The energy convergence of mixed methods of approximate analysis for problems involving linear self-adjoint operators is investigated. A new energy product and the associated energy norm are defined for such indefinite systems and then used in establishing the strain energy convergence and estimation of error for problems in continuum mechanics. In the process, the completeness requirements are laid out for approximate solutions. Also established is the mean convergence of the basic variable e.g. displacements and stresses. After accomplishing a new mathematical framework for the mixed methods in continuum, the theory is then extended to the finite element method. The completeness requirements, convergence criteria and the effect of continuity requirements on convergence are established. The flexibility offered by the mixed methods in incorporating the boundary con ditions is also demonstrated. For stress singular problems, the strain energy convergence is established and an energy release method for determining the crack intensity factor K. is presented. A detailed eigenvalue-eigenvector analysis of the mixed finite element matrix is carried out for various combinations of interpolations for the plane stress linear elasticity and the linear part of the Navier-Stokes equations. Also discussed is its relation to the completeness requirements. Finally, numerical results are obtained from applying the mixed finite element method to several examples. These include beam bending, a plane stress square plate with parabolically varying end loads, a plane stress cantilever and plane strain stress concentration around a circular hole. A plane stress example of a square plate with symmetric edge cracks is also solved to study the strain energy convergence. Lastly, two rectangular plates, one with symmetric edge cracks and the other with a central crack are considered to determine the crack intensity factor K. In most of the examples, the strain energy convergence rates are predicted and compared with the numerical results, and excellent agreement is observed. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

Ports and waterways are vital to the economy of the United States. In the contiguous United States, there are some 25,000 miles of channels and over 300 ports. Together, this system carries 2 billion tons of freight with a value of over $700 billion annually. Ninety percent of all United States imports and exports travel through these ports and waterways. Dredging of these waterways in the United States costs over $1 billion annually. As ship draft increases, more dredging would be required to keep these ports and waterways open. Fine sediments are very common in these systems and have properties that can reduce dredging efficiency, including easy resuspension into the water column and cohesion among individual particles. Fluid mud is a high concentration aqueous solution of fine sediments that exhibits unique properties, including movement under gravity. A numerical model of fluid mud could be used to predict sediment fate as well as evaluating potential channel modifications to reduce dredging. The goal of this research is to test the flow of fluid mud under shear from the water column and develop a numerical model to simulate the transport of fluid mud. First, laboratory experiments are conducted to ascertain the effects of shear from the water column on the fluid mud layer. Next, a finite element numerical model is developed to simulate the physics of fluid mud, including any effects from shear over the mud layer. Results from the numerical model are compared to laboratory experiments, and the fluid mud model is developed for easy linkage to existing hydrodynamic models for forcing information.

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This thesis introduces an optimization software system which supports two separate optimization approaches to solve structural optimization problems with small and large-scale finite element models. The approach for solving the structural optimization problems of small-scale finite element models consists of the gradient-based optimization method and input file regeneration program. The small-scale structural optimization system, requires users only to put in the parameters of the initial design, the system will run the optimization process and generate new models automatically until the solutions are obtained. The approach for solving structural optimization problems of large-scale finite element models combines parametric finite element modeling methods executed by Python scripts with response surface optimization methods (RSM). This approach reduces the number of finite element analyses as well as reduces the optimization process time. The optimization module of the system is performed by the MATLAB optimization toolbox and the Abaqus finite element program with scripts implemented in Python. A benchmark hollow-tube weight-minimization problem is conducted to test the optimization software system. The percent difference between the solution found by the graphical optimization method and the solution found by the 3D beam finite element model with Sequential Quadratic Programming (SQP) solver and the graphical optimization method is 1.99%. The percent difference between the results from the 3D beam finite element model with SQP solver and the result from 3D brick finite element model with response surface method is 8.16%. The percent difference between the results from the 3D brick finite element model with RSM and the result from the graphical optimization method is 10.31%. / Master of Science / Commercial structural optimization software packages which integrate modeling tools, optimization and extensive computational tools such as a finite element solver were developed and pushed to the market. However, some commercial approaches to structural optimization are not very general. In addition, the commercial codes are designed for a specific-purpose, and they may not be suitable in many cases. If the commercial codes do not properly represent the structural optimization problem, users have to write custom Python scripts to assist the software system in retrieving data from the .odb files generated by FEA software. This thesis introduces an optimization software system which supports two separate optimization approaches to solve structural optimization problems with small and large-scale finite element models. The optimization module of the system is performed by the MATLAB optimization toolbox and the Abaqus finite element program with scripts implemented in Python. This optimization software system allows users to extract and manipulate data for optimization without limitations. Furthermore, once the required parameters are input in the system, the scripting software creates the finite element model and proceeds with the optimization automatically.

The detection of internal log defects has been shown to have a potential for increasing the lumber value. As an alternative to other available expensive log scanning devices, a method using radio frequency waves has been used to detect the knots. The main focus of the current research is to investigate the effectiveness of using radio frequency waves to detect the knots. Electrostatic finite element analysis is performed to predict the defects in logs. A script has been written using the commercial finite element ANSYS software to predict defects in log sections. The results are then compared with the experimental data measured on actual log sections. Analysis proved that it is possible to detect presence of knots in the log sections.