Third-order Shear Deformation Beam Theory Research Articles

Shape Control of Smart Beams Using PZT and SMA Actuators with the Spline Finite Point Method

The spline finite point method (SFPM) that is based on the third order shear deformation beam theory (TSDT) is introduced to investigate the shape control of smart beam, which is integrated with PZT and SMA actuators. The governing equations of the smart beam are given by the SFPM and TSDT. The shape control problem is formulated as the problem of minimizing the objective function to study the shape control effects of the smart beam under the different control methods. To demonstrate the less computational cost and higher accuracy of the SFPM, several numerical examples are calculated. The advantages of both smart materials and the effective control of smart structure can be obtained by the hybrid actuators.

Shape Control of Smart Beams Using PZT and SMA Actuators with the Spline Finite Point Method

The spline finite point method (SFPM) that is based on the third order shear deformation beam theory (TSDT) is introduced to investigate the shape control of smart beam, which is integrated with PZT and SMA actuators. The governing equations of the smart beam are given by the SFPM and TSDT. The shape control problem is formulated as the problem of minimizing the objective function to study the shape control effects of the smart beam under the different control methods. To demonstrate the less computational cost and higher accuracy of the SFPM, several numerical examples are calculated. The advantages of both smart materials and the effective control of smart structure can be obtained by the hybrid actuators.

Size-dependent buckling analysis of functionally graded third-order shear deformable microbeams including thermal environment effect

Presented herein is the prediction of buckling behavior of size-dependent microbeams made of functionally graded materials (FGMs) including thermal environment effect. To this purpose, strain gradient elasticity theory is incorporated into the classical third-order shear deformation beam theory to develop a non-classical beam model which contains three additional internal material length scale parameters to consider the effects of size dependencies. The higher-order governing differential equations are derived on the basis of Hamilton’s principle. Afterward, the size-dependent differential equations and related boundary conditions are discretized along with commonly used end supports by employing generalized differential quadrature (GDQ) method. A parametric study is carried out to demonstrate the influences of the dimensionless length scale parameter, material property gradient index, temperature change, length-to-thickness aspect ratio and end supports on the buckling characteristics of FGM microbeams. It is revealed that temperature change plays more important role in the buckling behavior of FGM microbeams with higher values of dimensionless length scale parameter.

Free vibration analyses of axially loaded laminated composite beams based on higher-order shear deformation theory

The dynamic stiffness matrix method is introduced to solve exactly the free vibration and buckling problems of axially loaded laminated composite beams with arbitrary lay-ups. The Poisson effect, axial force, extensional deformation, shear deformation and rotary inertia are included in the mathematical formulation. The exact dynamic stiffness matrix is derived from the analytical solutions of the governing differential equations of the composite beams based on third-order shear deformation beam theory. The application of the present method is illustrated by two numerical examples, in which the effects of axial force and boundary condition on the natural frequencies, mode shapes and buckling loads are examined. Comparison of the current results to the existing solutions in the literature demonstrates the accuracy and effectiveness of the present method.

Higher-Order Beam Theories for Mode II Fracture of Unidirectional Composites

Mathematical models, for the stress analyses of unidirectional end notch flexure and end notch cantilever specimens using classical beam theory, first, second, and third-order shear deformation beam theories, have been developed to determine the interlaminar fracture toughness of unidirectional composites in mode II. In the present study, appropriate matching conditions, in terms of generalized displacements and stress resultants, have been derived and applied at the crack tip by enforcing the displacement continuity at the crack tip in conjunction with the variational equation. Strain energy release rate has been calculated using compliance approach. The compliance and strain energy release rate obtained from present formulations have been compared with the existing experimental, analytical, and finite element results and found that results from third-order shear deformation beam theory are in close agreement with the existing experimental and finite element results.