تحليل كمانش و ارتعاش آزاد صفحات مركب داراي الياف منحني با و بدون پيزوالكتريك به روش نوار محدود اسپلاين

Buckling an‎d Free Vibration Analysis of Curvilinear Fiber Composite Plates with an‎d without Piezoelectric Layers Using the Spline Finite Strip Method

مهندسي عمران

In this thesis, the numerical analysis of buckling an‎d free vibration of composite plates with curvilinear fibers, with an‎d without piezoelectric layers, is investigated based on various theories using the Spline Finite Strip Method. In this approach, a third-order B-spline function is employed along the longitudinal direction, Hermite functions are adopted in the transverse direction to describe edge displacements an‎d rotations, an‎d Lagrange functions are applied to model shear deformation an‎d in-plane displacements. In the present analysis, various plate theories, including the Classical Plate Theory (CLPT), First-Order Shear Deformation Theory (FSDT), Third-Order Shear Deformation Theory (TSDT) by Reddy, an‎d Zigzag Theory, are implemented. Initially, the relationships for curved fibers are presented, followed by the displacement fields of the mentioned theories an‎d then the relationships between stress, strain, an‎d displacement fields were formulated. To solve the buckling an‎d free vibration problems, the principle of virtual work is employed to extract the stiffness, geometric, an‎d mass matrices. These matrices are discretized using the Spline Finite Strip Method. Subsequently, the relations are extended to incorporate the presence of piezoelectric layers. After extracting the required matrices using the Spline Finite Strip Method, the results are first validated for composite plates with constant stiffness. Then, the buckling an‎d free vibration responses of variable stiffness composite plates, along with the effects of influencing factors such as boundary conditions, aspect an‎d thickness ratios, an‎d elasticity modulus ratios based on different theories, are examined. Furthermore, the influence of the piezoelectric layer under closed-circuit conditions on the buckling behavior of composite plates is studied. Finally, the results are presented in tables an‎d graphs. The results indicate that the spline strip method has a strong capability to model curvilinear fibers an‎d provides good accuracy for thin plates; in thick plates, accurate results can be achieved by increasing the number of nodal points. Increasing the number of layers generally leads to higher buckling loads. However, curvilinear fibers do not always yield better results than straight fibers, an‎d an optimal fiber angle should be selec‎ted. The results indicate that using curved fibers does not always provide better outcomes compared to straight fibers, an‎d the optimal fiber angle must be carefully selec‎ted. Moreover, the closer the fiber orientation at the center of the plate is to the principal axis, the higher the buckling load becomes. The non-dimensional buckling coefficient under biaxial loading is lower than that under uniaxial loading, an‎d the Classical Plate Theory, due to neglecting shear effects, predicts lower values compared to FSDT, TSDT, an‎d Zigzag theories. The free vibration results also show that increasing the corner fiber angle while keeping the central fiber angle constant leads to an increase in the natural frequency, whereas increasing the central fiber angle while keeping the corner fiber angle constant results in a decrease in the natural frequency. For composite plates with piezoelectric layers, increasing the thickness of the piezoelectric layers relative to the total plate thickness leads to an increase in the buckling coefficient.

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