• Korean Journal of Metals and Materials
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• v.47 no.3
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• pp.202-208
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• 2009

The effects of aging time on the microstructure and shear strength of the Low Temperature Co-fired Ceramic (LTCC)/Ag pad/Electroless Nickel Immersion Gold (ENIG)/BGA solder joints were investigated through isothermal aging at $150^{\circ}C$ for 1000 h with conventional Sn-37Pb and Sn-3Ag-0.5Cu. $Ni_3Sn_4$ intermetallic compound (IMC) layers was formed at the interface between Sn-37Pb solder and LTCC substrate as-reflowed state, while $(Ni,Cu)_3Sn_4$ IMC layer was formed between Sn-3Ag-0.5Cu solder and LTCC substrate. Additional $(Cu,Ni)_6Sn_5$ layer was found at the interface between the $(Ni,Cu)_3Sn_4$ layer and Sn-3Ag-0.5Cu solder after aging at $150^{\circ}C$ for 500 h. Thickness of the IMC layers increased and coarsened with increasing aging time. Shear strength of both solder joints increased with increasing aging time. Failure mode of BGA solder joints with LTCC substrate after shear testing revealed that shear strength of the joints depended on the adhesion between Ag metallization and LTCC. Fracture mechanism of Sn-37Pb solder joint was a mixture of ductile and pad lift, while that of Sn-3Ag-0.5Cu solder joint was a mixture of ductile and brittle $(Ni,Cu)_3Sn_4$ IMC fracture morphology. Failure mechanisms of LTCC/Ag pad/ENIG/BGA solder joints were also interpreted by finite element analyses.

• Steel and Composite Structures
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• v.47 no.5
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• pp.551-568
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• 2023

In this research, a new two-dimensional (2D) and quasi three-dimensional (quasi-3D) higher order shear deformation theory is devised to address the bending problem of functionally graded plates resting on an elastic foundation. The displacement field of the suggested theories takes into account a parabolic transverse shear deformation shape function and satisfies shear stress free boundary conditions on the plate surfaces. It is expressed as a combination of trigonometric and exponential shear shape functions. The Pasternak mathematical model is considered for the elastic foundation. The material properties vary constantly across the FG plate thickness using different distributions as power-law, exponential and Mori-Tanaka model. By using the virtual works principle and Navier's technique, the governing equations of FG plates exposed to sinusoidal and evenly distributed loads are developed. The effects of material composition, geometrical parameters, stretching effect and foundation parameters on deflection, axial displacements and stresses are discussed in detail in this work. The obtained results are compared with those reported in earlier works to show the precision and simplicity of the current formulations. A very good agreement is found between the predicted results and the available solutions of other higher order theories. Future mechanical analyses of three-dimensionally FG plate structures can use the study's findings as benchmarks.

• Steel and Composite Structures
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• v.44 no.5
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• pp.721-740
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• 2022

In this paper, an accurate kinematic model has been developed to study the mechanical response of functionally graded (FG) sandwich beams, mainly covering the bending, buckling and free vibration problems. The studied structure with homogeneous hardcore and softcore is considered to be simply supported in the edges. The present model uses a new refined shear deformation beam theory (RSDBT) in which the displacement field is improved over the other existing high-order shear deformation beam theories (HSDBTs). The present model provides good accuracy and considers a nonlinear transverse shear deformation shape function, since it is constructed with only two unknown variables as the Euler-Bernoulli beam theory but complies with the shear stress-free boundary conditions on the upper and lower surfaces of the beam without employing shear correction factors. The sandwich beams are composed of two FG skins and a homogeneous core wherein the material properties of the skins are assumed to vary gradually and continuously in the thickness direction according to the power-law distribution of volume fraction of the constituents. The governing equations are drawn by implementing Hamilton's principle and solved by means of the Navier's technique. Numerical computations in the non-dimensional terms of transverse displacement, stresses, critical buckling load and natural frequencies obtained by using the proposed model are compared with those predicted by other beam theories to confirm the performance of the proposed theory and to verify the accuracy of the kinematic model.

• Korean Journal of Radiology
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• v.23 no.2
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• pp.237-245
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• 2022

Objective: Viscoelasticity is an essential feature of nerves, although little is known about their viscous properties. The discovery of shear wave dispersion (SWD) imaging has presented a new approach for the non-invasive evaluation of tissue viscosity. The present study investigated the feasibility of using SWD imaging to evaluate diabetic neuropathy using the sciatic nerve in a diabetic rat model. Materials and Methods: This study included 11 diabetic rats in the diabetic group and 12 healthy rats in the control group. Bilateral sciatic nerves were evaluated 3 months after treatment with streptozotocin. We measured the nerve cross-sectional area (CSA), nerve stiffness using shear wave elastography (SWE), and nerve viscosity using SWD imaging. The motor nerve conduction velocity (MNCV) was also measured. These four indicators and the histology of the sciatic nerves were then compared between the two groups. The performance of CSA, SWE, and SWD imaging in distinguishing the two groups was assessed using receiver operating characteristic (ROC) analysis. Results: Nerve CSA, stiffness, and viscosity in the diabetic group was significantly higher than those in the control group (all p < 0.05). The results also revealed a significantly lower MNCV in the diabetic group (p = 0.005). Additionally, the density of myelinated fibers was significantly lower in the diabetic group (p = 0.004). The average thickness of the myelin sheath was also lower in the diabetic group (p = 0.012). The area under the ROC curve for distinguishing the diabetic neuropathy group from the control group was 0.876 for SWD imaging, which was significantly greater than 0.677 for CSA (p = 0.030) and 0.705 for SWE (p = 0.035). Conclusion: Sciatic nerve viscosity measured using SWD imaging was significantly higher in diabetic rats. The viscosity measured using SWD imaging performed well in distinguishing the diabetic neuropathy group from the control group. Therefore, SWD imaging may be a promising method for the evaluation of diabetic neuropathy.

• Structural Engineering and Mechanics
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• v.91 no.1
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• pp.1-23
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• 2024

This paper formulates a new integral shear deformation shell theory to investigate the free vibration response of carbon nanotube (CNT) reinforced structures with only four independent variables, unlike existing shell theories, which invariably and implicitly induce a host of unknowns. This approach guarantees traction-free boundary conditions without shear correction factors, using a non-polynomial hyperbolic warping function for transverse shear deformation and stress. By introducing undetermined integral terms, it will be possible to derive the motion equations with a low order of differentiation, which can facilitate a closed-form solution in conjunction with Navier's procedure. The mechanical properties of the CNT reinforcements are modeled to vary smoothly and gradually through the thickness coordinate, exhibiting different distribution patterns. A comparison study is performed to prove the efficacy of the formulated shell theory via obtained results from existing literature. Further numerical investigations are current and comprehensive in detailing the effects of CNT distribution patterns, volume fractions, and geometrical configurations on the fundamental frequencies of CNT-reinforced nanocomposite shells present here. The current shell theory is assumed to serve as a potent conceptual framework for designing reinforced structures and assessing their mechanical behavior.

• Structural Engineering and Mechanics
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• v.25 no.5
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• pp.501-518
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• 2007

In this work, a new approach is developed for dynamic analysis of a composite beam with an interply crack, based on finite element solution of partial differential equations with the use of the COMSOL Multiphysics package, allowing for fast and simple change of geometric characteristics of the delaminated area. The use of COMSOL Multiphysics package facilitates automatic mesh generation, which is needed if the problem has to be solved many times with different crack lengths. In the model, a physically impossible interpenetration of the crack faces is prevented by imposing a special constraint, leading to taking account of a force of contact interaction of the crack faces and to nonlinearity of the formulated boundary value problem. The model is based on the first order shear deformation theory, i.e., the longitudinal displacement is assumed to vary linearly through the beam's thickness. The shear deformation and rotary inertia terms are included into the formulation, to achieve better accuracy. Nonlinear partial differential equations of motion with boundary conditions are developed and written in the format acceptable by the COMSOL Multiphysics package. An example problem of a clamped-free beam with a piezoelectric actuator is considered, and its finite element solution is obtained. A noticeable difference of forced vibrations of the delaminated and undelaminated beams due to the contact interaction of the crack's faces is predicted by the developed model.

• Steel and Composite Structures
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• v.37 no.4
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• pp.431-446
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• 2020

This paper presents the flexural performance of double skin composite beams (DSCBs) at different Arctic low temperatures. 12 DSCBs were prepared and tested under two-point loading at different Arctic low temperatures of 20, -30, -50, and -70℃. The studied parameters include low-temperature level (T), steel-faceplate thickness (t), shear span ratio (λ), and spacing of headed studs (S). The experimental investigations under two-point loading tests showed that flexural failure occurred to all DSCBs, even including the specimen designed with the small λ ratio of 2.9. The ultimate strength behaviours of DSCBs were improved due to the improved mechanical properties of constructional materials and the confinement on shear connectors. The DSCB subjected to two-point loading and low temperatures exhibits a five-stage working mechanism. The stiffness and strength indexes of DSCBs increase linearly with temperature and t value increasing, while decreasing as shear span ratio boosts. In the contrast, the change of S value from 150 to 200 mm has little effect on the ultimate strength behavior of DSCB.

• 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.

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.5
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• pp.20-27
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• 1998

According as the member of the automobile body structure have been thinned their thickness and have become high strength, each part of the body structure has been put more severe stress condition. And, because fatigue strength of the spot welded lap joint is influenced by its geometrical and mechanical factors, welding condition and etc., there needs a quantitative and systematic evaluation method for them. In this study, by considering nugget edge of the spot weld part of the IB-type spot welded lap joint under tension-shear load to the ligament crack. fatigue strength of various IB-type spot welded lap joints was estimated with the stress intensity factor(S.I.F.) KIII which is fracture mechanical parameter. We could find that fatigue strength evaluation of the IB-type spot welded lap joints by KIII is more effective than the maximum principal stress ($\sigma$1max) at edge of the spot weld obtained from FEM analysis.

• Journal of Advanced Research in Ocean Engineering
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• v.1 no.1
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• pp.1-13
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• 2015

Post-Katrina investigations revealed that most earthen levee damage occurred on the levee crest and landward-side slope as a result of either wave overtopping, storm surge overflow, or a combination of both. In this paper, combined wave overtopping and storm surge overflow of a levee embankment strengthened with high performance turf reinforcement mat (HPTRM) system was studied in a purely Lagrangian and meshless approach, two-dimensional smoothed particle hydrodynamics (SPH) model. After the SPH model is calibrated with full-scale overtopping test results, the overtopping discharge, flow thickness, flow velocity, average overtopping velocity, shear stress, and soil erosion rate are calculated. New equations are developed for average overtopping discharge. The shear stresses on landward-side slope are calculated and the characteristics of soil loss are given. Equations are also provided to estimate soil loss rate. The range of the application of these equations is discussed.