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Genetic algorithms are well known for being expensive optimization tools, especially if the cost for the analysis of each individual design is high. In the past few years, significant effort has been put forth in addressing the high computational cost GAs. The research conducted in the first part of this thesis continues this effort by implementing new multiple elitist and variable elitist selection schemes for the creation of successive populations in the genetic search process. The new selection schemes allow the GA to take advantage of a greater amount of important genetic information that may be contained in the parent designs, information that is not utilized when using a traditional elitist method selection scheme. By varying the amount of information that may be passed to successive generations from the parent population, the explorative and exploitative characteristics of the GA can be adjusted throughout the genetic search also. The new schemes provided slight reductions in the computational cost of the GA and produced many designs with good fitness' in the final population, while maintaining a high level of reliability. Genetic algorithms can be easily adapted to many different optimization problems also. This capability is demonstrated by modifying the basic GA, which utilizes a single chromosome string, to include a second string so that composite laminates comprised of multiple materials can be studied with greater efficiently. By using two strings, only minor adjustments to the basic GA were required. The modified GA was used to simultaneously minimize the cost and weight of a simply supported composite plate under different combinations of axial loading. Two materials were used, with one significantly stronger, but more expensive than the other. The optimization formulation was implemented by using convex combinations of cost and weight objective functions into a single value for laminate fitness, and thus required no additional modifications to the GA. To obtain a Pareto-optimal set of designs, the influence of cost and weight on the overall fitness of a laminate configuration was adjusted from one extreme to the other by adjusting the scale factors accordingly. The modified GA provided a simple yet reliable means of designing high performance composite laminates at costs lower than laminates comprised of one material. / Master of Science

Composite laminates are increasingly being used as primary load bearing members in<br />structures.  However, because of the directional dependence of the properties of<br />composite materials, additional failure modes appear that are absent in<br />homogeneous, isotropic materials.  Therefore, a stress analysis of a composite<br />laminate is not complete without an accurate representation of the transverse<br />(out-of-plane) stresses.<br /><br />Stress recovery is a common method to estimate the transverse stresses from a<br />plate or shell analysis.  This dissertation extends stress recovery to problems<br />in which geometric nonlinearities, in the sense of von K\\\'rm\\\'{a}n,  are<br />important.  The current work presents a less complex formulation for the stress<br />recovery procedure for plate geometries, compared with other implementations,<br />and results in a post-processing procedure which can be applied to data from<br />any plate analyses; analytical or numerical methods, resulting in continuous or<br />discretized data.<br /><br />Recovered transverse stress results are presented for a variety of<br />geometrically nonlinear example problems: a semi-infinite plate subjected to<br />quasi-static transverse and shear loading, and a finite plate subjected to both<br />quasi-static and dynamic transverse loading.  For all cases, the corresponding<br />results from a fully three-dimensional stress analysis are shown alongside the<br />distributions from the stress recovery procedure.  Good agreement is observed<br />between the stresses obtained from each method for the cases considered.<br />Discussion is included regarding the applicability and accuracy of the<br />technique to varying plate geometries and varying degrees of nonlinearity, as<br />well as the viability of the procedure in replacing a three-dimensional<br />analysis in regard to the time required to obtain a solution.<br /><br />The proposed geometrically nonlinear stress recovery procedure results in<br />estimations for transverse stresses which show good correlation to the<br />three-dimensional finite element solutions.  The procedure is accurate for<br />quasi-static and dynamic loading cases and proves to be a viable replacement<br />for more computationally expensive analyses. / Ph. D.

This thesis describes the development of a general Fortran 90 framework for the solution of composite laminate design problems using a genetic algorithm (GA). The initial Fortran 90 module and package of operators result in a standard genetic algorithm (sGA). The sGA is extended to operate on a parallel processor, and a migration algorithm is introduced. These extensions result in the distributed genetic algorithm with migration (dGA). The performance of the dGA in terms of cost and reliability is studied and compared to an sGA baseline, using two types of composite laminate design problems. The nondeterminism of GAs and the migration and dynamic load balancing algorithm used in this work result in a changed (diminished) workload, so conventional measures of parallelizability are not meaningful. Thus, a set of experiments is devised to characterize the run time performance of the dGA. The migration algorithm is found to diminish the normalized cost and improve the reliability of a GA optimization run. An effective linear speedup for constant work is achieved, and the dynamic load balancing algorithm with distributed control and token ring termination detection yield improved run time performance. / Master of Science

The thesis aims to investigate the mechanical behavior and properties of a centrally notched hybrid Magnesium/Carbon-Fiber/PEEK laminate at elevated temperature. The high performance hybrid composite laminates of 0.5mm Magnesium sheets sandwiched by Carbon-Fiber/PEEK (APC-2) guasi-isotropic and cross-ply laminates were fabricated. The Magnesium sheets were polished and cleaned by acetone, then underwent the surface treatment by CrO3-base solvent etchants, cured by the improved diaphragm curing process. The finished laminates were cut into the specimen than drilled a 4mm diameter hole in the center of specimen. At first, the ultimate strength, stiffness and stress-strain diagram were obtained due to static tension tests at elevated temperature, such as 25¢XC(RT), 75¢XC, 100¢XC, 125¢XC, and 150¢XC. Compare of them, the notched quasi-isotropic ones drop almost 50% in strength, and the notched cross-ply ones are half of unnotched ones. The two lay-up notched specimens are slightly below the unnotched ones in stiffness. The strength of the specimens are decrease as temperature rise. As the temperature rise the stiffness of quasi-isotropic ones drop, but it just change little in cross-ply ones. Then the notched specimen fatigue life and load-cycle (P-N) curves were obtained by tension-tension fatigue test. The P-N curves were adopt to prevent the stress concretion of the notched specimen. Consider the same loading, notched specimens has worse fatigue behavior, but in the same load ratio, the normalized P-N curves of the unnotched ones were below the notched ones means notched ones has better fatigue behavior. Recording the specimen image by video camera during the testing process, the cracks at the edge of hole were found. However delamination was not found. Necking was observed in quasi-isotropic specimens, but not in cross-ply. Observed by optical microscopy, the improved surface treatment will decrease the probability of delamination from 20% to less than 10% after hot press.

The aim of this thesis is to manufacture Ti/APC-2 hybrid composite laminates and obtain its mechanical properties and fatigue characteristics at elevated temperatures. Ti/APC-2 laminates were composed of two layers of APC-2 and three layers of titanium sheets. For superior bonding ability between titanium and APC-2, chromic anodic method was adopted to treat titanium sheets in manufacturing process and APC-2 was stacked according to cross-ply [0/90]s and quasi-isotropic [0/45/90/-45] sequences. Then, the modified curing process was adopted to fabricate Ti/APC-2 hybrid composite laminates. Tension and fatigue tests carried out with MTS 810 and MTS 651 environmental control chamber to lift and maintain experimental temperatures, such as 25¢XC, 75¢XC, 100¢XC, 125¢XC and 150¢XC. From static tensile tests, the mechanical properties of cross-ply and quasi-isotropic composite laminates, such as ultimate strength, longitudinal stiffness were gained and the stress-strain diagrams of laminates were also plotted from testing data at elevated temperature. From fatigue tests we obtained laminate¡¦s fatigue resistance properties and the experimental data of applied stress vs. cycles were plotted as S-N diagrams at elevated temperature. From the tensile and fatigue tests, the important remarks were summarized as follows. First, no matter what the APC-2 stacking sequence was, the ultimate strength and longitudinal stiffness decreased while temperature rising, especially at 150¢XC; second, a turning point appeared at each stress-strain diagram that kink angle caused the decrease of stiffness while temperature rising; third, combining fatigue data and stress-strain diagrams we analogized a presumption that the region before turning point was in elastic behavior and after turning point in plastic deformation; fourth, quasi-isotropic laminates had better fatigue resistance than that of cross-ply laminates; sixth, the longitudinal stiffness before turning point was in good agreement with the prediction by using the modified ROM, however, after turning point the errors became large.

This thesis focuses on the investigation of behavior of thick and moderately thick laminates under transverse and horizontal loading for different boundary conditions and configurations. An efficient finite element solution is proposed for analyzing composite laminates. Based on a combination of composite theory and 3-D Elasticity Theory, a 3-D finite element program is developed in MATLAB for calculating the stresses, strains and deformations of composite laminates under transverse and/or horizontal loading for different boundary conditions. The applicability of the formulation to analysis of laminated rubber bearings is also examined in this study. Since it is very important to calculate the correct stress state when developing models for composite behavior, the 3-D Elasticity Theory is used in this research. Numerical results are presented for various problems with different lamination schemes, loading and boundary conditions. In order to verify the analysis and the numerical calculations, numerical solutions obtained in this study are compared with available closed form solutions in the literature, experiment results and a commercial finite element program, namely ANSYS. The results obtained using the present finite element is found to be in acceptable and good agreement with the closed form solutions in the literature for thick and moderately thick rectangular and square plates.

This study focuses on developing novel modeling techniques for fiber-reinforced composites with polymer and ceramic matrix based on Peridynamic approach. To capture the anisotropic material behaviors of composites under quasi-static and dynamic loading conditions, a new peridynamic model for composite laminate and a modified peridynamic approach for non-uniform discretization are proposed in this study. In order to achieve the numerical implementation of the proposed model and approach, a mixed implicit-explicit solver based on GPU parallel computing is developed as well. The new peridynamic model for composite laminates does not have any limitation in fiber orientation, material properties and stacking sequence. It can capture the expected orthotropic material properties and coupling behaviors in laminates with symmetric and asymmetric layups. Unlike the previous models, the new model enables the evaluation of stress and strain fields in each ply of the laminate. Therefore, it permits the use of existing stress- or strain-based failure criteria for damage prediction. The computation of strain energy stored at material points allows the energy-based failure criteria required for delamination propagation and fatigue crack growth. The capability of this approach is verified against benchmark solutions, and validated by comparison with the available experimental results for three laminate layups with an open hole under tension and compression. The modified peridynamic approach for non-uniform discretization enables computational efficiency and removes the effect of geometric truncations in the simulation. This approach is a modification to the original peridynamic theory by splitting the strain energy associated with an interaction between two material points according to the volumetric ratio arising from the presence of non-uniform discretization and variable horizon. It also removes the requirement for correction of peridynamic material parameters due to surface effects. The accuracy of this approach is verified against the benchmark solutions, and demonstrated by considering cracking in nuclear fuel pellet subjected to a thermal load with non-uniform discretizations. Unlike the previous peridynamic simulations which primarily employs explicit algorithm, this study introduces implicit algorithm to achieve peridynamic simulation under quasi-static loading condition. The Preconditioned Conjugate Gradient (PCG) and Generalized Minimal Residual (GMRES) algorithms are implemented with GPU parallel computing technology. Circulant preconditioner provides significant acceleration in the convergence of peridynamic analyses. To predict damage evolution, the simulation is continued with standard explicit algorithms. The validity and performance of this mixed implicit-explicit solver is established and demonstrated with benchmark tests.

Optimization is a decision making process to solve problems in a number of fields including engineering mechanics. Bio-inspired optimization algorithms, including genetic algorithm (GA), have been studied for many years. There is a large literature on applying the GA to mechanics problems. However, disadvantages of the GA include the high computational cost and the inability to get the global optimal solution that can be found by using a honeybee-inspired optimization algorithm, called the New Nest-Site Selection (NeSS). We use the NeSS to find optimal parameters for three mechanics problems by following the three processes: screening, identifying relationships, and optimization. The screening process identifies significant parameters from a set of input parameters of interest. Then, relationships between the significant input parameters and responses are established. Finally, the optimization process searches for an optimal solution to achieve objectives of a problem. For the first two problems, we use the NeSS algorithm in conjunction with a third order shear and normal deformable plate theory (TSNDT), the finite element method (FEM), a one-step stress recovery scheme (SRS) and the Tsai-Wu failure criterion to find the stacking sequence of composite laminates and the topology and materials for doubly curved sandwich shells to maximize the first failure load. It is followed by the progressive failure analysis to determine the ultimate failure load. For the sandwich shell, we use the maximum transverse shear stress criterion for delineating failure of the core, and also study simultaneously maximizing the first failure load and minimizing the mass subject to certain constraints. For composite laminates, it is found that the first failure load for an optimally designed stacking sequence exceeds that for the typical [0°/90°]₅ laminate by about 36%. Moreover, the design for the optimal first failure load need not have the maximum ultimate load. For clamped laminates and sandwich shells, the ultimate load is about 50% higher than the first failure load. However, for simply supported edges the ultimate load is generally only about 10% higher than the first failure load. For the atmospheric spray process, we employ the NeSS algorithm to find optimal values of four process input parameters, namely the argon flow rate, the hydrogen flow rate, the powder feed rate and the current, that result in the desired mean particle temperature and the mean particle velocity when they reach the substrate. These optimal values give the desired mean particle temperature and the mean particle velocity within 5% of their target values. / Ph. D. / An optimization process iteratively searches for the best solution from all feasible solutions in the search space that satisfy prespecified criteria. Optimization problems consist of sets of parameters, constraints, and objective functions. Here we use a honeybee-inspired optimization algorithm, called the New Nest-Site Selection (NeSS), to find optimal parameters for three mechanics problems. In the first problem, we optimize the design of an assembly of layers of unidirectional fiber-reinforced materials called composite laminates. Because of their high specific strength and directional-dependent stiffness as compared to those of metals, the composite laminates are being increasingly used in aerospace and automotive industries. After having analyzed deformations of a composite laminate, a failure criterion is used to determine if any point in the structure has failed. The minimum load for which the failure criterion is satisfied at a point is called the first ply failure load. Here we determine the fiber orientation angle in each layer of a rectangular laminate deformed statically by transverse loads applied on the top surface that maximizes the first ply failure load. Subsequently, the load is incrementally increased for the optimally designed laminate and the strength of the failed elements is degraded till the structure cannot support any additional load. The maximum load a structure can support is called the ultimate load. It is found that for a laminate with all edges clamped, the ultimate load can be 40% more than the first ply failure load. We extend the above work to design an optimal geometry and an optimal combination of materials of the facesheets and the core that simultaneously maximizes the first failure load, minimizes the weight of a doubly curved sandwich shell, and satisfies pre-specified constraints. The doubly curved sandwich structure of interest here is comprised of two thin parallel unidirectional fiber-reinforced facesheets bonded to and enclosing a relatively thick mid-layer made of a material softer and lighter than that of the facesheets. The sandwich structures are widely used in aircraft, marine, automobile, and civilian infrastructures. It is found that optimal designs for doubly curved sandwich shells strongly depend upon how the shell edges are supported, and shells designed for the maximum first failure load need not have the maximum ultimate load. An atmospheric plasma spray process (APSP) has been successfully used to coat components for gas turbines, airframe, engines and drive trains, and silicon chips. In the APSP, coating powder is injected into the plasma, which is a mixture of ionized gases such as argon, hydrogen, and helium, through a powder port generally oriented perpendicular to the plasma jet axis. Through interactions with the plasma jet, the particles are accelerated, heated and partially melted before they strike the substrate and are deposited on it to form a coating. It is believed that the coating properties and its quality depend on the particles’ temperature and velocity when they hit the substrate. Here we determine optimum values of four input parameters, namely, the argon flow rate, the hydrogen flow rate, the current, and the powder feed rate to achieve the desirable mean particles’ temperature and the mean particles’ velocity. It is found that the four processes input parameters can be optimized to attain particles’ characteristics within 5% of their prespecified desired values.

The primary focus of this thesis was to investigate the critical strain energy release rates (G) for mixed-mode (I/II) fracture of wood adhesive joints. The aims of the study were: (1) quantifying the fracture properties of two material systems, (2) analyzing the aspects that influence the fracture properties of bonded wood, (3) refining test procedures that particularly address layered orthotropic systems in which the layers are not parallel to the laminate faces, of which wood is often a particular case, and (4) developing testing methods that enhance the usefulness of performing mixed-mode tests with a dual-actuator load frame. The material systems evaluated experimentally involved yellow-poplar (Liriodendron tulipifera), a hardwood of the Magnoliaceae family, as adherends and two different adhesives: a moisture-cure polyurethane (PU) and a phenol/resorcinol/-formaldehyde (PRF) resin. The geometry tested in the study was the double cantilever beam that, in a dual-actuator load frame, can be used for testing different levels of mode-mixity. The mixed-mode loading condition is obtained by applying different displacement rates with the two independently controlled actuators of the testing machine. Characteristic aspects such as the large variability of the adhesive layer thickness and the intrinsic nature of many wood species, where latewood layers are alternated with earlywood layers, often combine to confound the measures of the critical values of strain energy release rate, Gc. Adhesive layer thickness variations were observed to be substantial also in specimens prepared with power-planed wood boards and affect the value of Gc of the specimens. The grain orientation of latewood and earlywood, materials that often have different densities and elastic moduli, limits the accuracy of traditional standard methods for the evaluation of Gc. The traditional methods, described in the standards ASTM D3433-99 and BS 7991:2001, were originally developed for uniform and isotropic materials but are widely used by researchers also for bonded wood, where they tend to confound stiffness variations with Gc variations. Experimental analysis and analytical computations were developed for quantifying the spread of Gc data that is expected to be caused by variability of the adhesive layer thickness and by the variability of the bending stiffness along wooden beams. / Ph. D.