A rather thorough and novel buckling analysis of an axially-loaded orthotropic circular cylindrical shell is formulated. The analysis assumes prebuckling rotations are negligible and uses a unique re-defining of the orthotropic material properties in terms of a so-called geometric mean isotropic (GMI) material. Closed-form expressions for the buckling stress in terms of cylinder geometry and orthotropic material properties are presented, the particular closed form depending on the specific character of the orthotropic material relative to the GMI material. With the formulation, the specific character of the buckling deformations - e.g., axisymmetric or nonaxisymmetric, the number of axial and circumferential waves - can be established. By using the maximum radius of curvature of an elliptical cross section in this formulation, the analysis is used to demonstrate the detrimental effects of an elliptical cross section on axial buckling capacity when compared to a circular cross section with the same circumference. Using the circumferentially-varying radius of curvature of an elliptical cross section, the analysis is then further used as the basis for developing two methods for improving the axial buckling capacity of elliptical cylinders. The first approach involves varying the wall thickness of an isotropic elliptical cylinder with circumferential position. Uniformly stable elliptical cross sections which preserve the same critical stress, critical load, or volume of an axially loaded circular cylinder of the same circumference are designed with the formulation. The second approach involves maintaining a uniform wall thickness but varying the orthotropic material properties with circumferential position. This approach is applied to a cylindrical lattice structure where it is assumed that the ribs are dense enough to be able to describe the lattice structure by means of an equivalent homogenized material. The orthotropic properties of the homogenized material are varied by varying the lattice rib angle with circumferential position. Considerable recovery of the axial buckling capacity of the variable-rib-angle design elliptical cylinder compared to the same cylinder constructed in isogrid fashion is demonstrated. In fact, recovery relative to an isogrid circular cylinder of the same circumference is demonstrated. For both approaches confirming finite element models are used to verify the findings. The two different approaches are compared, and finally the two approaches are recognized as special cases of a more general design philosophy. / Ph. D.

Cette thèse aborde la problématique de la conception optimale de structures composites stratifiées d’épaisseur variable. Les variables d’empilement définissent un problème d’optimisation combinatoire et des espaces de décisions de grande taille et potentiellement multimodaux. Les algorithmes d’optimisation stochastiques permettent de traiter ce type de problème et de tirer profit des performances et de l’anisotropie des plis composites pour l’allègement des structures composites stratifiées. Le but de cette étude est double : (i) développer un algorithme d’optimisation dédié aux composites stratifiés d’épaisseur variable et (ii) estimer le potentiel des composites stratifiés pour la maîtrise des performances aérodynamiques d’une pale de CROR composite.Dans la première partie de cette thèse, un algorithme évolutionnaire est spécialisé pour l’optimisation de tables de drapage et la gestion d’un ensemble de règles de conception représentatif des pratiques de l’industrie. Pour se faire, un encodage spécifique des solutions est proposé et des opérateurs de variations spécialisés sont développés.Dans la deuxième partie, l’algorithme est enrichi d’une technique de guidage basée sur l’exploitation d’un espace auxiliaire afin d'accroître son efficacité et d’intégrer davantage de connaissances des composites dans la résolution du problème.Finalement, la méthode est appliquée pour la conception d’une pale de CROR composite à l’échelle de la maquette de soufflerie. Au préalable, des processus itératifs de mise à froid et mise à chaud de la pale sont mis en place afin d’estimer la forme de la pale au repos et l’état de contraintes dans la pale en fonctionnement. / This thesis deals with the optimal design of variable-thickness laminated composite structures. The stacking variables define a combinatorial optimization problem and large decision spaces which are potentially multimodal. Stochastic optimization algorithms allow solving this type of problem and allow taking advantage from the performance and the anisotropic nature of unidirectional composite plies to lighten laminated composite structures.The purpose of this study is twofold: (i) developing an optimization algorithm dedicated to variable-thickness laminated composites and (ii) assessing the potential of laminated composites in influencing the aerodynamic performances of a composite CROR blade.Firstly, an evolutionary algorithm is specialized in order to optimize layup tables and handle a set of design guidelines which is representative of industrial practices. In this purpose, a specific encoding of the solutions is suggested and specialized variation operators are developed.Secondly, the algorithm is enriched with a guiding technique based on the exploitation of an auxiliary space in order to improve its efficiency and to include further composites-related knowledge for the resolution of the problem.Finally, the method is applied for the design of a reduced-scale composite CROR blade intended for wind-tunnel testing. Beforehand, iterative processes are implemented to estimate the shape of the non-operating blade and the stress state within the operating blade.

Residual state of stress in structural materials affect positively or negatively behaviour of component parts. The goal of this scope is not to deal with possible process of creating residual stresses neither about elimination of residual stress, but is focused how to determine magnitude of residual stress by hole-drilling method. We need to know magnitude and direction (angular orientation) of principal stresses to determine how residual state of stress affects behaviour of specimen. The most widely used modern technique for measuring residual stresses is hole-drilling strain-gage method. Hole-drilling method is in scope of this paper and is restricted only for measuring uniform residual stresses of steel specimens with finite dimensions. Structural, linear, elastic and isotropic material model is used with material properties =0,3 and E=2,1[10]^5 MPa. For correct application of this method we need to determine calibration coefficients “a“ and “b“ first. These coefficients are used to determine magnitude and direction of residual stresses in specific depth and diameter of drilled hole for materials with finite dimensions. Geometry and shape of model is simply represented by block with planar faces. Note that numerical determination of calibration coefficients is useful only for one type of strain gauge rosette RY 61 S. Main goals of this thesis are motivation and request to clearly report effectiveness, accuracy and applicability of calibration coefficients in relation to thickness of specimen, dimensions of drilled hole, condition of “through” or “blind” hole and number of drilled increments. High quality and accuracy of created numerical model is necessary too. Numerical simulation of residual stresses by MKP needs to be done to obtain requested results. All results are presented by 3D, 2D graphs and tables and compared with analytical results or results from other authors. Although is this publication focused on numerical modeling using FEM, hole-drilling method has many significant restrictions. The most substantial of them is influence of eccentricity of drilled hole, creation of stress concentration near drilled area and subsequent plastification, influence of geometrical inaccuracy of hole, etc. All these aspects have significant influence of determining calibration coefficients and can not be included into numerical simulation. These problems are closely discussed in background research. All obtained results should be helpful for practical use of calculated calibration coefficients to determine uniform residual stresses of specimens with various thickness and drilled hole. All these results are also applicable only for one type of strain gauge rosette, which is RY 61 S.