Stress analysis of laminated composite and soft core sandwich beams using a simple higher order shear deformation theory

Abstract

In this paper, the refined beam theory (RBT) is examined for the bending of simply supported isotropic, laminated composite and sandwich beams. The axial displacement field uses parabolic function in terms of thickness ordinate to include the effect of transverse shear deformation. The transverse displacement consists of bending and shear components. The present theory satisfies the traction free conditions on the upper and lower surfaces of the beam without using problem dependent shear correction factors of Timoshenko. Governing differential equations and boundary conditions associated with the assumed displacement field are obtained by using the principle of virtual work. To prove the credibility of the present theory, we applied it to the bending analysis of beams. A simply supported isotropic, laminated composite and sandwich beams are analyzed using Navier approach. The numerical results of non-dimensional displacements and stresses obtained by using the present theory are presented and compared with those of other refined theories available in the literature along with the elasticity solution.

Stress Analysis of Laminated Composite Beam by Using MATLAB Software

“…Mathematical modeling is the process by which a problem as it appears in the real world is interpreted and represented in terms of abstract symbols. This makes mathematical modeling challenging and at the same time demanding since the use of mathematics and computers for solving real world problems is very widespread and has an impact in all branches of learning [8] The coordinate system for a laminated beam used in the present paper is shown in fgure.4. The xyz coordinate system is assumed to have its origin at the corner of the middle plane of the beam.…”

“…The xyz coordinate system is assumed to have its origin at the corner of the middle plane of the beam. The surfaces of the beam are at z=+h/2 and h is the thickness of the beam .ɵ is the angle of fiber orientation with the respect to the axis.1-,2-and 3-directions are principal axes in the longitudinal, transverse and normal directions ,respectively, it is assumed that the transverse deflection is small, so that the out-of-plane components of the in plane results , and are negligible [8]. The analyzed angle-ply symmetric layered composite beams have been made from three orthotropic laminas with equal thickness that had bonded together normal to their principal plane (1,2).…”

“…Therefore, the relation between the stress and strain components in principal axes making an angle with respect to reference axes can be expressed using transformation matrices as, And (7) Where and are the transformation matrices for stress and strain, respectively. They are: (8) Where (9) Where the elements in the stiffness matrix, matrix are (10) (11) The analysis of layered structures is based on the classical lamination theory [1,2] and the orthotropic beam is analyzed with the coordinate system (x, y, z) on the middle surface of the beam (z = 0), Figure. The total constitutive equation or load-deformation relation for the laminate is as follows:…”

Information Measuring System of Numerical Differentiation for the Analysis of Elements of Mechanical Structures

“…The variants of placing the measuring transducers on separate elements of the mechanical structure were also investigated (Lü et al 2015, Dung andSasaki 2016). In the studies of deformation, deflection and relative displacement of points in a beam, the Euler-Bernoulli bending theory is used, the account of first-order shear deformations of Tymoshenko and the theory of higher orders (Gere and Timoshenko 1997, Loktionov 2009, Al-Azzawi and Theeban 2010, Sayyad et al 2015, Ozbey et al 2016, Kara 2016. Dung and Sasaki (2016) investigated the effect of the location of the sensor attached to the cantilever beam.…”

Finite element modelling to assess the effect of position and size of the piezoelectric layer of a hybrid beam

“…Trigonometric function is used in terms of thickness coordinate in the axial displacement field to incorporate the effect of transverse shear deformation. In another study the parabolic function is used to include this effect Sayyad et al, 2015a. Giunta et al 2016 used a mesh-free strong-form solution to examine the static response of functionally graded beams.…”