• Title/Summary/Keyword: elastic modulus equation

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An elasto-plastic solution for infinite solid containing a spherical precipitate under hydrostatic pressure (구형석출물을 갖는 무한 고체에 전수압이 가해지는 경우에 대한 탄소성해)

  • ;;Earmme, Youn Young
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.5 no.2
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    • pp.122-130
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    • 1981
  • Equation of equilibrium is derived and solved for an infinite isotropic solid under applied hydrostatic stress which is uniform at large distance, and disturbed by a spherical precipitate which has isotropoc elastic constants dirrerent form those of the matrix. A linear strain hardening behavior of the matrix is assumed, and an elasto-plastic sloution is obtained. The difference of the total strain energy stored inthe infinite solid with and without a precipitate is computed, and compared with that for purely elastic case. Finally the effect of the ratio of the bulk modulus of the precipitate to that of the matrix and the effct of linear strain hardening rate on the plastic zone size and the energy difference are discussed.

Quasi-static responses of time-dependent sandwich plates with viscoelastic honeycomb cores

  • Nasrin Jafari;Mojtaba Azhari
    • Structural Engineering and Mechanics
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    • v.88 no.6
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    • pp.589-598
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    • 2023
  • This article addresses the quasi-static analysis of time-dependent honeycomb sandwich plates with various geometrical properties based on the bending analysis of elastic honeycomb sandwich plates employing a time function with three unknown coefficients. The novel point of the developed method is that the responses of viscoelastic honeycomb sandwich plates under static transversal loads are clearly formulated in the space and time domains with very low computational costs. The mechanical properties of the sandwich plates are supposed to be elastic for the faces and viscoelastic honeycomb cells for the core. The Boltzmann superposition integral with the constant bulk modulus is used for modeling the viscoelastic material. The shear effect is expressed using the first-order shear deformation theory. The displacement field is predicted by the product of a determinate geometrical function and an indeterminate time function. The simple HP cloud mesh-free method is utilized for discretizing the equations in the space domain. Two coefficients of the time function are extracted by answering the equilibrium equation at two asymptotic times. And the last coefficient is easily determined by solving the first-order linear equation. Numerical results are presented to consider the effects of geometrical properties on the displacement history of viscoelastic honeycomb sandwich plates.

Dynamic Modulus of Three-Layer Boards with Different Furnish and Shelling Ratio

  • Rofii, Muhammad Navis;Prayitno, Tibertius Agus;Suzuki, Shigehiko
    • Journal of the Korean Wood Science and Technology
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    • v.44 no.2
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    • pp.274-282
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    • 2016
  • This aims of this study were to investigate the relationship between non-destructive evaluation (NDE) and actual bending properties of particleboard, and to predict the bending properties of three-layer particleboard. Three kinds of raw materials, i.e. Hinoki (Chamaecyparis obtusa Endl.) strand, knife-milled Douglas-fir (Pseudotsuga manziesii (Mirb) Franco), and hammer-milled matoa (Pometia spp.) obtained from wooden industry, were utilized as furnish for experimental panel with methylene diphenyl diisocyanate (MDI) resin as binder. The NDE test was conducted by hit sounds using an FFT analyzer according to the spectrum peak of wave frequency, while the static bending test was conducted according to JIS A-5908. The results reveal that the dynamic Young's modulus as an NDE test has a potential for being used to predict the elastic bending of particleboards by a specific equation for adjusting its proper values. The values of NDE and static test are significantly different with a deviation range at 3-20%. The bending stiffness of three-layer particleboards manufactured from different wood species is predictable by observing the bending stiffness of two elements based on the thickness of its layers. The predicted values of bending stiffness and static test are significantly different with a deviation range at 5-24%.

Fabrication and Performance Evaluation of Diaphragm-type Actuators using Biocompatible polymer (생체적합형 고분자를 이용한 박막형 이동기의 제작 및 특성평가)

  • Jung, Young-Dae;Jeong, Hae-Do
    • Proceedings of the KSME Conference
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    • 2007.05a
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    • pp.1254-1258
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    • 2007
  • Electro-active polymer (EAP), one of the smart materials, is a new alternative offering ultra-precise movements and bio-compatibility. We present the results of the design, fabrication, and performance evaluation of a fabricated diaphragm-type polymer actuator using segmented polyurethane(SPU). This paper illustrates the relationship between the elastic modulus and maximum deflection as a key property of the Maxwell stress effect and also presents the relationship between the dielectric constant and maximum deflection as a key property of the electrostriction effect, especially in polymer actuators using SPU. A diaphragm-type actuator was used to induce an equation of the vertically distributed load by using a fully clamped circular plate as the boundary condition. To verify the equation, the results were compared to the data measured from load cell. In the near future, a low-cost check valves and bio-robot can be applied by its actuators.

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Anti-Plane Shear Behavior of an Arbitrarily Oriented Crack in Bonded Materials with a Nonhomogeneous Interfacial Zone

  • Chung, Yong-Moon;Kim, Chul;Park, Hyung-Jip
    • Journal of Mechanical Science and Technology
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    • v.17 no.2
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    • pp.269-279
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    • 2003
  • The anti-plane shear problem of bonded elastic materials containing a crack at an arbitrary angle to the graded interfacial zone is investigated in this paper The interfacial zone is modeled as a nonhomogeneous interlayer of finite thickness with the continuously varying shear modulus between the two dissimilar, homogeneous half-planes. Formulation of the crack problem is based upon the use of the Fourier integral transform method and the coordinate transformations of basic field variables. The resulting Cauchy-type singular integral equation is solved numerically to provide the values of mode 111 stress intensity factors. A comprehensive parametric study is then presented of the influence of crack obliquity on the stress intensity factors for different crack size and locations and for different material combinations, in conjunction with the material nonhomogeneity within the graded interfacial zone.

Flexural Properties of Reinforced Steel and GFRP Reinforced Polymer Concrete T-Beams (철근 및 GFRP 보강 폴리머 콘크리트 T형 보의 휨 특성)

  • Yeon Kyu Seok;Kweon Taek Jeong;Jeong jung Ho;Jin Xing Qi
    • Proceedings of the Korea Concrete Institute Conference
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    • 2004.11a
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    • pp.695-698
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    • 2004
  • Recently, the usage of polymer concrete mortar gathering an interest as a new construction material rapidly increases inside and outside of the country because it is an environment-friendly and endurable material. However, up to these days, the researches about the polymer composite have not been satisfactorily conducted. The polymer concrete is superior to the general cement materials in the properties of strength and durability while it is inferior in elastic modulus. Because that the members using the polymer concrete have therefore higher strength and ductility than the members of general cement concrete, an analysis equation of high-strength cement concrete can be referenced but it is not applied for the researches about the polymer concrete members. In this study, the flexural properties of T-shaped beam of the steel- and GFRP-reinforced polymer concrete are analyzed to examine the suggested analysis equation. Results of this experimental researches are to be used as the basic data in a structural design of the polymer concrete.

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Stochastic dynamic instability response of piezoelectric functionally graded beams supported by elastic foundation

  • Shegokara, Niranjan L.;Lal, Achchhe
    • Advances in aircraft and spacecraft science
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    • v.3 no.4
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    • pp.471-502
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    • 2016
  • This paper presents the dynamic instability analysis of un-damped elastically supported piezoelectric functionally graded (FG) beams subjected to in-plane static and dynamic periodic thermomechanical loadings with uncertain system properties. The elastic foundation model is assumed as one parameter Pasternak foundation with Winkler cubic nonlinearity. The piezoelectric FG beam is subjected to non-uniform temperature distribution with temperature dependent material properties. The Young's modulus and Poison's ratio of ceramic, metal and piezoelectric, density of respective ceramic and metal, volume fraction exponent and foundation parameters are taken as uncertain system properties. The basic nonlinear formulation of the beam is based on higher order shear deformation theory (HSDT) with von-Karman strain kinematics. The governing deterministic static and dynamic random instability equation and regions is solved by Bolotin's approach with Newmark's time integration method combined with first order perturbation technique (FOPT). Typical numerical results in terms of the mean and standard deviation of dynamic instability analysis are presented to examine the effect of slenderness ratios, volume fraction exponents, foundation parameters, amplitude ratios, temperature increments and position of piezoelectric layers by changing the random system properties. The correctness of the present stochastic model is examined by comparing the results with direct Monte Caro simulation (MCS).

Estimate of Bolt Connection Strength of Reinforced Glulam using Glass Fiber (유리섬유 보강집성재 볼트 접합부 전단내력 예측)

  • Kim, Keon-ho;Hong, Soon-il
    • Journal of the Korean Wood Science and Technology
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    • v.44 no.1
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    • pp.67-74
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    • 2016
  • The yield shear strength of bolt connection in glass fiber reinforced glulam was predicted using a design-based equation, and was compared to the empirical yield shear strength. For the predicted equation, the mechanical properties of member (the elastic modulus, Poisson's ratio, shear modulus) was tested. The fracture toughness factor ($K_{ft}$) of glass fiber reinforced glulam was reflected to the revision of the design equation of bolted connection. The compressive strength properties to grain direction was influenced by annual ring angle and width of lamina. Compared with the revised yield shear strength of reinforced glulam, it was tended to be similar to the empirical yield shear strength on the diameter of bolt and the reinforcements. The revised yield shear strength from proposed formula of KBC was most appropriately matched in the bolt connection of the glass fiber reinforced glulam.

Static analysis of nonlinear FG-CNT reinforced nano-composite beam resting on Winkler/Pasternak foundation

  • Mostefa Sekkak;Rachid Zerrouki;Mohamed Zidour;Abdelouahed Tounsi;Mohamed Bourada;Mahmoud M Selim;Hosam A. Saad
    • Advances in nano research
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    • v.16 no.5
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    • pp.509-519
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    • 2024
  • In this study, the static analysis of carbon nanotube-reinforced composites (CNTRC) beams resting on a Winkler-Pasternak elastic foundation is presented. The developed theories account for higher-order variation of transverse shear strain through the depth of the beam and satisfy the stress-free boundary conditions on the top and bottom surfaces of the beam. To study the effect of carbon nanotubes distribution in functionally graded (FG-CNT), we introduce in the equation of CNT volume fraction a new exponent equation. The SWCNTs are assumed to be aligned and distributed in the polymeric matrix with different patterns of reinforcement. The rule of mixture is used to describe the material properties of the CNTRC beams. The governing equations were derived by employing Hamilton's principle. The models presented in this work are numerically provided to verify the accuracy of the present theory. The analytical solutions are presented, and the obtained results are compared with the existing solutions to verify the validity of the developed theories. Many parameters are investigated, such as the Pasternak shear modulus parameter, the Winkler modulus parameter, the volume fraction, and the order of the exponent in the volume fraction equation. New results obtained from bending and stresses are presented and discussed in detail. From the obtained results, it became clear the influence of the exponential CNTs distribution and Winkler-Pasternak model improved the mechanical properties of the CNTRC beams.

Application of Suggested Equations to determine the Elastic Constants of A Transversely Isotropic Rock from Single Specimen (평면이방성 암석의 단일시험편에서 탄성상수 결정에 제안된 수식들의 적용연구)

  • Park, Chul-Whan;Park, Chan;Jung, Yong-Bok;Park, Eui-Seob
    • Tunnel and Underground Space
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    • v.20 no.3
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    • pp.153-168
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    • 2010
  • A fifth equation is required to determine the five independent elastic constants of a transversely isotropic rock from compression test of a single specimen. As an approximation proposed by Saint-Venant has been used for long time, it may cause an erroneous result in some cases, especially for specimen with low angle of anisotropy. Three equations were suggested replacing this traditional equation and proved to be applicable by the model analysis in the previous studies. As Saint-Venant's approximation is turned out the same as the first one of them, it has the characteristics that the apparent Young's modulus is monotonously increasing according to the anisotropic angle. The methodology to analyze the elastic constants from four independent strain measurements by uniaxial compressive test of a single standard specimen is concisely described, and the necessity and compatibility of new suggested equations are discussed. Saint-Venant's approximation can determine the elastic constants close to true values and other equations may be unnecessary in specimens with medium to large angle. Nevertheless, they may become applicable because they can produce the almost same amount. For the specimens of small angle of anisotropy, Saint-Venant's approximation may result in out of general ranges or thermodynamic constraints, but other suggested equations can produce the almost true value. Thus they can be applied before other alternative equation is known. The guide map constructed by model study may decide the most compatible one of the three equations.