• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.5
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• pp.838-848
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• 1992

The objective of the study is to provide a theoretical tools for analyzing the fracture of leyered composites with a center crack. It is assumed that the composite is composed of successive accumulation of the fiber layer and resin layer with the fiber layer being perfectly bonded to the resin layer except the region of a center crack. In-plane shear loading (Mode II) and the anti-plane shear loading (Mode III) are considered separately. Boundary value problems are formulated by using a plane theory of elasticity and governing equations are reduced to a Fredholm integral equation of a second kind. The equation is solved numerically and the stress intensity factors are obtained. The normalized Mode II and Mode III stress intensity factors are evaluated for various combinations of material properties and for various geometrical parametes.

• Journal of the Microelectronics and Packaging Society
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• v.13 no.2 s.39
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• pp.1-7
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• 2006

In this paper, warpage magnitude and shape of printed-circuit board in case that properties of core and thickness of solder resist are varied are investigated. The cause of warpage is coefficient of thermal expansion differences of stacked materials. Therefore, we need small difference of coefficient of thermal expansion that laminated material, and need to decrease asymmetric of top side and bottom side in structure shape. Also, we can control occurrence of warpage heightening hardness of core in laminated material. Composite material that make core are exploited in connection with the structural bending twisting coupling resulting from directional properties of fiber reinforced composite materials and from ply stacking sequence. If we use such characteristic, we can control warpage with change of material properties. In this paper, warpage of two layer stacked chip scale package is investigated, and evaluate improvement result using an experiment and finite element method tool.

• Structural Engineering and Mechanics
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• v.87 no.6
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• pp.529-540
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• 2023

A novel laminated-hybrid-composite-beam (LHCB) of glass-epoxy infused with flyash and graphene is constructed for this study. The conventional mixture-rule and constitutive-relationship are modified to incorporate filler and lamina orientation. Eringen's non-local-theory is used to include the filler effect. Hamilton's principle based on fifth-order-layer-wise-shear-deformation-theory is applied to formulate the equation of motion. The analogous shear-spring-models for LHCB with multiple-cracks are employed in finite-element-analysis (FEA). Modal-experimentations are conducted (B&K-analyser) and the findings are compared with theoretical and FEA results. In terms of dimensionless relative-natural-frequencies (RNF), the dynamic-response in cantilevered support is investigated for various relative-crack-severities (RCSs) and relative-crack-positions (RCPs). The increase of RCS increases local-flexibility in LHCB thus reductions in RNFs are observed. RCP is found to play an important role, cracks present near the end-support cause an abrupt drop in RNFs. Further, multiple cracks are observed to enhance the nonlinearity of LHCB strength. Introduction of the first to third crack in an intact LHCB results drop of RNFs by 8%, 10%, and 11.5% correspondingly. Also, it is demonstrated that the RNF varies because of the lamina-orientation, and filler addition. For 0° lamina-orientation the RNF is maximum. Similarly, it is studied that the addition of graphene reduces weight and increases the stiffness of LHCB in contrast to the addition of flyash. Additionally, the response of LHCB to moving mass is accessed by appropriately modifying the numerical programs, and it is noted that the successive introduction of the first to ninth crack results in an approximately 40% to 120% increase in the dynamic-amplitude-ratio.

• Steel and Composite Structures
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• v.24 no.2
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• pp.151-176
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• 2017

This paper deals with general equations of motion for free vibration analysis response of thick three-layer doubly curved sandwich panels (DCSP) under simply supported boundary conditions (BCs) using higher order shear deformation theory. In this model, the face sheets are orthotropic laminated composite that follow the first order shear deformation theory (FSDT) based on Rissners-Mindlin (RM) kinematics field. The core is made of orthotropic material and its in-plane transverse displacements are modeled using the third order of the Taylor's series extension. It provides the potentiality for considering both compressible and incompressible cores. To find these equations and boundary conditions, Hamilton's principle is used. Also, the effect of trapezoidal shape factor for cross-section of curved panel element ($1{\pm}z/R$) is considered. The natural frequency parameters of DCSP are obtained using Galerkin Method. Convergence studies are performed with the appropriate formulas in general form for three-layer sandwich plate, cylindrical and spherical shells (both deep and shallow). The influences of core stiffness, ratio of core to face sheets thickness and radii of curvatures are investigated. Finally, for the first time, an optimum range for the core to face sheet stiffness ratio by considering the existence of in-plane stress which significantly affects the natural frequencies of DCSP are presented.

• Composites Research
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• v.16 no.4
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• pp.1-9
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• 2003

2 ply laminated composite is regarded to simulate the interply behavior of the belt layer of the tire. It was cone with 3 dimensional FE(Finite Element) analysis to determine interply shear stress and strain. Widthwise, the shear strain was measured by the pin method. These results are compared with those of CLT(classical lamination theory) in center region and those of Kassapoglou's and Kelsey's theory in edge region. In the FE analysis. rubber is assumed as linear elastic material. and rubber/cord laminate as the orthotropic material composed of cord and rubber In the FE result, interlaminar shear stress causing the interlaminar delamination has the largest value in the edge region of the inner rubber layer. Numerical results obtained coincides with CLT well in the center region, and agrees with other theoretical result little in the edge region.

• Composites Research
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• v.17 no.2
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• pp.28-33
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• 2004

Failure detection in a cross-ply laminated composite beam under tensile loading were performed using a fiber Bragg grating (FBG) sensor. A Passive Mach-Zehnder interferometric demodulator was proposed to enhance sensitivity and bandwidth. The proposed FBG sensor system without active device such as a phase modulator is very simple in configuration, easy to implement and enables the measurement of high-frequency vibration with low strain amplitude such as impact or failure signal. Failure signals detected by a FBG sensor had offset value corresponding to the strain shift with vibration at a maximum frequency of several hundreds of kilohertz. at the instant of transverse crack propagation in the 90 degree layer of composite beam.

• Steel and Composite Structures
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• v.26 no.6
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• pp.771-791
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• 2018

This paper deals with the low velocity impact response and dynamic stresses of composite sandwich truncated conical shells (STCS) with compressible or incompressible core. Impacts are assumed to occur normally over the top face-sheet and the interaction between the impactor and the structure is simulated using a new equivalent three-degree-of-freedom (TDOF) spring-mass-damper (SMD) model. The displacement fields of core and face sheets are considered by higher order and first order shear deformation theory (FSDT), respectively. Considering continuity boundary conditions between the layers, the motion equations are derived based on Hamilton's principal incorporating the curvature, in-plane stress of the core and the structural damping effects based on Kelvin-Voigt model. In order to obtain the contact force, the displacement histories and the dynamic stresses, the differential quadrature method (DQM) is used. The effects of different parameters such as number of the layers of the face sheets, boundary conditions, semi vertex angle of the cone, impact velocity of impactor, trapezoidal shape and in-plane stresses of the core are examined on the low velocity impact response of STCS. Comparison of the present results with those reported by other researchers, confirms the accuracy of the present method. Numerical results show that increasing the impact velocity of the impactor yields to increases in the maximum contact force and deflection, while the contact duration is decreased. In addition, the normal stresses induced in top layer are higher than bottom layer since the top layer is subjected to impact load. Furthermore, with considering structural damping, the contact force and dynamic deflection decrees.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.1
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• pp.115-126
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• 2001

In this paper, through a series of comparative experiments, effects of two different cure processing methods, cocure and precure, on the mechanical properties of honeycomb core materials for aircraft applications are considered. Mass of moisture accumulated into the closed cells of the sandwich panel specimen from the measured mass of moisture diffused to the full saturation state into the elements(skin, adhesive layer, Nomex honeycomb), consisting the honeycomb sandwich specimen has been calculated. Water reservoir of 70$\^{C}$ was used to have specimens absorb moisture to see the influence of moisture absorbed into sandwich panel on its mechanical properties. For the repair condition holding for 2 hours at 177$\^{C}$(350℉) temperature, a pressure due to the vapor expansion in each cell of the sandwich panel, which may result in the local separation of the interface between laminated skin and the surface of the honeycomb, has been estimated by vapor pressure-temperature relation from the thermodynamic steam table and compared to the pressure from the ideal gas state equation. The bonding strengths of the laminated skins on the flat surface of the Nomex honeycomb have been compared by the flatwise tension test and climbing drum peel test performed at room temperature for dry, wet and wet-repair specimens, respectively.

• Structural Engineering and Mechanics
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• v.50 no.6
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• pp.773-796
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• 2014

This paper deals with free vibration analysis of continuous grading fiber reinforced (CGFR) and bi-directional FG annular sector plates on two-parameter elastic foundations under various boundary conditions, based on the three-dimensional theory of elasticity. The plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. Results indicate that the non-dimensional natural frequency parameter of a functionally graded fiber volume fraction is larger than that of a discrete laminated and close to that of a 2-layer. It results that the CGFR plate attains natural frequency higher than those of traditional discretely laminated composite ones and this can be a benefit when higher stiffness of the plate is the goal and that is due to the reduction in spatial mismatch of material properties. Moreover, it is shown that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional one-dimensional functionally graded material. The multidirectional graded material can likely be designed according to the actual requirement and it is a potential alternative to the unidirectional functionally graded material. The new results can be used as benchmark solutions for future researches.

• International Journal of Aeronautical and Space Sciences
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• v.13 no.4
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• pp.458-467
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• 2012

In this study, the linear viscoelastic response of a rectangular laminated plate is investigated. The viscoelastic properties, expressed by two basic spring-dashpot models, that is Kelvin and Maxwell models, is assumed in the range to investigate the influence of viscoelastic coefficients to mechanical behavior. In the present study, viscoelastic responses are performed for two popular equivalent single-layered theories, such as the first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT). Compliance and relaxation modulus of time-dependent viscoelastic behavior are approximately determined by Prony series. The constitutive equation for linear viscoelastic material as the Boltzmann superposition integral equation is simplified by the convolution theorem of Laplace transformation to avoid direct time integration as well as to improve both accuracy and computational efficiency. The viscoelastic responses of composite laminates in the real time domain are obtained by applying the inverse Laplace transformation. The numerical results of viscoelastic phenomena such as creep, cyclic creep and recovery creep are presented.