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CONTENTS
Volume 8, Number 1, February 2019
 

Abstract
The present paper deals with delamination fracture analyses of the multilayered functionally graded non-linear elastic Symmetric Split Beam (SSB) configurations. The material is functionally graded in both width and height directions in each layer. It is assumed that the material properties are distributed non-symmetrically with respect to the centroidal axes of the beam cross-section. Sine laws are used to describe the continuous variation of the material properties in the cross-sections of the layers. The delamination fracture is analyzed in terms of the strain energy release rate by considering the balance of the energy. A comparison with the J-integral is performed for verification. The solution derived is used for parametric analyses of the delamination fracture behavior of the multilayered functionally graded SSB in order to evaluate the effects of the sine gradients of the three material properties in the width and height directions of the layers and the location of the crack along the beam width on the strain energy release rate. The solution obtained is valid for two-dimensional functionally graded non-linear elastic SSB configurations which are made of an arbitrary number of lengthwise vertical layers. A delamination crack is located arbitrary between layers. Thus, the two crack arms have different widths. Besides, the layers have individual widths and material properties.

Key Words
multilayered beam; delamination fracture; material non-linearity; two-dimensional sine material gradient

Address
Victor I. Rizov: Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy,
1 Chr. Smirnensky Blvd., 1046 – Sofia, Bulgaria


Abstract
The influence of torsional rigidity of hinged flexible appendage on the linear dynamics of flexible spacecrafts with liquid on board was analyzed by considering the spacecraft\'s main body as a rigid tank, its flexible appendages as two elastically supported elastic beams, and the onboard liquid as an ideal liquid. The meniscus of the liquid free surface due to surface tension was considered. Using the Lagrangian of the spacecraft\'s main body (rigid tank), onboard liquid, and two beams (flexible appendages) in addition to assuming the system moved symmetrically, the coupled system frequency equations were obtained by applying the Rayleigh-Ritz method. The influence of the torsional rigidity of the flexible appendages on the spacecraft\'s coupled vibration characteristics was primary focus of investigation. It was found that coupled vibration modes especially that of appendage considerably changed with torsion spring parameter kt of the flexible appendage. In addition, variation of the main body displacement with system parameters was investigated.

Key Words
hydroelastic vibration; space structure; coupled system; liquid sloshing; zero-gravity; elastic supported; torsional spring

Address
Masakatsu Chiba and Hidetake Magata: Department of Aerospace Engineering, Graduate School of Engineering,
Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan


Abstract
Here in this investigation, a two-dimensional thermoelastic problem of thick circular plate of finite thickness under fractional order theory of thermoelastic diffusion has been considered in frequency domain. The effect of frequency in the axisymmetric thick circular plate has been depicted. The upper and lower surfaces of the thick plate are traction free and subjected to an axisymmetric heat supply. The solution is found by using Hankel transform techniques. The analytical expressions of displacements, stresses and chemical potential, temperature change and mass concentration are computed in transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically. The effect frequency has been shown on the various components.

Key Words
fractional order; isotropic thermoelastic; frequency; hankel transform; plane axisymmetric; diffusion

Address
Parveen Lata: Department of Basic and Applied Sciences, Punjabi University, Patiala, Punjab, India

Abstract
This investigation is focused on the variations in transversely isotropic thick circular plate due to time harmonic thermomechanical sources. The homogeneous thick circular plate in presence and absence of energy dissipation and two temperatures has been considered. Hankel transform is used for solving field equations. The analytical expressions of conductive temperature, displacement components, and stress components are computed in the transformed domain. The effects of frequency at different values are represented graphically. Some specific cases are also figured out from the current research.

Key Words
frequency; hankel transformation; thermoelastic; thick circular plate; time harmonic sources; transversely isotropic

Address
Parveen Lata and Iqbal Kaur: Department of Basic and Applied Sciences, Punjabi University, Patiala, Punjab, India

Abstract
Finite element simulations of solid mechanics problems often involve the use of Non-Confirming Meshes (NCM) to increase accuracy in capturing nonlinear behavior, including damage and plasticity, in part of a solid domain without an undue increase in computational costs. In the presence of material nonlinearity and plasticity, higher-order variables are often needed to capture nonlinear behavior and material history on non-conforming interfaces. The most popular formulations for coupling non-conforming meshes are dual methods that involve the interpolation of a traction field on the interface. These methods are subject to the Ladyzhenskaya-Babuska-Brezzi (LBB) stability condition, and are therefore limited in their implementation with the higher-order elements needed to capture nonlinear material behavior. Alternatively, the enriched discontinuous Galerkin approach (EDGA) (Haikal and Hjelmstad 2010) is a primal method that provides higher order kinematic fields on the interface, and in which interface tractions are computed from local finite element estimates, therefore facilitating its implementation with nonlinear material models. The inclusion of higher-order interface variables, however, presents the issue of preserving material history at integration points when a increase in integration order is needed. In this study, the enriched discontinuous Galerkin approach (EDGA) is extended to the case of small-deformation plasticity. An interface-driven Gauss-Kronrod integration rule is proposed to enable adaptive enrichment on the interface while preserving history-dependent material data at existing integration points. The method is implemented using classical J2 plasticity theory as well as the pressure-dependent Drucker-Prager material model. We show that an efficient treatment of interface variables can improve algorithmic performance and provide a consistent approach for coupling non-conforming meshes in inelasticity.

Key Words
non-conforming mesh coupling; the enriched discontinuous Galerkin method; J2 plasticity; drucker-prager model; numerical integration

Address
Layla K. Amaireh: Applied Science Private University, Amman, Jordan
Ghadir Haikal: Lyles School of Civil Engineering, Purdue University, West Lafayette, Indiana, USA

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