Element free Galerkin method of composite beams with partial interaction

Composite beam with partial interaction behaviour has ignited many studies, not just on its mechanics but also on solutions of its one-dimensional partial differential equation. Inadequate solution by available analytical methods for this high order differential equation has demanded for numerical approach and therefore Element Free Galerkin (EFG) method is applied for the first time in this present work. The work consists of three parts; first is the formulation of Galerkin weak form and assemblage of the EFG discrete equilibrium equation. One-dimensional formulation of the weak form is performed by adopting the variational approach and the discrete equation, which is in matrix form and written using the Matlab programming code. Subsequently in second part, the EFG formulation is developed for both the slip and uplift models, where the former adopted equal curvature deflection assumption while the latter considered the unequal curvature. The proposed EFG formulation gives comparable results in both models, after been validated by established analytical solutions, thus signify its application in partial interaction problems. The third part provides numerical tests result on EFG numerical parameters such as size of support domain, polynomial basis and quadrature points with seven different types of weight functions for this composite beams behaviour. Conclusively, Cubic Spline and Quartic Spline weight functions yield better accuracy for the EFG formulation results, compares to other weight functions. The capability of the EFG formulation was also studied in terms of its application on free vibration problem and various composite beam cross-sections. Results from the numerical tests deduced the demand for optimised parameters value as the parameters are highly reliant on user-defined value. Additionally, the research supports the need for more efficient EFG code’s algorithm, stiffness matrix, shape function formulation and background integration methods, in approximating the higher order differential equation which refers to dynamics analysis

Desenvolvimento de algoritmos de otimização para métodos sem malha

Mestrado em Engenharia MecânicaRecentemente surgiu um novo tipo de métodos computacionais referenciados como métodos sem malha. Estes métodos têm sido amplamente usados no estudo e na resolução de problemas de engenharia, mais usualmente em problemas que contam com grandes deslocamentos, como a simulação de processos de conformação plástica e em problemas com elevadas taxas de deformação, com impacto e fratura estrutural. Devido ao caráter não interpolatório das funções de aproximação dos métodos sem malha, a definição das condições de fronteira é um dos maiores problemas destes métodos. Por outro lado, o facto de os nós poderem ser distribuídos aleatoriamente pelo domínio físico do problema em análise, sem ser necessário o recurso implícito a conetividades, torna os métodos sem malha bastante apelativos para problemas de contacto e impacto com fratura e desagregação de material. Este trabalho foca-se no desenvolvimento dos métodos sem malha, assim como na descrição e análise comparativa dos métodos sem malha mais relevantes nos dias de hoje e nos algoritmos e técnicas computacionais capazes de tornar estes métodos mais eficientes. São ainda propostos alguns algoritmos que resultam num substancial aumento de performance do método EFG (Element Free Galerkin) assim como uma implementação do método NEM (Natural Element Method) com base no algoritmo de Fortune e em funções de forma não Sibsonianas. Por fim conclui-se que o aumento de performance dos métodos sem malha pode ser conseguido recorrendo a técnicas e metodologias usadas com frequência nas ciências computacionais, tendo como desvantagem um aumento da complexidade de implementação.Recently, a new type of computational methods, referenced as mesheless methods, has emerged. These methods have been widely used in studying and solving engineering problems, most commonly problems that deal with large displacements, such as the simulation of plastic forming processes and problems envolving high rates of deformation, fracture or structural impact. Due to the non-interpolatory nature of the approximation functions of the meshless methods, to define the boundary conditions poses a major problem when dealing with such methods. However, the fact that nodes can be distributed randomly within the physical domain of the problem under analysis, without requiring the use of implicit connectivities, sets meshless methods as quite appealing when dealing with contact and impact problems involving fracture or material breakdown. This dissertation focuses on the development of meshless methods, as well as on the description and comparative analysis of the most relevant meshless methods nowadays, and in the algorithms and computational techniques able to render these methods more efficient. Some algorithms that result in a substantial performance increase of the EFG method (Element Free Galerkin) are also suggested, as well as an implementation of the NEM method (Natural Element Method) based on the use of the Fortune algorithm and on non Sibsonian shape functions. Finally, it is concluded that the increase in performance of meshless methods can be achieved using techniques and methodologies frequently used in computational science, being the disadvantage an increase in the implementation complexity

Numerical modelling of tyre-derived geo-composites

This thesis aims to study the property of rubber–sand mixtures as a geotechnical alternative. Previous studies have shown superior properties of this artificial composite such as high resiliency, light weight, and improved skin-resistance. Also, when mixed with conventional geotechnical materials, the composite often exhibits adjusted void ratio, high compressibility, high compression, high friction angle, and high attenuation of vibration. In the past, the major efforts were focused on the laboratory tests. There is limited research in numerical domain performed to predict the mechanical behaviour of rubber–soil. In these numerical studies, approximations are unsatisfactory because the past studies usually treat the compressible rubble granule as a rigid material. To address these research gaps, this study in this thesis develops and applies a series of numerical models to replicate the compressible nature of the rubber material and to examine the behaviour of the rubber-derived composite materials. The behaviour includes the shear strength, dynamic damping, mixture segregation, contact asperity, and contact deformation, from the macro-to microscale. The aims of this thesis contain the following aspects: 1) investigating the shear strength of rubber–sand mixture obtained in direct shear test; 2) assessing the segregation occurred when rubber–sand mixture is placed; 3) developing a coupled numerical method to replicate rigid–soft matters interaction; and 4) examining the influence of material surface asperity on energy dissipation. To attain these aims, the discrete element method (DEM), a numerical modelling tool, is employed to develop a series of modelling framework. The framework is validated, verified and applied through a blend of solutions, including test setups, analytical solutions, example problems and case studies. The DEM is used to replicate the discrete natural of rubber granules. Using this method, the macroscopic material response and particle flow can be monitored by determining granular properties such as contact stiffness, friction and damping coefficient. As a significant numerical tool, the commercial software package PFC is used to investigate the rubber and soil granular interactions.Thesis (Ph.D.) -- University of Adelaide, School of Civil, Environmental and Mining Engineering, 201