PhD Oral Exam - Saeid Khadem Moshir, Mechanical Engineering

When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.

Abstract

Due to high strength to weight ratio of thermoplastic composite structures, their use attracted industrial interests, especially in the aerospace industry. The application of composite curved tubes for landing gear of helicopters instead of aluminum is the subject of interest for the aerospace industry. The focus of the present work is to study mechanical behavior of composite straight and curved composite tubes subjected to the bending loading which is similar to the loading conditions of cross tubes for landing gear of helicopters during landing. The analysis of these structures with a large number of layers may be computationally expensive. The finite element method is widely used for stress analysis of initially curved composite tubes. This method is computationally expensive for design and optimization process. The main objective of the present thesis is to develop an efficient, simple-input method for stress analysis of initially curved and straight composite tubes under four-point bending loadings. To do so, different methodologies for stress analysis of straight and initially curve tubes are introduced. The advantages and disadvantages of the methods are presented. The first part of this thesis focuses on the stress analysis of straight composite cylinders under pure bending moment. The 3D elasticity of Lekhnitskii is employed to carry out the stress analysis of an anisotropic cylinders with many layers. In the second part, an analytical meshless polynomial based method in conjunction with dimensional reduction method are presented to carry out cross-sectional analysis as well as determining strain distribution in straight and curved composite tubes under bending loading (four-point bending loading) in which the effect of shear strains is taken into consideration. In order to obtain the stiffness constants of the cross-section and strains, the powerful mathematical Variational Asymptotic Method (VAM) is employed to decompose a three-dimensional elasticity problem into a two-dimensional cross-sectional analysis and a one-dimensional analysis along the length. The VAM presents Classical and Timoshenko beam models and cross-sectional stiffness matrices. In the Classical beam model cross-sectional stiffness matrix, the effect of shear is not considered. In order to achieve a more precise beam model for the analysis of initially curved and straight tubular beams, the Timoshenko-like beam model and the effect of shear strain is taken into consideration. The presented polynomial meshless dimensional reduction method is employed for tubes with circular and elliptical cross-sections. Based on the VAM, a commercial finite element based cross-sectional analysis software named Variational Asymptotic Beam Sectional Analysis (VABS) is released. In the present work, the utilization of the Pascal polynomials for the cross-sectional analysis of the b beams takes advantage of the meshless method compared with the three-dimensional finite element method or VABS. Moreover, a one-dimensional finite element solution is provided for straight and initially curved composite tubes. The presented method for the analysis of initially curved and straight tubes is computationally more efficient and simple-input compared to the 3D finite element method. In addition, it eliminates generating two-dimensional cross-sectional mesh and dividing the cross-section into different segments for straight and curved tubes compared to Variational Asymptotic Beam Sectional Analysis (VABS) software. So, the present method can be more efficient and straightforward in terms of modeling procedure compared to VABS. The parametric study such as determining cross-sectional stiffness constants, strains and displacements for design and optimization will be more straightforward.

The experimental tests are carried out to validate the present method of solution. Test setups for four-point bending test of the straight and initially curved tubes are provided by a teamwork at Concordia Center for Composites (CONCOM). The obtained strains at different spots of the tubes as well as the transverse displacement are compared with the theoretical solution. The effect of lay-up sequence, initial curvature on the mechanical behavior of the composite tubes are studied.