Higher-order Shear Deformation Beam Theory Research Articles

Vibration Analysis and Transient Response of an FGPM Beam under Thermo-Electro-Mechanical Loads using Higher-Order Shear Deformation Theory

This article presents the free and forced vibration characteristics of an FGPM beam under thermo-electro-mechanical loads using the higher-order shear deformation beam theory. The beam properties are assumed to vary through the thickness direction following the power law distribution in terms of the volume fractions of the constituent materials. The governing equations of motion are derived using Hamilton’s principle. The resulting system of differential equations of vibration is solved using the finite element method. The effects of boundary conditions, material composition, slenderness ratio, mechanical, thermal and electric loading, and transverse shear deformation on natural frequencies and transient response are investigated.

Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories

In this paper, fundamental frequency analysis of functionally graded (FG) beams having different boundary conditions is analyzed within the framework of the classical, the first-order and different higher-order shear deformation beam theories. The material properties of the beams vary continuously in the thickness direction according to the power-law form. Two types of formulation are developed. In the first formulation, total bending rotation measured on the beam middle surface is taken as unknown function whereas the shear rotation measured on the beam middle surface is taken as unknown function in the second formulation. The frequency equation is obtained by using Lagrange's equations and the boundary conditions of beams are satisfied with Lagrange multipliers. The unknown functions denoting the axial and the transverse deflections, the bending and the shear rotations of the cross-section of the beam are expressed in the polynomial form. In this study, the effects of slenderness ratio, material variations, the different formulations and the beam theories on the fundamental frequencies are examined. It is believed that the tabulated results will be a reference with which other researchers can compare their results.

Fracture Behavior of Multidirectional DCB Specimen: Higher-Order Beam Theories

Mathematical models, for the stress analysis of symmetric multidirectional double cantilever beam (DCB) specimen using classical beam theory, first and higher-order shear deformation beam theories, have been developed to determine the Mode I strain energy release rate (SERR) for symmetric multidirectional composites. The SERR has been calculated using the compliance approach. In the present study, both variationally and nonvariationally derived matching conditions have been applied at the crack tip of DCB specimen. For the unidirectional and cross-ply composite DCB specimens, beam models under both plane stress and plane strain conditions in the width direction are applicable with good performance where as for the multidirectional composite DCB specimen, only the beam model under plane strain condition in the width direction appears to be applicable with moderate performance. Among the shear deformation beam theories considered, the performance of higher-order shear deformation beam theory, having quadratic variation for transverse displacement over the thickness, is superior in determining the SERR for multidirectional DCB specimen.

Nonlinear transient response of a thick composite beam with shape memory alloy layers

This study presents a nonlinear transient finite element model for the elastodynamic response of thick shape memory alloy (SMA) composite beams. A three-dimensional thick beam with a matrix material and embedded SMA ribbons or wires is investigated. To predict the behavior of the beam, a higher-order shear-deformation beam theory and the von-Karman strain field are employed. A one-dimensional constitutive model and sinusoidal phase transformation kinetics are utilized to model the thermo-mechanical behavior of the SMA layers. A finite element model is developed to predict both passive and active performance. Numerical results are obtained for a beam composed of a polycarbonate layer as the matrix, and a segment of Nitinol ribbon embedded in the polycarbonate layer at its neutral surface. The numerical results demonstrate an effective vibration suppression of the beam when the SMA layer is activated. A parametric study is conducted to demonstrate the effects of different material and geometric properties on the active vibration response of the SMA composite beam.

Deflection analysis of beams with extension and shear piezoelectricpatches using discontinuity functions

The actuation performance of smart beams with extension and shearmode segments is investigated. The beam models are based on the first-orderand higher-order shear deformation beam theories. The piezoelectric stressresultants are expressed in terms of Heaviside discontinuity functions. Thestate-space approach along with the Jordan canonical form is used to obtainan analytical solution for the static deflection of smart beams with arbitraryboundary conditions. Through demonstrative examples, a comparative study of abeam with extension mode actuators and the corresponding beam with a shearmode actuator is attained. The effects of actuator length and location on thedeflected shape of the beam are studied. Results show that shear patches createthe largest deflection if they are placed near the support, whereas extensionpatches create the largest deflection if they are placed at the beam center.For clamped-hinged and clamped-clamped beams, the actuation performance ofthe shear patches is superior to that of the extension patches.

Transverse Shear and Normal Deformation Theory for Bending Analysis of Laminated and Sandwich Elastic Beams

The influence of transverse normal strain on bending analysis of cross-ply laminated and sandwich beams is presented. A higher-order shear deformation beam theory is developed. Euler-Bernoulli classical, Timoshenko first-order and simple higher-order theories have been also used in the analysis. The governing equations for a beam composed of orthotropic layers and subjected to any given mechanical load distribution are derived. Making use of Navier-like approach, exact solutions are obtained for cross-ply laminated and sandwich beams subjected to arbitrary loadings. Numerical results for beams with the simply-supported boundary conditions are presented. The effects due to transverse normal strain, transverse shear deformation and number of layers on the static response of the beams are investigated.

Effect of Shear Deformation on Bending of Laminated Composite Beams

Abstract A higher-order shear deformation beam theory is utilized to analyze the bending of thick laminated composite beams. This theory accounts for parabolic distribution of shear strain through the thickness of the beam. The predicted displacements show improvement over the Bresse-Timoshenko beam theory. Mixed finite element results are obtained for those cases where closed-form solutions are not available. The finite element and exact solutions are in close agreement. Numerical results are presented for single, two and three-layer beams under uniform and sinusoidal distributed transverse loadings.

Nonlinear bending of thick beams laminated from bimodular composite materials

A higher-order shear deformation beam theory is presented to analyze geometrically nonliner bending of thick, rectangular beams made from bimodular materials. This is performed by using a mixed finite element model. Results are reported for maximum deflections of simply-supported and clamped-clamped beams under a uniformly distributed load. The effect of material bimodularity on the nonlinear transverse deflection is investigated.