Influence of neutral surface position on the nonlinear stability behavior of functionally graded plates

Nonlinear behavior of functionally graded material (FGM) skew plates under in-plane load is investigated here using a shear deformable finite element method. The material is graded in the thickness direction and a simple power law based on the rule of mixture is used to estimate the effective material properties. The neutral surface position for such FGM plates is determined and the first order shear deformation theory based on exact neutral surface position is employed here. The present model is compared with the conventional mid-surface based formulation, which uses extension-bending coupling matrix to include the noncoincidence of neutral surface with the geometric mid-surface for unsymmetric plates. The nonlinear governing equations are solved through Newton–Raphson technique. The nonlinear behavior of FGM skew plates under compressive and tensile in-plane load are examined considering different system parameters such as constituent gradient index, boundary condition, thickness-to-span ratio and skew angle. An erratum to this article can be found at     

Barium hexaferrite (M-phase) exhibiting superstructure

Barium hexaferrite (M-phase) prepared by the flux method is found to exhibit a $\text{√3}\text{a}\text{× √3}\text{a}$ superstructure similar to barium hexaaluminate.     

Toward p-type conduction in Cs-doped ZnO: an eco-friendly synthesis method

An alcohol-free, eco-friendly technique was adapted for the synthesis of undoped ZnO and Cs-(cesium) doped ZnO nanoparticles (NPs). The effect of annealing and dopant concentration on its structural and optical properties was investigated. X-ray diffraction results confirmed the formation of polycrystalline hexagonal wurtzite structure and enhanced crystallinity was observed for 1 mol%: Cs-doped ZnO NPs. Scanning electron microscopy results revealed triangular-shaped NPs and increase in the crystallite size is noticed with increase in dopant concentration. UV–visible results showed shift in the band edge toward higher wave length side with increasing Cs concentration. Reduction in bandgap was observed for Cs-doped ZnO NPs, due to quantum confinement effect. Transmittance value increased to 86 % with the inclusion of Cs in ZnO lattice. Room temperature photoluminescence analysis of Cs-doped ZnO NPs reveals bandedge emission along with 450 nm emission due to Zn vacancy and Zn interstitial defects. Electrical measurements confirmed the realization of p-type conductivity in Cs-doped ZnO NPs with a carrier concentration of 1.3 × 10¹⁸/cm³.     

A C1 finite element including transverse shear and torsion warping for rectangular sandwich beams

A new three‐noded C¹ beam finite element is derived for the analysis of sandwich beams. The formulation includes transverse shear and warping due to torsion. It also accounts for the interlaminar continuity conditions at the interfaces between the layers, and the boundary conditions at the upper and lower surfaces of the beam. The transverse shear deformation is represented by a cosine function of a higher order. This allows us to avoid using shear correction factors. A warping function obtained from a three‐dimensional elasticity solution is used in the present model. Since the field consistency approach is accounted for interpolating the transverse strain and torsional strain, an exact integration scheme is employed in evaluating the strain energy terms. Performance of the element is tested by comparing the present results with exact three‐dimensional solu‐tions available for laminates under bending, and the elasticity three‐dimensional solution deduced from the de Saint‐Venant solution including both torsion with warping and bending. In addition, three‐dimensional solid finite elements using 27 noded‐brick elements have been used to bring out a reference solution not available for sandwich structures having high shear modular ratio between skins and core. A detailed parametric study is carried out to show the effects of various parameters such as length‐to‐thickness ratio, shear modular ratio, boundary conditions, free (de Saint‐Venant) and constrained torsion. Copyright © 1999 John Wiley & Sons, Ltd.     

Shear flexible field‐consistent curved spline beam element for vibration analysis

In this paper, an efficient curved cubic B‐spline beam element is developed based on the field consistency principle, for vibration analysis. The formulation is general in the sense that it includes anisotropy, transverse shear deformation, in‐plane and rotary inertia effects. The element is based on laminated refined beam theory, which satisfies the interface transverse shear stress and displacement continuity, and has a vanishing shear stress on the top and bottom surfaces of the beam. The lack of consistency in the shear and membrane strain field interpolations in their constrained physical limits causes poor convergence and unacceptable results due to locking. Hence, numerical experimentation is conducted to check these deficiencies with a series of assumed shear/membrane strain functions, redistributed in a field‐consistent manner. The performance of the element is assessed by studying the free vibration behaviour of a variety of problems ranging from a straight beam to a circular ring. Copyright © 1999 John Wiley & Sons, Ltd.     

Non‐linear dynamic stability analysis of composite laminates under periodic in‐plane compressive loads

This work deals with the investigation of the non‐linear instability behaviour of the composite laminates subjected to periodic in‐plane/axial load, through the finite element formulation with dynamic response analysis. Here, C¹ eight‐noded shear‐flexible plate element, based on a new kind of kinematics which allows to exactly ensure the continuity conditions for displacements and stresses at the interfaces between the layers of the laminate, and also the boundary conditions at the top and bottom surfaces of the laminate, is employed. The non‐linear governing equations obtained are solved using the Newmark direct integration method coupled with a modified Newton–Raphson iteration procedure. The analysis brings out various characteristic features of the dynamic stability such as existence of beats, their dependency on the forcing frequency, and the typical character of vibrations in the different regions. Numerical results are also presented to highlight the influence of ply‐angle and lay‐up of the laminate on dynamic stability behaviour of the composite laminates. Copyright © 1999 John Wiley & Sons, Ltd.