This study presents an upper bound plastic limit analysis for predicting drag anchor trajectory and load capacity. The shank and fluke of the anchor are idealized as simple plates. The failure mechanism involves the motion of the anchor about a center of rotation, the coordinates of which are systematically optimized to determine the minimum load at the shackle. For a given anchor orientation, the direction of the shackle force is varied to establish a relationship between the magnitude and direction of the shackle load. Coupling this relationship to the Neubecker-Randolph anchor line solution produces a unique solution for the magnitude and orientation of the shackle force. The anchor is then advanced a small increment about the optimum center of rotation and the process is repeated. The upper bound method (UBM) provides a practical means to determine the trajectory of the anchor and the anchor load capacity at any point in the trajectory. To better understand of the anchor behavior, extensive parameter studies were carried out varying the properties of the anchor, anchor line, and soil. The UBM show good agreement with six full-scale tests covering several different anchor types and centrifuge model tests.

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Extrusion is a metal forming process used extensively in industry to produce different structural, mechanical, electrical, architectural, automotive and aerospace application parts. Currently after extrusion, the rod is subjected to environmental wear due to long storage time and hence requires an additional cleaning process before further use. This cleaning process can be eliminated by extruding a polymer coated metal rod workpiece such that the polymer coating is sustained on the final product after the extrusion process. In the present research study a new upper bound analytical model is developed to predict the forces required to conduct extrusion of a polymer coated metal rod successfully. The search for the lower upper bound power functional is modeled as a non linear optimization problem. Optimizing the functional also determines the set of constraints defining the shape of rigid plastic deformation boundaries and the final coating thickness. Also an upper bound analytical model was developed to predict forces for failure of the polymer coating during the extrusion. Both the analytical models for successful and failed extrusion are compared to obtain critical die angle which can provide tooling and process design guidelines. Finite element analysis simulations were modeled using commercially available software package, ABAQUS. Predictions of FEA simulations were in good agreement with published results and with the predictions of analytical model developed in this study.

Exact solution to the vibration of rectangular plates is available only for plates with two opposite edges subject to simply supported conditions. Otherwise, they are analysed by using approximate methods. There are several approximate methods to conduct a vibration analysis, such as the Rayleigh-Ritz method, the Finite Element Method, the Finite Difference Method, and the Superposition Method. The Rayleigh-Ritz method and the finite element method give upper bound results for the natural frequencies of plates. However, there is a disadvantage in using this method in that the error due to discretisation cannot be calculated easily. Therefore, it would be good to find a suitable method that gives lower bound results for the natural frequencies to complement the results from the Rayleigh-Ritz method. The superposition method is also a convenient and efficient method but it gives lower bound solution only in some cases. Whether it gives upper bound or lower bound results for the natural frequencies depends on the boundary conditions. It is also known that the finite difference method always gives lower bound results. This thesis presents bounded eigenvalues, which are dimensionless form of natural frequencies, calculated using the superposition method and the finite difference method. All computations were done using the MATLAB software package. The convergence tests show that the superposition method gives a lower bound for the eigenvalues of fully clamped plates, and an upper bound for the completely free plates. It is also shown that the finite difference method gives a lower bound for the eigenvalues of completely free plates. Finally, the upper bounds and lower bounds for the eigenvalues of fully clamped and completely free plates are given.

The multiprocessor task graph scheduling problem has been extensively studied asacademic optimization problem which occurs in optimizing the execution time of parallelalgorithm with parallel computer. The problem is already being known as one of the NPhardproblems. There are many good approaches made with many optimizing algorithmto find out the optimum solution for this problem with less computational time. One ofthem is branch and bound algorithm.In this paper, we propose a branch and bound algorithm for the multiprocessor schedulingproblem. We investigate the algorithm by comparing two different lower bounds withtheir computational costs and the size of the pruned tree.Several experiments are made with small set of problems and results are compared indifferent sections.

Indentation is a practical and easy method, therefore, is a preferred method of material characterization. Main aim of this thesis study is to determine anisotropic properties of metals by indentation tests. The basic property of the indenter used in the finite element analyses and experiments is that it is specific to this process. Thesis includes studies on optimization of the indenter geometry, analyses of effects of friction coefficient, multiple indentations, tilting of the indenter and clamping of the specimen on force-displacements curves during indentation by finite element analyses. This study also includes finite element analyses of compression tests where these experiments have been necessary to prove anisotropic behavior of the specimen material. In addition to compression, tension tests are done to have a reference for indentation tests. On the other hand, the upper bound method which is an analytical solution is applied on the assumption of plane strain indentation.

Le thème central de cette thèse porte sur des partitions en n parties de l'intervalle entier [1, N] = {1,2,...,N} excluant la présence, dans chaque partie, de solution de l'équation x + y = z dans le cas classique, ou seulement de telles solutions avec x ≠ y dans le cas faible. Pour n donné, le plus grand N admissible dans le cas classique se note S(n) et s'appelle le n-ème nombre de Schur ; dans le cas faible, il se note WS(n) et s'appelle le n-ème nombre de Schur faible. Bien qu'introduits il y a plusieurs décénnies déjà, et même il y a un siècle dans le cas classique, on ne sait encore que très peu de choses au sujet de ces nombres. En particulier, S(n) et WS(n) ne sont exactement connus que pour n ≤ 4. Cette thèse est composée de deux chapitres : le premier revisite des encadrements connus sur les nombres de Schur classiques et faibles, et le second est consacré à la construction de nouveaux minorants des nombres de Schur faibles WS(n) pour n = 7, 8 et 9. Nous introduisons, dans le premier chapitre, les ensembles t-libres de sommes, t ∊ ℕ, dont l'utilisation permet de généraliser et d'unifier diverses démonstrations de majorants des S(n) et WS(n). Nous obtenons également une relation entre WS(n + 1) et WS(n). Dans le second chapitre, nous initions l'étude de certaines partitions hautement structurées présentant un potentiel intéressant pour le problème de minorer les nombres WS(n). Effectivement, avec des algorithmes de recherche ne portant que sur ces partitions, nous retrouvons les meilleurs minorants connus sur WS(n) pour 1 ≤ n ≤ 6, et nous améliorons significativement ceux pour 7 ≤ n ≤ 9. / The main theme of this thesis is about partitions in n parts of the integer interval [1, N] = {1,2,...N} excluding the presence, in each part, of solutions of the equation x + y = z in the classical case, or only of such solution with x ≠ y in the weak case. For given n, the largest admissible N in the classical case, it is denoted S(n) and called the n-th Schur number ; in the weak case, it is denoted WS(n) and called the n-th weak Schur number. Even though these numbers were already introduced several decades ago, and even a century ago in the classical case, almost nothing is known about them. In particular, S(n) and WS(n) are exactly known for n ≤ 4. This thesis comprises two chapters :the first one revisits known lower and upper bounds on the classical weak Schur numbers, and the second one is dedicated to the construction of the new lower bounds on the weak Schur numbers WS(n) for n = 7,8 and 9. In the first chapter, we introduce the t-sumfree sets, t ∊ ℕ, which allow us to generalize and unify various proofs concerning upper bounds on S(n) and WS(n). We also obtain a new relationship between WS(n + 1) and WS(n).In the second chapter, we initiate the study of certain highly structured partitions which present an interesting potential for the problem of bounding the numbers WS(n) from below. Indeed, with search algorithms considering only partitions, we rediscover the best known lower bounds on WS(n) for 1 ≤ n ≤ 6, and we significatively improve those for 7 ≤ n ≤ 9.

A numerical technique based on the theory of plasticity is developed to predict an optimum failure surface generatrix and concrete breakout capacity of single anchors away from edges under tensile loads. Concrete is regarded as a rigid, perfectly plastic material obeying a modified coulomb failure criteria with effective compressive and tensile strengths. The failure mode is idealized as an assemblage of two rigid blocks separated by failure surfaces of displacement discontinuity. Minimization of the collapse load predicted by the energy equation produces the optimum shape of the failure surface generatrix. A simplified solution is also developed by approximating the failure surface as two straight lines. The effect of different parameters on the concrete breakout capacity of anchors is reviewed using the developed mechanism analysis, ACI 318-05, and test results of 501 cast-in-place and 442 post-installed anchor specimens. The shape of failure surface and concrete breakout capacity of anchors predicted by the mechanism analysis are significantly affected by the ratio between effective tensile and compressive strengths of concrete. For anchors installed in concrete having a low ratio between effective tensile and compressive strengths, a much larger horizontal extent of failure planes in concrete surface is predicted by the mechanism analysis than recommended by ACI 318-05, similar to test results. Experimental concrete breakout capacity of anchors is closer to the prediction obtained from the mechanism analysis than ACI 318-05. ACI 318-05 provisions for anchors sharply underestimate the breakout capacity of cast-in-place and post-installed anchors having effective embedment depths exceeding 200 and 80 mm (7.87 to 3.15 in.), respectively, installed in concrete of compressive strength larger than 50 MPa (7250 psi).

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