Structural Integrity of Functionally Graded Composite Structure using Mindlin-Type Finite Elements.

In this paper, two new Mindlin-type plate bending elements have been derived for the modelling of functionally graded plate subjected to various loading conditions such as tensile loading, in-plane bending and out-of-plane bending. The properties of the first Mindlin-type element (i.e. Average Mindlin element) are computed by using an average fibre distribution technique which averages the macro-mechanical properties over each element. The properties of the second Mindlin-type element (i.e. Smooth Mindlin element) are computed by using a smooth fibre distribution technique, which directly uses the macro-mechanical properties at Gaussian quadrature points of each element. There were two types of non-linearity considered in the modelling of the plate, which include finite strain and material degradation. The composite plate considered in this paper is functionally graded in the longitudinal direction only, but the FE code developed is capable of analysing composite plates with functional gradation in transverse and radial direction as well. This study was able to show that the structural integrity enhancement and strength maximisation of composite structures are achievable through functional gradation of material properties over the structure

Nonlinear static and dynamic analysis of composite layered plates and shells using finite strip methods

In this thesis, a new concept of finite strip elements is introduced. Lagrangian, Hermitian and spline-type interpolations have been used independently along the two axes of the plate mid-plane. Different plate-bending theories; Mindlin, Reissner and Kirchhoff theories have been applied in the derivations of the new finitestrip elements, for isotropic and composite materials. The new elements have also been extended to work as faceted shell elements for the analysis of cylindrical shells, folded plates and stiffened plates. An efficient modular programming package based on those elements was designed, and it is capable of performing linear and non-linear stress analysis, buckling analysis and natural frequency analysis. The modular package, which was coded in FORTRAN has different solvers and a built-in mesh generator for different types of plate structures. A number of case studies have been employed for the validation of the package and testing its different capabilities. The package has proved to be an efficient tool for numerical modelling of plates, cylindrical shells, folded plates and stiffened plates made of isotropic and composite layered materials.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Structural integrity of engineering components made of functionally graded materials

Functionally graded materials (FGM) are composite materials with microstructure gradation optimized for the functioning of engineering components. For the case of fibrous composites, the fibre density is varied spatially, leading to variable material properties tailored to specific optimization requirements. There is an increasing demand for the use of such intelligent materials in space and aircraft industries. The current preferred methods to study engineering components made of FGM are mainly modelling particularly those that are finite element (FE) based as experimental methods have not yet sufficiently matured. Hence this thesis reports the development of a new Mindlin-type element and new Reissner-type element for the FE modelling of functionally graded composite (FGC) structures subjected to various loadings such as tensile loading, in-plane bending and out-of-plane bending, buckling and free vibration. The Mindlin-type element formulation is based on averaging of transverse shear distribution over plate thickness using Lagrangian interpolation. Two types of Mindlintype element were developed in this report. The properties of the first Mindlin-type element (i.e. Average Mindlin-type element) are computed by using an average fibre distribution technique which averages the macro-mechanical properties over each element. The properties of the second Mindlin-type element (i.e. Smooth Mindlin-type element) are computed by using a smooth fibre distribution technique, which directly uses the macro-mechanical properties at Gaussian quadrature points of each element. The Reissner-type element formulation is based on parabolic transverse shear distribution over plate thickness using Lagrangian and Hermitian interpolation. Two types of Reissner-type element were developed in this report, which include the Average and Smooth Reissner-type elements. There were two types of non-linearity considered in the modelling of the composite structures, which include finite strain and material degradation. The composite structures considered in this paper are functionally graded in a single direction only, but the FE code developed is capable of analysing composite structures with multidirectional functional gradation. This study was able to show that the structural integrity enhancement and strength maximisation of composite structures are achievable through functional gradation of material properties over the composite structures.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Solitary waves for linearly coupled nonlinear Schrodinger equations with inhomogeneous coefficients

Motivated by the study of matter waves in Bose-Einstein condensates and coupled nonlinear optical systems, we study a system of two coupled nonlinear Schrodinger equations with inhomogeneous parameters, including a linear coupling. For that system we prove the existence of two different kinds of homoclinic solutions to the origin describing solitary waves of physical relevance. We use a Krasnoselskii fixed point theorem together with a suitable compactness criterion.Comment: 16 page

Buckling and vibration analysis of functionally graded composite structures using the finite element method

The authors [Oyekoya OO, Mba DU, El-Zafrany AM. Structural integrity of functionally graded composite structure using Mindlin-type finite elements. ICCES 2008:172(l): 1-6] have previously written a paper Oil Structural integrity of functionally graded composite (FGC) structure using Mindlin-type finite elements. In this paper, the Mindlin-type element and Reissner-type element have been further developed for the modelling of FGC plate Subjected to buckling and free vibration. The Mindlin-type element formulation is based on averaging Of transverse shear distribution over plate thickness using Lagrangian interpolation. The Reissner-type element formulation is based on parabolic transverse shear distribution over plate thickness using Lagrangian and Hermitian interpolation. The composite plate considered in this paper is functionally graded in the longitudinal direction only, but the FE code developed is capable of analysing composite plates with functional gradation in transverse and radial direction as well. This Study was able to show that the structural integrity enhancement and strength maximisation of composite Structures are achievable through functional gradation of material properties over the structure

Numerical modelling of elastomers using the boundary element method

The FEM analysis of hyper elastic, elastomeric materials has been formulated and implemented for various material models (strain energy functions) over the years. More recently, the analysis of elastomeric materials has been attempted in the boundary element method. This has been achieved by the addition of non-linear domain terms to the basic linear boundary element equation. These non-linear domain terms require the evaluation of the displacement derivative components directly from displacement derivative boundary integral equations. In the solution to the boundary problem it is required to regularize the different types of singularities occurring in the system of non-linear boundary integral equations. This paper discusses the necessary theory for the boundary element method as applied to elastomers and presents a comparison between semi-analytical and numerical solutions for various test cases

The coupling of the FEM and the BEM for the solution of elastoplasticity and contact problems

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The numerical modelling of elastomers

This thesis reports onreview and research work carried out on the numerical analysis of elastomers. The two numerical techniques investigated for this purpose are the finite and boundary element methods. The finite element method is studied so that existing theory is used to develop a finite element code both to review the finite element method as applied to the stress analysis of elastomers and to provide a comparison of results and numerical approach with the boundary element method. The research work supported on in this thesis covers the application of the boundary element method to the stress analysis of elastomers. To this end a simplified regularization approach is discussed for the removal of strong and hypersingularities generated in the system on non-linear boundary integral equations. The necessary programming details for the implementation of the boundary element method are discussed based on the code developed for this research. Both the finite and boundary element codes developed for this research use the Mooney-Rivlin material model as the strain energy based constitutive stress strain function. For validation purposes four test cases are investigated. These are the uni-axial patch test, pressurized thick wall cylinder, centrifugal loading of a rotating disk and the J-Integral evaluation for a centrally cracked plate. For the patch test and pressurized cylinder, both plane stress and strain have been investigated. For the centrifugal loading and centrally cracked plate test cases only plane stress has been investigated. For each test case the equivalent results for an equivalent FEM program mesh have been presented. The test results included in this thesis prove that the FE and BE derivations detailed in this work are correct. Specifically the simplified domain integral singular and hyper-singular regularization approach was shown to lead to accurate results for the test cases detailed. Various algorithm findings specific to the BEM implementation of the theory are also discussed.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Finite element and boundary element methods for elasto-plastic stress analysis of two-dimensional and axisymmetric problems

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