| Titre : | Contribution à l’optimisation du comportement des plaques stratifiées contenant des singularités géométriques |
| Auteurs : | Khechai Abdelhak, Auteur ; Abdelhamid Guettala, Directeur de thèse |
| Type de document : | Monographie imprimée |
| Editeur : | Biskra [Algerie] : Université Mohamed Kheider, 2018 |
| Langues: | Français |
| Mots-clés: | Stress concentration,Failure load,Finite Element Method,Genetic algorithm,In-plane loading,Composite material,Holes and cutouts,Digital image correlation. |
| Résumé : |
The design of high performance composite structures frequently includes discontinuities to reduce the weight and fastener holes for joining. To understand the complex behavior of laminated
panels with multiple cutouts, it is necessary to have access to accurate stress and failure prediction theories for perforated composite plates under various types of loading conditions. The main aim of the present work is to examine the existing methods to estimate the stress distribution and failure load in composite plates with single and multiple holes, and subsequently join or modify them to provide a simple and an accurate tool for a quick estimation of the stress and failure load. In order to minimize the stress concentration and maximize the failure load in laminates with multiple holes, the logic of Defense Hole Theory (DHT) is used. Defense hole theory deals with introducing auxiliary holes beside the main hole to reduce the stress developed around the main cutout. The failure theory was implemented in ABAQUS c using user material (UMAT) subroutine. The optimum configurations are obtained using Genetic Algorithm (GA) interfaced with a CAE solver. The obtained results are verified and validated with the available results and experimental data. This methodology is able to accurately determine the optimum cutout configurations to minimize the maximum von-Mises stress and maximize the minimum failure load |
| Sommaire : |
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v ‘ jÊÓ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiv General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 Mechanical Behavior of Composite Materials . . . . . . . . . . . . . . . . 2 2 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 Objective of the Present Study . . . . . . . . . . . . . . . . . . . . . . . . . 4 5 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 6 Layout of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Chapter 1: Literature Review 8 1.1 Preliminary Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Review of Stress Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.1 Review of analytic stress analysis . . . . . . . . . . . . . . . . . . . . 9 1.2.1.a Stress analysis of perforated isotropic plates under in-plane loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.1.b Stress analysis of perforated anisotropic plates under in-plane loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.2 Finite element analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.3 Strength Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 x 1.3.1 Unnotched strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.3.2 Notched strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.4 Optimization of Perforated Laminates . . . . . . . . . . . . . . . . . . . . . . 26 1.4.1 Optimization of laminates with a single hole . . . . . . . . . . . . . . 28 1.4.2 Optimization of laminates with multiple holes . . . . . . . . . . . . . . 30 1.5 Gaps Identified in the Literatures . . . . . . . . . . . . . . . . . . . . . . . . . 32 Chapter 2: Mathematical Formulation 33 2.1 Preliminary Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.2 Mathematical Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.2.1 Stresses in composite plate with a cutout . . . . . . . . . . . . . . . . 34 2.2.1.a Stresses in infinite orthotropic plate with a cutout . . . . . . 34 2.2.1.b Stresses in infinite anisotropic plate with a cutout . . . . . . 36 2.2.1.c Stresses in infinite multilayered plates with cutouts . . . . . . 38 2.2.2 General solution for in-plane loading with arbitrary biaxial and shear loading conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.2.3 Finite-width correction factor for anisotropic plate containing a central circular hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.2.4 Failure load (strength) . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.3 Genetic Algorithm for Optimization Process . . . . . . . . . . . . . . . . . . . 43 2.4 Notched Strength of Laminates With Circular Holes . . . . . . . . . . . . . . . 47 2.5 Finite Element Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.5.1 Differential or strong form of the equations of solid mechanics . . . . . 50 2.5.2 Weak form of the equilibrium equations of solid mechanics . . . . . . 50 2.5.2.a Isotropic material . . . . . . . . . . . . . . . . . . . . . . . 51 2.5.2.b Composite material . . . . . . . . . . . . . . . . . . . . . . 51 I Results and Discussion 54 Chapter 3: Validation of the Analytical Solution 55 3.1 Preliminary Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.2 Study of Stress Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 xi 3.2.1 Stress distribution around a circular hole . . . . . . . . . . . . . . . . . 56 3.2.2 Plywood plates under oriented uniaxial and shear stress . . . . . . . . . 56 3.2.3 Boron-Epoxy plates under biaxial stress . . . . . . . . . . . . . . . . . 58 3.2.4 Isotropic and Graphite/Epoxy plates under uniaxial and equibiaxial loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.2.5 Factors affecting stress distribution around hole . . . . . . . . . . . . . 60 3.2.5.a Effect of fiber orientation, type of in-plane load and material 60 3.2.5.b Effect of degree of orthotropy . . . . . . . . . . . . . . . . . 62 3.2.5.c Effect of loading angle . . . . . . . . . . . . . . . . . . . . 63 3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Chapter 4: Analytical Optimization of Composite Plates 66 4.1 Preliminary Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.2 Optimization Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.3 Validation and Results and Discussion . . . . . . . . . . . . . . . . . . . . . . 67 4.3.1 Validation of the analytical approach . . . . . . . . . . . . . . . . . . . 67 4.3.2 Stress and strength distributions . . . . . . . . . . . . . . . . . . . . . 69 4.3.3 Optimization of a single lamina . . . . . . . . . . . . . . . . . . . . . 73 4.3.3.a Effect of population size in GA . . . . . . . . . . . . . . . . 74 4.3.3.b Effect of crossover probability . . . . . . . . . . . . . . . . 75 4.3.3.c Effect of mutation probability . . . . . . . . . . . . . . . . . 76 4.3.3.d Lamina under various in-plane loading conditions . . . . . . 77 4.3.4 Optimization of symmetric laminates . . . . . . . . . . . . . . . . . . 78 4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 II Experimental Study 86 Chapter 5: Strength Degradation of Plates with Sin 5.4 Experimental Unnotched Tensile Proprieties . . . . . . . . . . . . . . . . . . . 92 5.5 Laminated Plates with Different Fiber Orientations . . . . . . . . . . . . . . . 95 5.6 Experimental Notched Tensile Strength Degradation . . . . . . . . . . . . . . 100 5.7 Open Hole Stress Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.8 Open Hole DIC Strain Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.8.1 Strain distributions around circular holes . . . . . . . . . . . . . . . . 106 5.8.2 Strain distributions around square and rectangular holes . . . . . . . . 110 5.9 Experimental and Analytical Open Hole Tensile Strength . . . . . . . . . . . . 117 5.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Chapter 6: Numerical and Experimental Optimization 123 6.1 Preliminary Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6.2 Finite Element Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 6.2.1 Plate with a single hole (SH) . . . . . . . . . . . . . . . . . . . . . . . 124 6.2.2 Plate with multiple cutouts . . . . . . . . . . . . . . . . . . . . . . . . 125 6.3 Genetic Algorithm and Finite Element Method Coupling . . . . . . . . . . . . 126 6.4 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 6.4.1 Materials and specimen preparation . . . . . . . . . . . . . . . . . . . 131 6.4.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 6.5.1 Laminated plates with a single notch . . . . . . . . . . . . . . . . . . . 134 6.5.2 Laminated plates with defense hole system . . . . . . . . . . . . . . . 137 6.5.2.a Numerical optimization of stress concentration . . . . . . . . 137 6.5.2.b Numerical optimization of failure load . . . . . . . . . . . . 139 6.5.3 Experimental notched tensile strength . . . . . . . . . . . . . . . . . . 143 6.5.3.a Laminated plates with the same main hole diameter . . . . . 143 6.5.3.b Laminated plates with various main hole diameters . . . . . 144 6.5.3.c Strain distributions and failure mechanisms . . . . . . . . . . 146 6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 General Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 xiii 1 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 2 Suggestions for Future Works . . . . . . . . . . . . . . . . . . . . . . . . . 153 Bibliography |
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