Investigation Of Stretching Effect With Mixed Finite Element Formulations For Laminated Beams And Plates

A complete knowledge of the behavior of structural applications under applied loads is necessary for the engineering design process. Finite element formulations have been shown to be one of the most effective analysis method in engineering applications. This information is crucial since it has always been a top objective for engineers and researchers to offer solutions that are as accurate as possible. Construction, biomechanics, mobile, industrial, aerospace, defense, and nuclear engineering are just a few of the engineering fields where composite structures are increasingly widely employed. In the constructions in which they are used, a variety of composite materials, which are based on the collaboration of many materials, provide some advantages including sound, temperature, water insulation, fire prevention and so on. In the structural design of composite materials, load bearing capability, failure load, and damage detection are crucial factors. Regarding to find a closer solution to expected results of all those parameters, a proper static analysis is unavoidable. It will be effective to choose the right and efficient formulation that reflects the real physics behavior accurate enough because either the financial condition or other factors may not be available for experimental work. The modeling and analysis of laminated composite beams and plates using higher order shear deformation theory (HSDTs) is performed in this thesis. This thesis' main goal is to introduce the stretching effect with the higher order shear deformation theory into a single formulation using polynomial, exponential, and trigonometric functions. To develop a weak form based on the generalized displacement fields of the higher order shear deformation theories, the notion of virtual displacements is used within a mixed formulation. In order to adequately represent the nonlinear and parabolic variability of transverse shear stress, it is discovered that even for the different functions, results with elasticity method theoretically compatible with used HSDT model. In addition, when compared to the theories that are already accessible in the literature, presented higher order shear deformation theory converges the responses for laminated composite plates and beams. The first variation of the functional for both laminated beam and plate structures are obtained through the application of the Hellinger-Reissner variational principle. Due to this, displacements and stress resultants, namely two independent fields, are included in finite element equations. Two-noded, one-dimensional straight elements are utilized for the laminated beams, whereas four-noded, two-dimensional quadrilateral elements are used for laminated plates. While the generated functional initially had C1 continuity, as an advantage of the mixed finite element formulation integration by parts is performed resulting with functionals requiring only C0 continuity. The kinematical variables of the beam model involve one deflection, one axial displacement, one additional deflection parameter to introduce transverse stretching, and one shear rotation. The plate's kinematics consist of deflection parameters w and beta , two in-plane displacement u and w, representing the displacement components for x and y directions, and shear rotations tetax and tetay associated with y and x axes, respectively. One advantage of this mixed finite element method is the accurate derivation of displacements and stress components at the nodes. To compute axial stress and in-plane shear stress Hooke's law is employed, while with the help of the equilibrium equations of elasticity, transverse shear components are acquired. To demonstrate the applicability of the proposed mixed finite element formulation, different types of examples for composite beams and plates based on various higher order shear deformation theories are presented. In addition, buckling analysis is performed for isotropic plate and laminated composite beams using the presented theory. The performance of the proposed solution procedure is evaluated through comparison and convergence assessments with various layouts and boundary conditions.