• Title/Summary/Keyword: shear stress-strain

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Orthotropic Beam Analogy for Analysis of Shear Stresses in Framed-Tube Structures (구형등가보 원리에 의한 튜브 구조물의 전단응력 해석)

  • 이강건;이리형
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2001.10a
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    • pp.393-400
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    • 2001
  • A simple numerical modelling technique is proposed for estimating the shear stress distribution in beams of framed tube structures with multiple internal tubes. The structures are analysed using a continuum approach in which each tube is individually modelled by a tube beam that accounts for the flexural and shear deformations, as well as the shear lag effects. The method idealises the discrete tubes-in-tube structures as an assemblage of equivalent multiple beams, each composed of orthotropic plate panels. The numerical analysis of shear stress is based on the elastic theory in conjunction with the minimum potential energy principle. By simplifying assumptions regarding the form of strain distributions in external and internal tubes, the shear stress distributions are expressed in terms of a series of linear functions of the second moments of area of the structures and the corresponding geometric and material properties, as well as the applied loads. The simplicity and accuracy of the proposed method are demonstrated through the solutions of three numerical examples.

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Combined Two-Back Stress Models with Damage Mechanics Incorporated (파손역학이 조합된 이중 후방응력 이동경화 구성방정식 모델)

  • Yun, Su-Jin
    • Transactions of Materials Processing
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    • v.17 no.3
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    • pp.161-169
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    • 2008
  • In the present work, the two-back stress model is proposed and continuum damage mechanics (CDM) is incorporated into the plastic constitutive relation in order to describe the plastic deformation localization and the damage evolution in a deforming continuum body. Coupling between damage mechanics and isothermal rate independent plasticity is performed using the kinematic hardening rule, which in turn is formulated by combining the nonlinear Armstrong-Frederick rule and the Phillips rule. The numerical analyses are carried out within h deformation theory. It is noted that the damage evolution within a work piece accelerates the plastic deformation localization such that the material with lower hardening exponent results in a rapid shear band formation. Moreover, the results from the numerical analysis reflected closely with the micro-structures around the fractured regime. The effects of the various hardening parameters on deformation localization are also investigated. As the nonlinear strain rate description in the back stress evolution becomes dominant, the strain localization becomes intensified as well as the damage evolution.

Flexure of cross-ply laminated plates using equivalent single layer trigonometric shear deformation theory

  • Sayyad, Atteshamuddin S.;Ghugal, Yuwaraj M.
    • Structural Engineering and Mechanics
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    • v.51 no.5
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    • pp.867-891
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    • 2014
  • An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is presented for static flexure of cross-ply laminated composite and sandwich plates. The inplane displacement field uses sinusoidal function in terms of thickness coordinate to include the transverse shear deformation effect. The cosine function in thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. The kinematics of the present theory is much richer than those of the other higher order shear deformation theories, because if the trigonometric term (involving thickness coordinate z) is expanded in power series, the kinematics of higher order theories (which are usually obtained by power series in thickness coordinate z) are implicitly taken into account to good deal of extent. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The closed-form solutions of simply supported cross-ply laminated composite and sandwich plates have been obtained. The results of present theory are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory.

Nonlinear vibration of functionally graded nano-tubes using nonlocal strain gradient theory and a two-steps perturbation method

  • Gao, Yang;Xiao, Wan-Shen;Zhu, Haiping
    • Structural Engineering and Mechanics
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    • v.69 no.2
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    • pp.205-219
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    • 2019
  • This paper analyzes nonlinear free vibration of the circular nano-tubes made of functionally graded materials in the framework of nonlocal strain gradient theory in conjunction with a refined higher order shear deformation beam model. The effective material properties of the tube related to the change of temperature are assumed to vary along the radius of tube based on the power law. The refined beam model is introduced which not only contains transverse shear deformation but also satisfies the stress boundary conditions where shear stress cancels each other out on the inner and outer surfaces. Moreover, it can degenerate the Euler beam model, the Timoshenko beam model and the Reddy beam model. By incorporating this model with Hamilton's principle, the nonlinear vibration equations are established. The equations, including a material length scale parameter as well as a nonlocal parameter, can describe the size-dependent in linear and nonlinear vibration of FGM nanotubes. Analytical solution is obtained by using a two-steps perturbation method. Several comparisons are performed to validate the present analysis. Eventually, the effects of various physical parameters on nonlinear and linear natural frequencies of FGM nanotubes are analyzed, such as inner radius, temperature, nonlocal parameter, strain gradient parameter, scale parameter ratio, slenderness ratio, volume indexes, different beam models.

Pinching Mechanism of Reinforced Concrete Elements (철근콘크리트 부재의 핀칭 메커니즘에 대한 연구)

  • Kim, Ji-Hyun;Lee, Jung-Yoon
    • Proceedings of the Korea Concrete Institute Conference
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    • 2006.05a
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    • pp.482-485
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    • 2006
  • The response of a reinforced concrete element under cyclic shear is characterized by the hysteretic loops of the shear stress-strain curves. These hysteretic loops can exhibit strength deterioration, stiffness degradation, and a pinched shape. Recent tests have shown that the orientation of steel grids in RC shear elements has a strong effect on the "pinching effect" in the post-yield hysteretic loops. When the steel grid was set at a 45 degree angle to the shear plane, there was no pinching effect and no strength deterioration. However, when the steel grid was set parallel to the shear plane, there was a severe pinching effect and severe strength deterioration with increasing shear strain magnitude. In this paper, two RC elements subjected to revered cyclic shear stresses are considered to study the effect of the steel grid orientation. The presence and absence of the pinching mechanism in the post-yield shear hysteretic loops is studied using the Rotating Angle Softened Truss Model (RA-STM) theory.

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Cylindrical bending of multilayered composite laminates and sandwiches

  • Sayyad, Atteshamuddin S.;Ghugal, Yuwaraj M.
    • Advances in aircraft and spacecraft science
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    • v.3 no.2
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    • pp.113-148
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    • 2016
  • In a whole variety of higher order plate theories existing in the literature no consideration is given to the transverse normal strain / deformation effects on flexural response when these higher order theories are applied to shear flexible composite plates in view of minimizing the number of unknown variables. The objective of this study is to carry out cylindrical bending of simply supported laminated composite and sandwich plates using sinusoidal shear and normal deformation plate theory. The most important feature of the present theory is that it includes the effects of transverse normal strain/deformation. The displacement field of the presented theory is built upon classical plate theory and uses sine and cosine functions in terms of thickness coordinate to include the effects of shear deformation and transverse normal strain. The theory accounts for realistic variation of the transverse shear stress through the thickness and satisfies the shear stress free conditions at the top and bottom surfaces of the plate without using the problem dependent shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of minimum potential energy. The accuracy of the proposed theory is examined for several configurations of laminates under various static loadings. Some problems are presented for the first time in this paper which can become the base for future research. For the comparison purpose, the numerical results are also generated by using higher order shear deformation theory of Reddy, first-order shear deformation plate theory of Mindlin and classical plate theory. The numerical results show that the present theory provides displacements and stresses very accurately as compared to those obtained by using other theories.

A STUDY OF POLYMERIZATION SHRINKAGE OF COMPOSITE RESIN ACCORDING TO FILLING METHODS USING STRAIN GAUGE (스트레인 게이지를 이용한 적층방법에 따른 복합레진의 중합수축에 관한 연구)

  • Kim, Eung-Hag;Kim, Jong-Soo;Yoo, Seung-Hoon
    • Journal of the korean academy of Pediatric Dentistry
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    • v.35 no.1
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    • pp.18-29
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    • 2008
  • The purpose of this study was to compare the polymerization shrinkage of several filling methods using strain gauges. In this study, a light-emitting diode(LED) curing unit(Elipar Freeligh2, 3M EPSE, USA) and plasma arc lamp(PAL) curing unit(Flipo, LOKKI, France) were used for curing, Filtek $Z350^{TM}$(3M EPSE, USA) composite resin was used for the cavity filling. Sixty permanent bicuspid teeth, that were extracted for orthodontic treatment, were studied. The cavities were prepared on the occlusal surface and were filled using the following methods : 1) bulk filling, 2) parallel filling, 3) oblique filling The strain was recorded on the buccal, lingual, mesial and distal surfaces and the strain values were computed into stress values. The shear bond strength of each filling method was tested using a Micro Universal Testing machine. The results can be summarized as follows: 1. In the strain changes, all LED and PAL curing groups showed an increase on the buccal surface and a slow decrease as time elapsed. 2. In the strain changes of the mesial and distal surfaces, the decreases and increases were shown repeatedly and reduced as time elapsed. 3. There were no significant statistical strain changes among filling methods in the LED or PAL curing groups. 4. There were significant statistical strain changes between the LED and PAL curing groups on the buccal surface(p<0.05). 5. From the shear bond strength results, in the LED curing group, filling method 3 showed lower surface stress than filling method 1 and 2(p<0.05). In the PAL curing group, there were no significant statistical strain changes between each filling method. 6. The surface stress of each group was lower than the shear bond strength.

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Two Node Meridional Strain-based Axisymmetric Shell Elements (자오 변형률에 근거한 2절검 축대칭 셸요소)

  • Ryu, Ha-Sang;Sin, Hyo-Chol
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.21 no.6
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    • pp.925-932
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    • 1997
  • Two shear-flexible curved axisymmetric shell elements with two nodes, LCCS(linear curvature and constant strain) and CCCS(constant curvature and constant strain) are designed based on the assumed meridional strain fields and shallow shell geometry. At the element level, meridional curvature, membrane strain and shear strain fields are assumed by using polynomials and the displacement fields are obtained by integrating the assumed strain fields along the shallowly curved meridian. The formulated elements have high order displacement fields consistent with the strain field. Several test problems are given to demonstrate the performance of the two elements. Analysis results obtained reveal that the elements are very accurate in the displacement and the stress predictions.

Effects of strain hardening of steel reinforcement on flexural strength and ductility of concrete beams

  • Ho, J.C.M.;Au, F.T.K.;Kwan, A.K.H.
    • Structural Engineering and Mechanics
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    • v.19 no.2
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    • pp.185-198
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    • 2005
  • In the design of reinforced concrete beams, it is a standard practice to use the yield stress of the steel reinforcement for the evaluation of the flexural strength. However, because of strain hardening, the tensile strength of the steel reinforcement is often substantially higher than the yield stress. Thus, it is a common belief that the actual flexural strength should be higher than the theoretical flexural strength evaluated with strain hardening ignored. The possible increase in flexural strength due to strain hardening is a two-edge sword. In some cases, it may be treated as strength reserve contributing to extra safety. In other cases, it could lead to greater shear demand causing brittle shear failure of the beam or unexpected greater capacity of the beam causing violation of the strong column-weak beam design philosophy. Strain hardening may also have certain effect on the flexural ductility. In this paper, the effects of strain hardening on the post-peak flexural behaviour, particularly the flexural strength and ductility, of reinforced normal- and high-strength concrete beams are studied. The results reveal that the effects of strain hardening could be quite significant when the tension steel ratio is relatively small.

High Strain Rate Deformation Behavior of 5083 Aluminum Alloy Prepared via Equal Channel Angular Extrusion (ECAE 전단 가공된 5083 알루미늄 합금의 고변형률 변형거동)

  • Kim, Yang Gon;Ko, Young Gun;Shin, Dong Hyuk;Lee, Sunghak
    • Korean Journal of Metals and Materials
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    • v.47 no.7
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    • pp.397-405
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    • 2009
  • The high strain rate deformation behavior of ultra-fine grained 5083 aluminum alloys prepared via equal channel angular (ECA) extrusion was investigated in this study. The microstructure of ECA extruded specimens consisted of ultra-fine grains, and contained a considerable amount of second phase particles, which were fragmented and distributed homogeneously in the matrix. According to the dynamic torsion test results, the maximum shear stress and fracture shear strain of the route A (no rotation) specimen were lower than those of route C ($180^{\circ}$ rotation) specimen since that adiabatic shear bands of $100{\mu}m$ in width were formed in the route A specimen. The formation of adiabatic shear bands was addressed by concepts of critical shear strain, deformation energy required for void initiation, and microstructural homogeneity associated with ECA operations.