• Transactions of Materials Processing
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• v.10 no.6
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• pp.449-456
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• 2001

The concept of stress wave was introduced through the quantized kinetic energy which is related to the potentional energy change of atom, molecular bond energy. Differentiated molecular bond energy $\varphi$() by the lst order displacement u becomes force F(F = d$\varphi$($u_i$)/du), if resversely stated, causing physically atomic displacement $u_i$. Such physical phenomena lead stress(force/area of applied force) can be expressed by wave equation of linearly quantized physical property. Through the stress wave concept, formation of dislocation, which could not explained easily from a theory of continuum mechanics, can be explained. Moreover, this linearly quantized stress wave equation with a stress concept for grains in a crystalline solid was applied to three typical metallic microstructures and a simple shape. The result appears to be a product from well treated equations of a quantized stress wave. From this result, it can be expected to answer the reason why the defect free and very fine diameters of long crystalline shapes exhibit ideal tensile strength of materials.

• Structural Engineering and Mechanics
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• v.59 no.3
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• pp.475-502
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• 2016

Nanobeams are widely used as a structural element for nanodevices and nanomachines. The development of nano-sized machines depends on proper understanding of mechanical behavior of these nano-sized beam elements. Small length scales such as lattice spacing between atoms, surface properties, grain size etc. are need to be considered when applying any classical continuum model. In this study, Eringen's nonlocal elasticity theory is incorporated into classical beam model considering the effects of axial extension and the shear deformation to capture unique static behavior of the nanobeams under continuum mechanics theory. The governing differential equations are obtained for curved beams and solved exactly by using the initial value method. Circular uniform beam with concentrated loads are considered. The displacements, slopes and the stress resultants are obtained analytically. A detailed parametric study is conducted to examine the effect of the nonlocal parameter, mechanical loadings, opening angle, boundary conditions, and slenderness ratio on the static behavior of the nanobeam.

• Proceedings of the Korean Geotechical Society Conference
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• 2009.09a
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• pp.3-26
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• 2009

Superloading yield surface concept is newly introduced together with subloading yield surface conception in order to describe full gradation continuously of the mechanical behavior of soils from typical sand through intermediate soil to typical clay (All Soils). Finite deformation theory has been applied to the soil skeleton-pore water coupled continuum mechanics, which enables us to discuss things in a perpetual stream from stable state to unstable state like from deformation to failure and vice versa like from liquefaction to post liquefaction consolidation of sand (All States). Incremental form of the equation of motion has been employed in the continuum mechanics in order to incorporate a rate type constitutive equation, which is "All Round" enough to predict ground behavior under both static and dynamic conditions. The present paper is the shortened version of the lecture note delivered in 2008 Theoretical and Applied Mechanics Conference, Science Council Japan, but with newly developed application examples.

• Journal of Information Display
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• v.4 no.1
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• pp.24-28
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• 2003

We studied the anchoring properties in photo-aligned periodic domains of liquid crystals (LCs) in an alternating homeotropic and hybrid geometry. In this geometry, the surface anchoring energy was determined in using the director-distorted length of the LC near domain boundary, calculated in a linear approximation of the director profile within the continuum theory. The measurements were made using the LC diffraction grating with the phase profile in the form of a trapezoid.

• Journal of Institute of Convergence Technology
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• v.6 no.1
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• pp.17-21
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• 2016

The analysis of circular plates under the constant pressure are simplified as the loading conditions of the circular manhole. The theoretical solution of circular plates with respect to the constant pressures are derived by using the governing equation of plate deflection. The deflection and the radial stress distributions were calculated by the theory. Finite element solutions were conducted with respect to the element types of the continuum elements. The most accurate element was selected by comparisons of the theoretical solutions and simulated solutions. The C3D8I element type in brick-type continuum elements gave in a good accordance with the theoretical solutions.

• Interaction and multiscale mechanics
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• v.5 no.2
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• pp.157-168
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• 2012

The dilatancy of granular materials has significant influence on its mechanical behaviors. The dilation angle is taken as a constant in conventional associated or non-associated flow rules based on Drucker-Prager yields theory. However, various experimental results show the dilatancy changes during progressive failure of granular materials. A non-associated flow rule with evolution of dilation angle is adopted in this study, and Cosserat continuum theory is used to describe the behaviors of granular materials for considering to some extent the its internal structure. Numerical examples focus on the bearing capacity and localization of granular materials, and results illustrate the capability and performance of the presented model in modeling the effect on failure behavior of granular materials.

• Structural Engineering and Mechanics
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• v.77 no.6
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• pp.765-777
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• 2021

Recently, the plate bending analysis has been interpreted in terms of the tensor's components of curvatures and bending moments by presenting the conceptual perspectives of the Hydrostatic Method of Analysis (HM) and theoretical formulations that combine the continuum mechanics with the graphical statics analysis, the theory of thin orthotropic and isotropic plates, and the elasticity theory. In pursuance of uncovering a genuine formulation of the plate's flexural differential equations, that possess the general-covariance and coordinates-independency. This study had then, tackled various natural and structural problems in both solid and fluid branches of the continuum mechanics in a description of such theoretical and conceptual attainment in uncovering the dimensional independent diffeomorphism covariant partial differential laws.

• Steel and Composite Structures
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• v.19 no.4
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• pp.861-876
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• 2015

Composite sections design consists on checking that the point defined by axial load and bending moment keeps included within the surface enclosed by the section interaction curve. Eurocode 4 suggests a method for tracing this diagram based on the plastic stress distribution method. However curves obtained according to this criterion overvalue concrete encased sections bearing capacity, especially when axial force comes with high bending moment values, so a correction factor is required. This article proposes a method for tracing this diagram based on the strain compatibility method. When stresses on the section are integrated by considering the Navier hypothesis, the use of the materials nonlinear constitutive equations provides curves much more adjusted to reality. This process requires the use of rather complex software which might reveal as too complex for practitioners. Preserving the same criteria of an elastic-plastic stress distribution, this article presents alternative expressions to obtain the failure internal forces in five significant points of the interaction diagram having considered five different positions of the neutral axis. These expressions are simply enough for their practical application. Concordance of curves traced strictly relying on these five points with those obtained by computer assisted stress integration considering the strain compatibility method and even with Eurocode 4 weighted curves will be presented for three different cross-sections and two different concrete strengths, revealing very good results.

• Journal of Theoretical and Applied Mechanics
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• v.2 no.1
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• pp.31-50
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• 1996

In this paper, a finite element analysis based on the local approach concept to fracture in the continuum damage mechanics is performed to analyze ductile fracture in two dimensional quasi-static state. First an isotropic damage model based on the generalized concept of effective stress is proposed for structural materials in the context of large deformation. In this model, the stiffness degradation is taken as a measure of damage and so, the fracture phenomenon can be explained as the critical deterioration of stiffness at a material point. The modified Riks' continuation technique is used to solve incremental iterative equations. Crack propagation is achieved by removing critically damaged elements. The mesh size sensitivity analysis and the simulation of the well known shearing mode failure in plane strain state are carried out to verify the present formulation. As numerical examples, an edge cracked plate and the specimen with a circular hole under plane stress are taken. Load-displacement curves and successively fractured shapes are shown. From the results, it can be concluded that the proposed model based on the local approach concept in the continuum damage mechanics may be stated as a reasonable tool to explain ductile fracture initiation and crack propagation.

• Steel and Composite Structures
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• v.36 no.3
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• pp.293-305
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• 2020

This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded (FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS structure manufactured by porous functionally graded materials.