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The primary aim of this study is to assess the applicability and performance of the finite element method (FEM) in solving structural optimization problems with stability constraints. In order to reach this goal, several optimization problems are solved using FEM which are briefly described as follows: The strongest column problem is one of the oldest optimization problems for which analytical solutions exist only for some special cases. Here, both unimodal and bimodal optimization of columns under concentrated and/or distributed compressive loads with several different boundary conditions and constraints are performed using an iterative method based on finite elements. The analytical solutions available in the literature for columns under concentrated loads and an analytical solution derived for simply supported columns under distributed loads are used for verification purposes. Optimization results are presented for fibre-reinforced composite rectangular plates under inplane loads. The non-uniformity of the in-plane stresses due to stress diffusion and/or in-plane boundary conditions is taken into account, and its influence on optimal buckling load is investigated. It is shown that the exclusion of the in-plane restraints may lead to errors in stability calculations and consequently in optimal design. The influences of the panel aspect ratio, stacking sequence, panel thickness, and the rotational edge restraints on the optimal axially compressed cylindrical and non-cylindrical curved panels are investigated, where the optimal panel is the one with the highest failure load. The prebuckling and the first-ply failure loads of the panels are calculated and minimum of these two is selected as the failure load. The results show that there are distinct differences between the behaviour of cylindrical and non-cylindrical panels. The formulations of the finite elements which are used throughout the study are given and several verification problems are solved to verify the accuracy of the methodology. The computer codes written in Matlab are also given in the appendix sections accompanied with the selected codes used for optimization purposes. / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2006.

In the first part of the study, finite element solutions are presented for the optimal design of symmetrically laminated rectangular plates subject to a combination of simply supported, clamped and free boundary conditions. The design objective is the maximisation of the biaxial buckling load by determining the fibre orientations optimally with the effects of bending-twisting coupling taken into account. The finite element method coupled with an optimisation routine is employed in analysing and optimising the laminated plate designs. The effect of boundary conditions, the number of layers and bending-twisting coupling on the optimal ply angles and the buckling load are numerically studied. Optimal buckling designs of symmetrically laminated rectangular plates under in-plane uniaxial loads which have a nonuniform distribution along the edges are presented in the second part of the study. In particular, point loads, partial uniform loads and nonuniform loads are considered in addition to uniformly distributed in-plane loads which provide the benchmark solutions. Poisson's effect is taken into account when in-plane restraints are present along the unloaded edges. Restraints give rise to in-plane loads at unloaded edges which lead to biaxial loading, and may cause premature instability. The laminate behavior with respect to fiber orientation changes significantly in the presence of Poisson's effect as compared to that of a laminate where this effect is neglected. This change in behavior has significant implications for design optimisation as the optimal values of design variables with or without restraints differ substantially. In the present study, the design objective is the maximisation of the uniaxial buckling load by optimally determining the fiber orientations. Numerical results, determined using the finite element method, are given for a number of boundary conditions and for uniformly and non-uniformly distributed buckling loads. In the third part of the study, finite element solutions are presented for the optimal design of symmetrically laminated rectangular plates with central circular cut-outs subject to a combination of simply supported, clamped and free boundary conditions. The design objective is the maximisation of the biaxial buckling load by determining the fiber orientations optimally. The effect of boundary conditions and bending-twisting coupling on the optimal ply angles and the buckling load are numerically studied. The results are compared to those for laminates without holes. The fourth part of the present study gives optimal designs of symmetrically laminated angle-ply plates, which are obtained with the objective of maximising the initial post buckling stiffness. The design involves optimisation over the ply angles and the stacking sequence to obtain the best laminate configuration. The stacking sequence is chosen from amongst five candidate designs. It is shown that the best configuration depends on the ratio of the in-plane loads in the x and y directions. Results are also given for two additional configurations which do not exhibit bending-twisting coupling. The final section of the present study deals with the optimal design of uniaxially loaded laminated plates subject to elastic in-plane restraints along the unloaded edges for a maximum combination of prebuckling stiffness, postbuckling stiffness and buckling load. This multiobjective study illustrates that improved buckling and post buckling performance can be obtained from plates which are designed in this fashion. The multiobjective results are also compared to single objective design results. / Thesis (Ph.D.)-University of Natal, Durban, 1994.

Transient Liquid Phase bonding under Temperature Gradient (TG-TLP bonding) is a relatively new process of TLP diffusion bonding family for joining difficult-to-weld aerospace materials. Earlier studies have suggested that in contrast to the conventional TLP bonding process, liquid state diffusion drives joint solidification in TG-TLP bonding process. In the present work, a mass conservative numerical model that considers asymmetry in joint solidification is developed using finite element method to properly study the TG-TLP bonding process. The numerical results, which are experimentally verified, show that unlike what has been previously reported, solid state diffusion plays a major role in controlling the solidification behavior during TG-TLP bonding process. The newly developed model provides a vital tool for further elucidation of the TG-TLP bonding process.

The aims of the thesis were to study the response of temporary soil-filled walls both experimentally and numerically, and to develop an efficient and accurate analytical model to predict 2-D planar response from blast loading which could be used to efficiently calculate a pressure-impulse (P-I) curve. An explicit finite element (FE) formulation was constructed using LS-Dyna software, and two analytical models were also derived and presented: a Rigid-Body Rotation model as a preliminary model, and the Rigid-Body Hybrid model as the proposed model of this thesis. Seven full-scale experiments which consisted of blast loading simple free-standing soil-filled Hesco Bastion (HB) walls are presented. Apart from comparison of an experimental result where the soil-fill in the wall possessed sizable cohesion, the response of the Rigid-Body Hybrid model was in very good agreement with the experiments overall (within 10 %). A soil sensitivity study was conducted and overall very good agreement was reached between the Rigid-Body Hybrid model in comparison with the FE model in its ability to capture differences in displacement-time histories from differences in soil parameters. Comparison with the FE model for different height-to-width ratios of walls showed that the Rigid-Body Hybrid model was within 10 % for all rotation angles and predictions of critical overturning impulse for height-to-width ratios of walls . P-I curves were developed using the analytical and FE models for the three different wall configurations studied in the experiments. The results demonstrated that the proposed Rigid-Body Hybrid model is useful for calculating a P-I curve for a HB wall efficiently and yielded very accurate results (within 5 % for the impulse asymptotes).

To evaluate the impact of reduced truck tire pressure on strain response of low volume spring-restricted roads, research was conducted on two instrumented pavement sections in Manitoba, Canada. Tire pressure control systems tests were carried out at the sections in spring and fall 2009. Measured maximum tensile strain at the bottom of asphalt layer decreased by 15-20% when tire pressure was reduced by 50%. Measured strain at the bottom of asphalt layer in fall is about 50% less than in spring. The effects of gauge orientation, truck speed, and tire offset from the strain gauge were also analyzed. A finite element model with static load was developed and verified. The bearing capacity is lower in spring than in normal condition for flexible pavements subject to deep frost action. Reduced tire pressure is effective to reduce bottom up failure of the pavement, and is less effective to prevent rutting.

A computational model for the prediction of articular and backside polyethylene (PE) wear of total knee replacements (TKRs) could enable the optimization of TKRs for the reduction of polyethylene wear, thereby improving the long term success of TKRs. A finite element model was developed for the TKR and the results were implemented in a computational wear model to assess PE wear. The wear factors of Archard’s wear law were identified by implementing the finite element simulation results along with knee simulator wear test results. Archard’s wear law was found to have insufficient accuracy for the purpose of optimization. Therefore, a novel computational wear model was developed by the author based on a theoretical understanding of the molecular behavior of PE. The model predicted result fell within the standard deviation of the independent knee simulator wear test results, indicating a high level of accuracy for the novel computational wear model.

In this thesis, a two-dimensional (2D) finite element (FE) model was developed from the patient’s hip DXA image to evaluate osteoporotic fracture risk. The loading configuration was designed to simulate a lateral fall onto the greater trochanter. Bone inhomogeneous mechanical properties (e.g. Young’s modulus) assigned to the FE model were correlated to bone mineral density captured in DXA image using empirical functions. In-house MATLAB codes were developed to investigate the effects of different factors such as bone mineral density, femoral neck length, neck diameter, neck angle and patient’s body weight on fracture risk. The 2D FE model constructed from DXA image was able to de-termine the factors which affect fracture risk to a greater extent based on the location of femur. The model developed here can be considered as a first attempt for investigating the effects of different parameters on fracture risk using patient specific 2D FE method.

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