• Structural Engineering and Mechanics
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• v.90 no.1
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• pp.83-96
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• 2024

This paper suggests an analytical approach to investigate the free vibration and stability of functionally graded (FG) beams with both perfect and imperfect characteristics using a quasi-3D higher-order shear deformation theory (HSDT) with stretching effect. The study specifically focuses on FG beams resting on variable elastic foundations. In contrast to other shear deformation theories, this particular theory employs only four unknown functions instead of five. Moreover, this theory satisfies the boundary conditions of zero tension on the beam surfaces and facilitates hyperbolic distributions of transverse shear stresses without the necessity of shear correction factors. The elastic medium in consideration assumes the presence of two parameters, specifically Winkler-Pasternak foundations. The Winkler parameter exhibits variable variations in the longitudinal direction, including linear, parabolic, sinusoidal, cosine, exponential, and uniform, while the Pasternak parameter remains constant. The effective material characteristics of the functionally graded (FG) beam are assumed to follow a straightforward power-law distribution along the thickness direction. Additionally, the investigation of porosity includes the consideration of four different types of porosity distribution patterns, allowing for a comprehensive examination of its influence on the behavior of the beam. Using the virtual work principle, equations of motion are derived and solved analytically using Navier's method for simply supported FG beams. The accuracy is verified through comparisons with literature results. Parametric studies explore the impact of different parameters on free vibration and buckling behavior, demonstrating the theory's correctness and simplicity.

• Structural Engineering and Mechanics
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• v.16 no.3
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• pp.259-274
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• 2003

In this paper, a novel numerical solution technique, the differential cubature method is employed to study the buckling problems of thick plates with arbitrary quadrilateral planforms and non-uniform boundary constraints based on the first order shear deformation theory. By using this method, the governing differential equations at each discrete point are transformed into sets of linear homogeneous algebraic equations. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Detailed formulation and implementation of this method are presented. The buckling parameters are calculated through solving a standard eigenvalue problem by subspace iterative method. Convergence and comparison studies are carried out to verify the reliability and accuracy of the numerical solutions. The applicability, efficiency, and simplicity of the present method are demonstrated through solving several sample plate buckling problems with various mixed boundary constraints. It is shown that the differential cubature method yields comparable numerical solutions with 2.77-times less degrees of freedom than the differential quadrature element method and 2-times less degrees of freedom than the energy method. Due to the lack of published solutions for buckling of thick rectangular plates with mixed edge conditions, the present solutions may serve as benchmark values for further studies in the future.

• Steel and Composite Structures
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• v.15 no.4
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• pp.399-423
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• 2013

In the present study, the thermal buckling behavior of functionally graded sandwich plates is studied using a new hyperbolic displacement model. Unlike any other theory, the theory is variationally consistent and gives four governing equations. Number of unknown functions involved in displacement field is only four, as against five in case of other shear deformation theories. This present model takes into account the parabolic distribution of transverse shear stresses and satisfies the condition of zero shear stresses on the top and bottom surfaces without using shear correction factor. Material properties and thermal expansion coefficient of the sandwich plate faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The thermal loads are assumed as uniform, linear and non-linear temperature rises across the thickness direction. The results reveal that the volume fraction index, loading type and functionally graded layers thickness have significant influence on the thermal buckling of functionally graded sandwich plates.

• Structural Engineering and Mechanics
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• v.52 no.4
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• pp.787-813
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• 2014

Starting with Hamilton's variational principle, the governing field equations for the steady state response of thin-walled beams under harmonic forces are derived. The formulation captures shear deformation effects due to bending and warping, translational and rotary inertia effects and as well as torsional flexural coupling effects due to the cross section mono-symmetry. The equations of motion consist of four coupled differential equations in the unknown displacement field variables. A general closed form solution is then developed for the coupled system of equations. The solution is subsequently used to develop a family of shape functions which exactly satisfy the homogeneous form of the governing field equations. A super-convergent finite element is then formulated based on the exact shape functions. Key features of the element developed include its ability to (a) isolate the steady state response component of the response to make the solution amenable to fatigue design, (b) capture coupling effects arising as a result of section mono-symmetry, (c) eliminate spatial discretization arising in commonly used finite elements, (d) avoiding shear locking phenomena, and (e) eliminate the need for time discretization. The results based on the present solution are found to be in excellent agreement with those based on finite element solutions at a small fraction of the computational and modelling cost involved.

• Journal of the Korean Geotechnical Society
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• v.20 no.8
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• pp.167-180
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• 2004

In this study finite element analysis using hyperbolic model was performed to predict the characteristics of stress-strain behaviour on concrete face earth dam (CFED : a tentative name) raised with coarse-grained materials corresponding to the face slab bedding zone of concrete face rockfill dam (CFRD). The results of finite element analysis were compared with field monitoring data, and the comparison showed a good agreement. And, the analysis results including locus of maximum displacement, maximum stress, stress concentration, and irregular load transfer would be used to devise rational field monitoring schemes for construction management and quality control during construction of CFED.

• Smart Structures and Systems
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• v.13 no.4
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• pp.659-683
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• 2014

The static analysis of structures with arbitrary cross-section geometry and material lamination via a refined one-dimensional (1D) approach is presented in this paper. Higher-order 1D models with a variable order of expansion for the displacement field are developed on the basis of Carrera Unified Formulation (CUF). Classical Euler-Bernoulli and Timoshenko beam theories are obtained as particular cases of the first-order model. Numerical results of displacement, strain and stress are provided by using the finite element method (FEM) along the longitudinal direction for different configurations in excellent agreement with three-dimensional (3D) finite element solutions. In particular, a layered thin-walled cylinder is considered as first assessment with a laminated conventional cross-section. An atherosclerotic plaque is introduced as a typical structure with arbitrary cross-section geometry and studied for both the homogeneous and nonhomogeneous material cases through the 1D variable kinematic models. The analyses highlight limitations of classical beam theories and the importance of higher-order terms in accurately detecting in-plane cross-section deformation without introducing additional numerical problems. Comparisons with 3D finite element solutions prove that 1D CUF provides remarkable three-dimensional accuracy in the analysis of even short and nonhomogeneous structures with arbitrary geometry through a significant reduction in computational cost.

• Journal of Biosystems Engineering
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• v.27 no.4
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• pp.293-300
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• 2002

Surface crack detection is an important aspect in the quality control process of egg markets. The acoustic vibration of an egg could be used as a critical factor in evaluating the eggshell quality. The mode shape indicates the egg vibration behavior at different locations with respect to the input impulse and provides important information for the optimum sensor location to obtain the desired acoustic measurements. Theoretical analysis and experimental measurements were conducted to determine the acoustic vibration modes in eggs. The resonant fiequencies of the first and second resonance mode of intact eggs were found to be distributed between 2kHz and 7kHz range. The measured mode shapes of an egg were similar to theoretical shapes of homogeneous, elastic spheres. An elliptical deformation at the equator ring of the egg was observed. The frequency peak of this mode was dominantly present in the frequency spectrum of an intact egg impacted at its sharp position. The mode shapes related to the first resonant frequency of an egg shelved that the optimum location for the measuring sensor was the 180 degrees position. A optimum location for the egg support was found to be the 90 degrees position having the smallest vibration magnitude.

• Journal of Korea Foundry Society
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• v.28 no.6
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• pp.261-267
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• 2008

In-situ quasicrystalline icosahedral (I) phase reinforced Ti-based bulk metallic glass (BMG) matrix composites have been successfully fabricated by using two distinct thermal histories for BMG forming alloy. The BMG composite containing micron-scale Iphase has been introduced by controlling cooling rate during solidification, whereas nano-scale I-phase reinforced BMG composite has been produced by partial crystallization of BMG. For mechanical properties, micron-scale I-phase distributed BMG composite exhibited lower strength and plasticity compared to the monolithic BMG. On the other hand, nano-scale icosahedral phase embedded BMG composite showed enhanced strength and plasticity. These improved mechanical properties were attributed to the multiplication of shear bands and blocking of the shear band propagation in terms of isolation and homogeneous distribution of nanosize icosahdral phases in the glassy matrix, followed by stabilizing the mechanical and deformation instabilities.

• BMB Reports
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• v.28 no.6
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• pp.477-483
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• 1995

The recombinant human interferon alpha 2a ($rhIFN-{\alpha}2a$), expressed in Saccharomyces cerevtsiae, was purified from insoluble aggregates. The inclusion body of $rhIFN-{\alpha}$ was solubilized by guanidine salt in the presence of disulfide reducing agent. The refolding of denatured $rhIFN-{\alpha}2a$ was achieved by simple dilution. The authentic interferon alpha, which has two correctly matched disulfide bonds, was seperated from incompletely oxidized $IFN-{\alpha}$ and dimeric $IFN-{\alpha}$ by use of a CM-Sepharose column, followed by size exclusion columns at two different pH conditions. The purified protein has been subjected to detailed physicochemical characterization including sequence determination. Unlike other $rhIFN-{\alpha}2a$ from E. coli reported, the $rhIFN-{\alpha}2a$ from S. cerevisiae has no methionine residue at its N-terminus originating from the start codon, ATG. The pI of the protein was determined to be 6.05 with a single band in the pI gel, which demonstrated that the purified $rhIFN-{\alpha}$ was homogeneous. The structural study using circular dichroism showed that the protein retains its three dimensional structure in the wide range of pH conditions between pH 3 and 9, and only minor strucural deformation was observed at pH 1.0.

• Journal of the Korea Institute of Military Science and Technology
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• v.11 no.4
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• pp.83-91
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• 2008

The development of the equal channel angular pressing(ECAP) process in metals has recently provided a feasible solution to produce ultra-fine or nano-grained bulk materials with tailored material properties. However, ECAP process is difficult to scale up commercially due to requirements of an excessive load. In this paper, a new Hybrid-ECAP process with torsional die is considered to obtain materials of ultra-fine grain structure under low forming load. An upper bound analysis and numerical simulation (DEFORM 3D, a commercial FEM code) are carried out on the torsional die. By the upper bound analysis, analytical expression for the compression force and rotation speed are obtained. By the FEM analysis, the distribution of strain, stress and deformation are obtained. These results show that the Hybrid-ECAP is a useful process because this process can obtain the homogeneous deformations with relatively low forming load. Additionally, due to decreased forming load, die life can be improve.