• Journal of the Korean Electrochemical Society
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• v.4 no.2
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• pp.70-76
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• 2001

The present work describes the capabilities of laser beam deflection (LBD) technique for the analysis of the stresses developed during hydrogen diffusion through Pd foil electrode. First, we explain briefly the elasto-diffusive (Gorsky effect) and diffusion-elastic phenomena. A model for the diffusion-elastic phenomenon is theoretically derived from the solution of the Fick's equation for given initial and boundary conditions, Vegard's second law and Hooke's law. Second, we introduce how to apply the principle of LBD technique to the study on the stresses generated during hydrogen diffusion. From the comparison of the deflection transients numerically calculated with those experimentally measured, we finally discuss the change in the tensile deflection with time in terms of hydrogen concentration profile transient and hydrogen diffusivity.

• Journal of Biosystems Engineering
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• v.28 no.6
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• pp.485-490
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• 2003

Flexural rigidity(EI) and deflection characteristics of rice stalks were studied to investigate the mechanical interaction between a rice stalk and a combine reel in harvesting. Deflection of a rice stalk caused by reel operation is so large that conventional equation of small deflection fer elastic beam cannot be applied to the study of deflection characteristics. Therefore, an equation of large deflection for elastic beam was introduced in this study. Feasibility of this equation was examined by comparing theoretical calculation with the measured results for piano wire, and by the relationship between deflection and load acting on a rice stalk which was presumed by this equation. Results showed that the large deflection equation could predict the measurement data quite well. From this research, the following results were obtained. 1. Flexural rigidity(EI) calculated from the equation of large deflection was 4.0${\times}$l0$^4$N$.$$\textrm{mm}^2$(diameter 1.4mm, deflection 300mm) while the actual EI value of a piano wire(diameter 1.4mm) was 3.9${\times}$10$^4$N$.$$\textrm{mm}^2$. 2. The relationship between deflection and load acting on a rice stalk could be presumed by the large deflection equation. Flexural rigidity values of tested rice stalks calculated from the equation of large deflection were 1.6∼2.4${\times}$ l0$^4$N$.$$\textrm{mm}^2$(Hwa sung), 2.7∼3.5${\times}$ l0$^4$N$.$$\textrm{mm}^2$(Il pum) and 1.7∼2.4${\times}$ l0$^4$N$.$$\textrm{mm}^2$(Damakum)

• Proceedings of the Korea Concrete Institute Conference
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• 2001.11a
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• pp.579-584
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• 2001

The reinforced concrete(RC) beam is developed cracks because the compression strength of concrete is strong but the tensile strength is weak. The structural strength and stiffness is decreased by reduction of tension resistance capacity of concrete due to the developed cracks. Using the fiber reinforced concrete that is increased the flexural strength and tensile strength at tensile part can enhance the strength and stiffness of concrete structure and decrease the tensile flexural cracks and deflection. Therefore, The reinforced concrete used the fiber reinforced concrete at tensile part ensure the safety and serviceability of the concrete structures. In this study, analytical model of a dual concrete beam that is composed of the normal strength concrete at compression part and the high tensile strength concrete at tensile part is developed by using the equilibrium condition of forces and compatibility condition of strains and is parted into elastic analytical model and ultimate analytical model. Three group of test beam that is formed of one reinforced concrete beam and two dual concrete beams for each steel reinforcement ratio is tested to examine the flexural behavior of dual concrete beams. The comparative study of total nine test beams is shown that the ultimate load of a dual concrete beams relative to the reinforced concrete beams have an increase in approximately 30%. In addition, the initial flexural rigidity, as used here, refer to the slope of load-deflection curves in elastic state is increased and the deflection is decreased.

• Structural Engineering and Mechanics
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• v.21 no.5
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• pp.519-537
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• 2005

A new generalized Bernoulli/Timoshenko beam-column element on a two-parameter elastic foundation is presented herein. This element is based on the exact solution of the differential equation which describes the deflection of the axially loaded beam resting on a two-parameter elastic foundation, and can take into account shear deformations, semi - rigid connections, and rigid offsets. The equations of equilibrium are formulated for the deformed configuration, so as to account for axial force effects. Apart from the stiffness matrix, load vectors for uniform load and non-uniform temperature variation are also formulated. The efficiency and usefulness of the new element in reinforced concrete or steel structures analysis is demonstrated by two examples.

• Structural Engineering and Mechanics
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• v.54 no.3
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• pp.433-451
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• 2015

This paper focuses on large deflection static behavior of edge cracked simple supported beams subjected to a non-follower transversal point load at the midpoint of the beam by using the total Lagrangian Timoshenko beam element approximation. The cross section of the beam is circular. The cracked beam is modeled as an assembly of two sub-beams connected through a massless elastic rotational spring. It is known that large deflection problems are geometrically nonlinear problems. The considered highly nonlinear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of Aluminum. In the study, the effects of the location of crack and the depth of the crack on the non-linear static response of the beam are investigated in detail. The relationships between deflections, end rotational angles, end constraint forces, deflection configuration, Cauchy stresses of the edge-cracked beams and load rising are illustrated in detail in nonlinear case. Also, the difference between the geometrically linear and nonlinear analysis of edge-cracked beam is investigated in detail.

• Advances in Computational Design
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• v.7 no.1
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• pp.1-17
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• 2022

In this study, a new strategy is presented to transmit the fundamental elastic beam problem into the modern optimization platform and solve it by using artificial intelligence (AI) tools. As a practical example, deflection of Euler-Bernoulli beam is mathematically formulated by 2nd-order ordinary differential equations (ODEs) in accordance to the classical beam theory. This fundamental engineer problem is then transmitted from classic formulation to its artificial-intelligence presentation where the behavior of the beam is simulated by using neural networks (NNs). The supervised training strategy is employed in the developed NNs implemented in the heuristic optimization algorithms as the fitness function. Different evolutionary optimization tools such as genetic algorithm (GA) and particle swarm optimization (PSO) are used to solve this non-linear optimization problem. The step-by-step procedure of the proposed method is presented in the form of a practical flowchart. The results indicate that the proposed method of using AI toolsin solving beam ODEs can efficiently lead to accurate solutions with low computational costs, and should prove useful to solve more complex practical applications.

• Structural Engineering and Mechanics
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• v.44 no.3
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• pp.405-416
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• 2012

In this study the investigation of large deflections subject in compliant mechanisms is presented using homotopy perturbation method (HPM). The main purpose is to propose a convenient method of solution for the large deflection problem in compliant mechanisms in order to overcome the difficulty and complexity of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, a cantilever beam of linear elastic material under horizontal, vertical and bending moment end point load is considered. The results show that the applied method is very accurate and capable for cantilever beams and can be used for a large category of practical problems for the aim of optimization. Also the consequence of effective parameters on the large deflection is analyzed and presented.

• International Journal of Ocean System Engineering
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• v.2 no.3
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• pp.195-199
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• 2012

This paper reports a new analytical method to calculate the planar displacement of structures. The cross-sections were assumed to remain in plane and the deflection curve was evaluated using the curvature values geometrically, despite being solved with differential equations. The deflection curve was parameterized with the arc-length of the curvature values, and was taken as an assembly of chains of circular arcs. Fast and accurate solutions of complex deflections can be obtained easily. This paper includes a comparison of the nonlinear displacements of an elastic tapered cantilever beam with a uniform moment distribution among the proposed analytical method, numerical method of the theory and large deflection FEM solutions.

• Computers and Concrete
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• v.22 no.6
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• pp.501-514
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• 2018

The paper presents the thermo-mechanically induced non-linear response of multiwall carbon nanotube reinforced laminated composite beam (MWCNTRCB) supported by elastic foundation using higher order shear deformation theory and von-Karman non-linear kinematics. The elastic properties of MWCNT reinforced composites are evaluated using Halpin-Tsai model by considering MWCNT reinforced polymer matrix as new matrix by dispersing in it and then reinforced with E-glass fiber in an orthotropic manner. The laminated beam is supported by Pasternak elastic foundation with Winkler cubic nonlinearity. A generalized static analysis is formulated using finite element method (FEM) through principle of minimum potential energy approach.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.1
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• pp.17-35
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• 2016

In this study, the dynamic behaviour of a rotating Timoshenko beam when under the actions of a variable magnitude load moving at non-uniform speed is carried out. The effect of cross-sectional dimension and damping on the flexural motions of the elastic beam was neglected. The coupled second order partial differential equations incorporating the effects of rotary and gyroscopic moment describing the motions of the beam was scrutinized in order to obtain the expression for the dynamic deflection and rotation of the vibrating system using an elegant technique called Galerkin's Method. Analyses of the solutions obtained were carried out and various results were displayed in plotted curve. It was found that the response amplitude of the simply supported beam increases with an increase in the value of the foundation reaction modulus. Effects of other vital structural parameters were also established.