• Journal of the Korean Society for Precision Engineering
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• v.19 no.10
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• pp.52-59
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• 2002

The thermo-mechanical characteristics of high temperature NITINOL shape memory alloy were evaluated using DSC with small samples and DMA with three-point bending specimens. The shape memory alloy of 54.4Ni/45.5Ti wt.% was used so that the phase transformation temperatures were in the range of 50~11$0^{\circ}C$. Two types of sample were tested in the experiments corresponding to as-received and annealed conditions. Simple beam bending theory was used to calculate the dynamic moduli of the shape memory alloy. According to the results, a large discrepancy in transformation temperatures was found between DSC and DMA techniques. Annealing treatment was found to suppress the R-phase transformation during cooling and the secondary plateau in the austenite transformation. Such a heat treatment was also significantly influenced to raise the transformation temperatures and the moduli of the shape memory alloy.

• Steel and Composite Structures
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• v.39 no.5
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• pp.631-643
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• 2021

The aim of this work is to study the hygro-thermo-mechanical bending responses of simply supported FG plate resting on a Winkler-Pasternak elastic foundation. The effect transverse shear strains is taken into account in which the zero transverse shear stress condition on the top and bottom surfaces of the plate is ensured without using any shear correction factors. The developed model contains only four unknowns variable which is reduced compared to other HSDTs models. The material properties of FG-plate are supposed to vary across the thickness of the plate according to power-law mixture. The differential governing equations are derived based on the virtual working principle. Numerical outcomes of bending analysis of FG plates under hygro-thermo-mechanical loads are performed and compared with those available in the literature. The effects of the temperature, moisture concentration, elastic foundation parameters, shear deformation, geometrical parameters, and power-law-index on the dimensionless deflections, axial and transverse shear stresses of the FG-plate are presented and discussed.

• Geomechanics and Engineering
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• v.22 no.1
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• pp.65-80
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• 2020

This paper presents a theoretical investigation on the response of the thermo-mechanical bending of FG plate on variable elastic foundation. A quasi-3D higher shear deformation theory is used that contains undetermined integral forms and involves only four unknowns to derive. The FG plates are supposed simply supported with temperature-dependent material properties and subjected to nonlinear temperature rise. Various homogenization models are used to estimate the effective material properties such as temperature-dependent thermoelastic properties. Equations of motion are derived from the principle of virtual displacements and Navier's solution is used to solve the problem of simply supported plates. Numerical results for deflections and stresses of FG plate with temperature-dependent material properties are investigated. It can be concluded that the proposed theory is accurate and simple in solving the thermoelastic bending behavior of FG thick plates.

• Steel and Composite Structures
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• v.47 no.6
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• pp.693-707
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• 2023

This article investigates the static thermo-mechanical response of anisotropic thick laminated composite plates on Visco-Pasternak foundations under various thermal load conditions (linear, non-linear, and uniform) along the transverse direction (thickness) of the plate, while keeping the mechanical load constant. The governing equations, which represent the thermo-mechanical behavior of the composite plate, are derived from the principle of virtual displacements. Using Navier's type solution, these equations are solved for the composite plate with simply supported condition. The Visco-Pasternak foundation type is included by considering the impact of the damping on the classical foundation model, which is modeled by Winkler's linear modulus and Pasternak's shear modulus. The excellent accuracy of the present solution is confirmed by comparing the results with those available in the literature. The study investigates the impact of geometric ratios, thermal expansion coefficient ratio, damping coefficient and foundation parameters on the thermo-mechanical flexural response of the composite plate. Overall, this article provides insights into the behavior of composite plates on visco-Pasternak foundations and may be useful for designing and analyzing composite structures in practical applications.

• Journal of Welding and Joining
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• v.25 no.2
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• pp.70-75
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• 2007

Simplified mathematical formulas are presented to predict deformations during the plate forming process when the heating parameters are given. To obtain the formulas, firstly, the thermal analysis for steel plate is performed, and the thermo-mechanical analysis is followed with actual heating conditions. The analyses have been carried out by the commercial software MARC, which is programmed based on the FEM. Secondary, the results of the mechanical analysis are synthesized with their variables for a statistical approach, which results in simplified formulas. The results of the analysis are well compared with those of experimental measurements.

• Journal of the Microelectronics and Packaging Society
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• v.13 no.4
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• pp.17-25
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• 2006

Thermo-mechanical behavior of flip-chip plastic ball grid array (FC-PBGA) packages are characterized by high sensitive $moir\'{e}$ interferometry. $Moir\'{e}$ fringe patterns are recorded and analyzed for several temperatures. Deformation analysis of bending displacements of the packages and average strains in the solder balls for both single and double-sided package assemblies are presented. The bending displacement of the double-sided package assembly is smaller than that of the single-sided one because of its symmetric structure. The largest effective strain occurred at the solder ball located on the edge of the chip and its magnitude of the double-sided package assembly is greater than that of single-sided one by 50%.

• Coupled systems mechanics
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• v.8 no.5
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• pp.439-457
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• 2019

In this paper, a new application of a four variable refined plate theory to analyze the nonlinear bending of functionally graded plates exposed to thermo-mechanical loadings, is presented. This recent theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces, and similarly, the shear components do not contribute toward bending moments. The derived transverse shear strains has a quadratic variation across the thickness that satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. The solutions are achieved by minimizing the total potential energy. The non-linear strain-displacement relations in the von Karman sense are used to derive the effect of geometric non-linearity. It is concluded that the proposed theory is accurate and simple in solving the nonlinear bending behavior of functionally graded plates.

• Structural Engineering and Mechanics
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• v.86 no.2
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• pp.167-180
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• 2023

This work applies a four-known quasi-3D shear deformation theory to investigate the bending behavior of a functionally graded plate resting on a viscoelastic foundation and subjected to hygro-thermo-mechanical loading. The theory utilizes a hyperbolic shape function to predict the transverse shear stress, and the transverse stretching effect of the plate is considered. The principle of virtual displacement is applied to obtain the governing differential equations, and the Navier method, which comprises an exponential term, is used to obtain the solution. Novel to the current study, the impact of the viscoelastic foundation model, which includes a time-dependent viscosity parameter in addition to Winkler's and Pasternak parameters, is carefully investigated. Numerical examples are presented to validate the theory. A parametric study is conducted to study the effect of the damping coefficient, the linear and nonlinear loadings, the power-law index, and the plate width-tothickness ratio on the plate bending response. The results show that the presence of the viscoelastic foundation causes an 18% decrease in the plate deflection and about a 10% increase in transverse shear stresses under both linear and nonlinear loading conditions. Additionally, nonlinear loading causes a one-and-a-half times increase in horizontal stresses and a nearly two-times increase in normal transverse stresses compared to linear loading. Based on the article's findings, it can be concluded that the viscosity effect plays a significant role in the bending response of plates in hygrothermal environments. Hence it shall be considered in the design.

• Smart Structures and Systems
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• v.18 no.4
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• pp.755-786
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• 2016

The hygro-thermo-mechanical bending behavior of sigmoid functionally graded material (S-FGM) plate resting on variable two-parameter elastic foundations is discussed using a four-variable refined plate theory. The material characteristics are distributed within the thickness direction according to the two power law variation in terms of volume fractions of the constituents of the material. By employing a four variable refined plate model, both a trigonometric distribution of the transverse shear strains within the thickness and the zero traction boundary conditions on the top and bottom surfaces of the plate are respected without utilizing shear correction factors. The number of independent variables of the current formulation is four, as against five in other shear deformation models. The governing equations are deduced based on the four-variable refined plate theory incorporating the external load and hygro-thermal influences. The results of this work are compared with those of other shear deformation models. Various numerical examples introducing the influence of power-law index, plate aspect ratio, temperature difference, elastic foundation parameters, and side-to-thickness ratio on the static behavior of S-FGM plates are investigated.

• Proceedings of the KSME Conference
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• 2001.06a
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• pp.90-95
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• 2001

Thermo-mechanical and flexural behavior of a wire-bond plastic ball grid array (WB-PBGA) are characterized by high sensitive $moir{\acute{e}}$ interferometry. $Moir{\acute{e}}$ fringe patterns are recorded and analyzed at several various bending loads and temperature steps. At the temperature higher that $100^{\circ}C$, the inelastic deformation in solder balls became more dominant. As a result the bending of the molding compound decreased while temperature increased. The strain results show that the solder ball located at the edge of the chip has largest shear strain by the thermal load while the maximum average shear strain by the bending moment occurs in the end solder. The results also show that $moir{\acute{e}}$ interferometry is a powerful and effective tool in experimental studies of electronic packaging.