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ÖgeMixed finite element formulations for laminated beams and plates based on higher order shear deformation theories(İTÜ Graduate School, 2021) Bab, Yonca ; Kutlu, Akif ; Structure EngineeringThe engineering design process requires a thorough understanding of the behavior of structural applications under applied loads. In engineering applications, finite element formulations have been proven to be one of the most efficient analyses tools. This content is essential because it has always been a priority for ngineers/researchers to provide answers that are as close to the actual problems as possible. Composite structures are now widely used in a variety of engineering sectors, including construction, biomechanics, automobile, industrial, aircraft, defense, and nuclear. Several types of composite materials, which are based on the cooperation of several materials, offer some benefits such as sound, heat, and water insulation, fire safety, high strength, corrosion resistance, lightness, and low cost in the structures in which they are employed. Load carrying capacity, failure load and damage detection are critical in the structural design of composite materials. In this context, the need for detailed static analysis is inevitable. Since the financial situation or the physical environment is not always suitable for experimental work, it will be an efficient way to determine the formulation closest to the real behavior according to the problem type and to work theoretically. In this thesis, applying linear static analysis, a mixed finite element formulation is proposed to evaluate the stress and displacement components of thin to relatively thick laminated composite beams and plates. The formulations rely on the HigherOrder Shear Deformation Theories, which eliminates the necessity for the shear correction factor required by the FirstOrder Shear Deformation Theory. Instead of imposing a constant transverse shear deformation through the thickness of the laminate several studies have proposed trigonometric, exponential, and polynomial type shear functions that meet the nonuniform shear stress distribution in the crosssection. In this study, four different shear functions were utilized and their predictive capabilities are compared in plate analysis through numerical examples. Whereas, for the stress analysis of laminated composite beams, the famous third order shear function was adopted to all solved problems. To be more specific; while the shear functions of Reissner, Reddy, Touratier and NguyenXuan et al. were applied for plate analysis, Reddy's shear function was applied for beam analysis. In the formulation part of this thesis, the HellingerReissner variational principle was used and the first variation of the functional based on this principle was obtained separately for the laminated beam and plate elements. In this way, finite element equations possessing two independent field variables of displacement and stress resultant type were obtained. In the finite element discretization, twonoded, onedimensional straight elements were employed for beams and fournoded, twodimensional quadrilateral elements were employed for plates. Field variables are interpolated with linear shape functions as the proposed mixed finite element formulation requires C0 continuity. The beam kinematical variables consist of a deflection, axial displacement, and a shear rotation, while the plate displacement field consists of a deflection, two inplane displacements and two shear rotations. The displacements and stress components are derived precisely at the nodes as an advantage of mixed finite element equations. Axial stress and inplane shear components of both beam and plate structures are calculated directly at the nodes in terms of the stress resultants and sectional compliance matrix by employing Hooke's law. The continuous transverse shear stresses of the laminated composite beam are calculated with the help of the equilibrium equations of elasticity. On the other hand, the equivalent section principle is employed for the determination of the transverse shear stress components of the laminated plate. In order to reflect the extendibility of the proposed mixed finite element formulation for other types of analyses a viscoelastic formulation is also presented for isotropic plates based on higher order shear deformation theory. By employing the correspondence principle the material constants of the plate is replaced by their complex counterparts and static analyses are conducted in Laplace space. In order to call back the parameters of the quasistatic analyses to the time space the modified Durbin's algorithm is implemented. The quasistatic analysis of simply supported and clamped viscoelastic plate is conducted by adopting standard model. Comparison and convergence assessments for several lamination schemes were performed under various boundary conditions in order to reflect the performance of the proposed solution procedure.