• Advances in nano research
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• 제16권3호
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• pp.265-272
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• 2024

In this paper, the problem of static bending of axially functionally graded (AFG) nanobeam is formulated with the local stress(Lσ)- and strain-driven(εD) two-phase local/nonlocal integral models (TPNIMs). The novelty of the present study aims to compare the size-effects of nonlocal integral models on bending deflections of AFG Euler-Bernoulli nano-beams. The integral relation between strain and nonlocal stress components based on two types nonlocal integral models is transformed unitedly and equivalently into differential form with constitutive boundary conditions. Purely LσD- and εD-NIMs would lead to ill-posed mathematical formulation, and Purely εD- and LσD-nonlocal differential models (NDM) may result in inconsistent size-dependent bending responses. The general differential quadrature method is applied to obtain the numerical results for bending deflection and moment of AFG nanobeam subjected to different boundary and loading conditions. The influence of AFG index, nonlocal models, and nonlocal parameters on the bending deflections of AFG Euler-Bernoulli nanobeams is investigated numerically. A consistent softening effects can be obtained for both LσD- and εD-TPNIMs. The results from current work may provide useful guidelines for designing and optimizing AFG Euler-Bernoulli beam based nano instruments.

• 소음진동
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• 제5권3호
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• pp.327-335
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• 1995

The study deals with the vibration of a beam whose flexural and centroidal axes are not coincident. The elementary bending-twisting theory is employed to derive the equation of motion, in which the effects of rotary inertia are added to the bending displacements and the effects of warping are added to the twist. Bending translation is restricted to one direction so that one bending equation is used instead of two. The equations of motion are solved by using the boundary value problem. The exact natural frequencies are fund from the frequency equation, which is obtained from the condition that the homogeneous system of algebraic equations representing the spatial solution shall not yield a trivial solution. The orthogonal conditions are established, and the principal mode equations of forced vibration are derived. As an example, the cantilevered beam is chosen and the first some natural frequencies and their modal shapes are found.

• Steel and Composite Structures
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• 제9권3호
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• pp.275-301
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• 2009

The long-term behaviour of simply supported composite steel-concrete beams with deformable connectors subjected to skew bending and torsion is presented. The problem is dealt with by recurring to the displacement method, assuming the bending and torsional curvatures and the longitudinal deformations of each sectional part as unknowns and obtaining a system of differential and integro-differential equations. Some solving methods are presented, in order to obtain exact and approximate solutions and evaluate the precision of the approximate ones. A case study is then presented. For the sake of clearness, the responses of the composite beam under loads applied in different directions are studied separately, in order to correctly evaluate the effects of each load condition.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2000년도 춘계학술대회 논문집
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• pp.730-734
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• 2000

Once the Chip has developed a mixed mode of side-curl and up-curl, it would generally curl to strike the too] flank. The development of the bending stresses and shear in the chip would ultimately lead to chip failure. This paper attacks this problem from a mechanics-based approach. by treating the chip as a 3-D elastic curved beam, and applying appropriate constraints and forces. The expressions for bending. shear and direct stresses are developed through an energy-based criterion. The location of the maximum stresses is also identified and explained for simulated test conditions.

• 소성∙가공
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• 제21권6호
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• pp.384-388
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• 2012

Sheet metal forming processes induce residual stress in the final product due to plastic deformation. The residual stress leads to elastic recovery of the formed part called springback, which causes shape errors in the final product. This error is a serious issue, especially for high strength steels, which are widely used in auto-body structures. Therefore, the evaluation of the amount of springback becomes critical for high strength steels. This paper investigates the springback behavior of DP780 steel sheets after the U-bending process using the geometry of the standard U-shape tool from the NUMISHEET'93 benchmark problem. The amounts of springback were measured as a function of the intrusion direction, forming speed and blank holding force.

• Smart Structures and Systems
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• 제30권3호
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• pp.245-253
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• 2022

A two-layer beam consisting of an elastoplastic layer and a functional layer made of shape memory alloy (SMA) TiNi is considered. Constitutive relations for SMA are set by a microstructural model capable to calculate strain increment produced by arbitrary increments of stress and temperature. This model exploits the approximation of small strains. The equations to calculate the variations of the strain and the internal variables are based on the experimentally registered temperature kinetics of the martensitic transformations with an account of the crystallographic features of the transformation and the laws of equilibrium thermodynamics. Stress and phase distributions over the beam height are calculated by steps, by solving on each step the boundary-value problem for given increments of the bending moment (or curvature) and the tensile force (or relative elongation). Simplifying Bernoulli's hypotheses are applied. The temperature is considered homogeneous. The first stage of the numerical experiment is modeling of preliminary deformation of the beam by bending or stretching at a temperature corresponding to the martensitic state of the SMA layer. The second stage simulates heating and subsequent cooling across the temperature interval of the martensitic transformation. The curvature variation depends both on the total thickness of the beam and on the ratio of the layer's thicknesses.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1994년도 봄 학술발표회 논문집
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• pp.9-16
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• 1994

In this paper, a boundary integral equation for transient plate bending problem is proposed. Approach, using laplace transform is considered. The boundary integral equations with respect to deflection, normal slope, bending moment effective shear are presented and the effect of corner point is considered.

• 드라이브 ㆍ 컨트롤
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• 제13권4호
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• pp.45-51
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• 2016

The power train of a hydro-mechanical, continuously variable transmission for forklifts makes use of hydro-static units, hydraulic multi-wet disc brakes & clutches, and complex helical & planetary gears. The complex helical & planetary gears are very important parts of the transmission because of a strength problem. In the present study, we calculated the specifications of the complex helical & planetary gear train, and analyzed the gear bending and compressive stresses of the gears. It is necessary to analyze the gear bending and compressive stresses thoroughly for optimal design of the complex helical & planetary gears with respect to cost and reliability. In this paper, we analyze the actual gear bending and compressive stresses of complex helical & planetary gears using the Lewes & Hertz equation, and we also verify the calculated specifications of the complex helical & planetary gears by evaluating the results of the data of allowable bending and compressive stress using the Stress vrs Number of Cycles curves of gears.

• Structural Engineering and Mechanics
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• 제67권4호
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• pp.417-425
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• 2018

The main aim of this paper is to investigate the bending of Euler-Bernouilli nano-beams made of bi-directional functionally graded materials (BDFGMs) using Eringen's non-local elasticity theory in the integral form with compare the differential form. To the best of the researchers' knowledge, in the literature, there is no study carried out into integral form of Eringen's non-local elasticity theory for bending analysis of BDFGM Euler-Bernoulli nano-beams with arbitrary functions. Material properties of nano-beam are assumed to change along the thickness and length directions according to arbitrary function. The approximate analytical solutions to the bending analysis of the BDFG nano-beam are derived by using the Rayleigh-Ritz method. The differential form of Eringen's non-local elasticity theory reveals with increasing size effect parameter, the flexibility of the nano-beam decreases, that this is unreasonable. This problem has been resolved in the integral form of the Eringen's model. For all boundary conditions, it is clearly seen that the integral form of Eringen's model predicts the softening effect of the non-local parameter as expected. Finally, the effects of changes of some important parameters such as material length scale, BDFG index on the values of deflection of nano-beam are studied.

• 드라이브 ㆍ 컨트롤
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• 제12권4호
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• pp.77-81
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• 2015

In general, the gears of mixer reducer for concrete mixer truck make use of the differential type planetary gear system to rotate mixer drum smoothly on the initial conditions. The planetary gear system is very important part of mixer reducer for concrete mixer truck because of strength problem. In the present study, calculating the gear specifications and analyzing the gear bending & compressive stresses of the differential planetary gear system for mixer reducer are necessary to analyze gear bending and compressive stresses confidently, for optimal design of the planetary gear system in respect to cost and reliability. As a result, analyzing actual gear bending and compressive stresses of the planetary gear system using Lewes & Hertz equation and verifying the calculated specifications of the planetary gear system, evaluate the results with the data of allowable bending and compressive stress from the Stress-No. of cycles curves of gears.