Axial-flexural coupled vibration and buckling of composite beams using sinusoidal shear deformation theory

A finite element model based on sinusoidal shear deformation theory is developed to study vibration and buckling analysis of composite beams with arbitrary lay-ups. This theory satisfies the zero traction boundary conditions on the top and bottom surfaces of beam without using shear correction factors. Besides, it has strong similarity with Euler–Bernoulli beam theory in some aspects such as governing equations, boundary conditions, and stress resultant expressions. By using Hamilton’s principle, governing equations of motion are derived. A displacement-based one-dimensional finite element model is developed to solve the problem. Numerical results for cross-ply and angle-ply composite beams are obtained as special cases and are compared with other solutions available in the literature. A variety of parametric studies are conducted to demonstrate the effect of fiber orientation and modulus ratio on the natural frequencies, critical buckling loads, and load-frequency curves as well as corresponding mode shapes of composite beams

Thermal Deformation of Antisymmetric Angle-ply Laminated Plate Strips in Cylindrical Bending

Exact analytical solutions for the thermal deformations of antisymmetric angle-ply laminated plate strips in cylindrical bending are developed. The state variable technique in conjunction with Jordan canonical form is used to obtain these solutions for plate strips with arbitrary boundary conditions. Deflections are computed for laminates subjected to linearly varying transverse temperature distribution. Numerical results are presented emphasizing the effects of shear deformation, number of layers, ply-angles, transverse shear correction factor and boundary conditions on the thermal response

Analysis of the Dynamic Response of Cross-ply Laminated Shallow Shells with Various Boundary Conditions

Analytical solutions of the dynamic response of the classical, first-order and third-order theories of cross-ply laminated shallow shells are developed for various boundary conditions. The solutions are applicable to laminated shells with two opposite edges simply supported and the remaining ones can have arbitrary combinations of free, clamped and simply supported boundary conditions. A Levy type method in conjunction with generalized modal approach is used to obtain these solutions. For thick shells, the classical shell theory predicts deflections and stresses significantly different from those of the third-order theory. The third-order theory and first-order theory results are very close to each other for response and normal stress. However, the third-order theory does not require the use of shear correction factors

Exact deflection solutions of beams with shear piezoelectric actuators

Exact deflection models of beams with n actuators of shear piezoelectric are developed analytically. To formulate the models, the first-order and higher-order beam theories are used. The exact solutions are obtained with the aid of the state-space approach and Jordan canonical form. A case study is presented to evaluate the performance of the authors' previously reported models. Through a demonstrative example, a comparative study of the first-order and higher-order beams with two shear piezoelectric actuators is attained. It is shown that the first-order beam cannot predict the beam behavior when compared with the results of the higher-order beam. Further applications of the solutions are presented by investigating the effects of actuators lengths and locations on the deflected shapes of beams with two piezoelectric actuators. Some interesting deflection curves are presented. For example, the deflection curve of a H-H beam resembles saw teeth that rotate clockwise about the central location with the increase of actuators lengths. The presented exact solutions can be used in the design process to obtain detailed deformation information of beams with various boundary conditions. Moreover, the presented analysis can be readily used to perform precise shape control of beams with n actuators of shear piezoelectric.King Saud Universit

Exact deflection solutions of beams with shear piezoelectric actuators

Exact deflection models of beams with n actuators of shear piezoelectric are developed analytically. To formulate the models, the first-order and higher-order beam theories are used. The exact solutions are obtained with the aid of the state-space approach and Jordan canonical form. A case study is presented to evaluate the performance of the authors' previously reported models. Through a demonstrative example, a comparative study of the first-order and higher-order beams with two shear piezoelectric actuators is attained. It is shown that the first-order beam cannot predict the beam behavior when compared with the results of the higher-order beam. Further applications of the solutions are presented by investigating the effects of actuators lengths and locations on the deflected shapes of beams with two piezoelectric actuators. Some interesting deflection curves are presented. For example, the deflection curve of a H-H beam resembles saw teeth that rotate clockwise about the central location with the increase of actuators lengths. The presented exact solutions can be used in the design process to obtain detailed deformation information of beams with various boundary conditions. Moreover, the presented analysis can be readily used to perform precise shape control of beams with n actuators of shear piezoelectric.King Saud Universit

Smart beams with extension and thickness-shear piezoelectric actuators

Analytical models and exact solutions for beams with thickness-shear and extension piezoelectric actuators are formulated and developed. The models are based on the first-order beam theory (FOBT) and higher-order beam theory (HOBT). The beam bending problem is solved by using the state-space approach along with the Jordan canonical form. Numerical examples of beams incorporating piezoelectric actuators with various boundary conditions are presented. In these examples, the validity of the proposed models and the feasibility of using shear-mode actuators in smart beams are investigated. For the extension-mode actuators there is slight difference between the deflections of the FOBT and that of the HOBT. For the shear-mode actuators there is pronounced difference between the deflections of the FOBT and that of the HOBT. The results of the FOBT are very sensitive to the value of the shear correction factor. The results of the present work are compared with the previously reported results in the literature, where available.King Saud Universit