these materials. The damage area detected by C-scan is observed to develop linearly with the impact velocity for impact velocities higher than a threshold value. Brittle material systems have lower threshold velocities and higher damage area growth rates than toughened systems. The impact damage resistance of each material system can be characterized with threshold velocity V_c and damage area growth rate C. The residual compressive Strength after impact was observed to decrease linearly with the damage area equivalent diameter. The rate of compressive strength reduction, K_d, has been observed to be independent of the material properties. The impact damage can be simulated from quasi-static indentation test in which the damage due to these two loading conditions are quite similar. The residual compressive strength can also be simulated from specimens with similar damage size resulting from quasi-static indentation load. / Ph. D.

An iterative penalty finite element model is developed for the analysis of three-dimensional coupled incompressible fluid flow and heat transfer problems. The pressure is calculated by solving the momentum equation using known values of velocities, velocity gradients, and flow stresses from previous iteration. An iterative solution algorithm which employs the element-by-element data structure of the finite element equations is used to solve large systems of algebraic equations resulting from finite element models of real world problems. Three different iterative methods (ORTHOMIN, ORTHORES and GMRES) are implemented and tested to determine the efficiency of each algorithm terms of CPU time and storage requirements. Jacobi/Diagonal preconditioning is used to scale the system of equations and improve the convergence of the iterative solvers. The developed iterative penalty finite element model is extended to analyse three-dimensional manufacturing processes such as casting, extrusion and forming of metals. For numerical simulation of extrusion and forming, flow formulation is used since these operations involve large deformations. The viscosity of the metal at elevated temperatures is calculated from the flow stress. The formulation uses the enthalpy method to account for the transfer of latent heat during phase change. The fluid inside the mushy region (between liquid and solid regions) is assumed to obey D’Arcy’s law for flow through porous materials. The permeability of the material is determined as a function of liquid fraction. This forces the velocities in the solid region to zero. In the finite element model, the effects of convection during phase change of the material are included. A method for calculation of the movement of liquid metal-air interface during mold filling process is presented. The developed model predicts the location of the interface (defined by a pseudo-concentration value) by solving for its movement due to forced convection. Also during filling analysis, only the filled and interface elements are used for flow field calculations. / Ph. D.