• Title/Summary/Keyword: strain plane

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The effect of in-plane deformations on the nonlinear dynamic response of laminated plates

  • Kazanci, Zafer;Turkmen, Halit S.
    • Structural Engineering and Mechanics
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    • v.42 no.4
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    • pp.589-608
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    • 2012
  • In this study, the effect of in-plane deformations on the dynamic behavior of laminated plates is investigated. For this purpose, the displacement-time and strain-time histories obtained from the large deflection analysis of laminated plates are compared for the cases with and without including in-plane deformations. For the first one, in-plane stiffness and inertia effects are considered when formulating the dynamic response of the laminated composite plate subjected to the blast loading. Then, the problem is solved without considering the in-plane deformations. The geometric nonlinearity effects are taken into account by using the von Karman large deflection theory of thin plates and transverse shear stresses are ignored for both cases. The equations of motion for the plate are derived by the use of the virtual work principle. Approximate solution functions are assumed for the space domain and substituted into the equations of motion. Then, the Galerkin method is used to obtain the nonlinear algebraic differential equations in the time domain. The effects of the magnitude of the blast load, the thickness of the plate and boundary conditions on the in-plane deformations are investigated.

A Study on Remaining Efficiency of Thermal Straightening after Block Lifting

  • Ha, Yunsok;Yi, Myungsu
    • Journal of Advanced Research in Ocean Engineering
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    • v.1 no.3
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    • pp.148-156
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    • 2015
  • Deck plates of ships or offshore structures would make out-of-plane distortion for their thin thickness. These distortions are usually straightened by thermal straightening such as flame heating method. After thermal straightening, the blocks are lifted and moved by cranes to assemble it at dry-dock stage. After this lifting process, out-of-plane deformation again happens frequently. And then, they continuously cause quality and accuracy problems in the final dry-dock process. So, it takes more time for repair and correction working. According to preceding research, the lifting process by cranes would offset the effect on thermal straightening. The target of this study is to develop a methodology analyzing the remaining efficiency of thermal straightening after block lifting. The development was based on the assumption of yield state at straightening region. Therefore the remaining efficiency was obtained by different stiffness slope while lifting & relieving. The efficiency formula was designed using inherent strain, and we made a table of zero-efficiency by cooling speed and class rule's steels. As a result, if the stress orthogonal to straightened line is calculated during lifting analysis by FEA, the efficiency can be obtained linearly to the values in the table. Finally, even optimized carling position can be designed by considering the regional data from series project and welding region on deck.

Initiation and Propagation Behaviors of Micro-Surface-Fatigue Cracks under In-Plane Tension Fatigue Tests (引張 軸荷重 疲勞 에 의한 微小表面 균열 의 發생 . 成長擧動)

  • 서창민
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.9 no.1
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    • pp.1-9
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    • 1985
  • In-plane tension fatigue tests (R = 0.05) were carried out to investigate the initiation and propagation behaviors of micro-surface-fatigue cracks on smooth surfaces of a mild steel. Also, the investigations of saturated cyclic strain which can be obtained by the fatigue tests have been made via the cyclic strain intensity factor, .DELTA. $K_{\epsilon}$/, for the purpose of unifying two approaches of the study of fatigue; the one approach is based on the fracture mechanics concept and the other on lowcycle fatigue concept. Some of the results are as follows; The growth rate, d(2a)/dN, of small cracks cannot be represented by one straight line as a function of .DELTA.K for various of the nominal stress range, .DELTA..sigma., and is higher than that of a larger through crack. The rearrangement of the d(2a)/dN by .DELTA..epsilon..root..pi.s( = .DELTA. $K_{\epsilon}$/) with the stress range .DELTA..epsilon. in .DELTA.K replaced by .DELTA..epsilon., strain range, gives one straight line of the .DELTA. $K_{\epsilon}$-d(2a)/dN relation for various values of stress range .DELTA.$_{\epsilon}$../.X>../.

Evolution of sandstone shear strength parameters and its mesoscopic mechanism

  • Shi, Hao;Zhang, Houquan;Song, Lei
    • Geomechanics and Engineering
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    • v.20 no.1
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    • pp.29-41
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    • 2020
  • It is extremely important to obtain rock strength parameters for geological engineering. In this paper, the evolution of sandstone cohesion and internal friction angle with plastic shear strain was obtained by simulating the cyclic loading and unloading tests under different confining pressures using Particle Flow Code software. By which and combined with the micro-crack propagation process, the mesoscopic mechanism of parameter evolution was studied. The results show that with the increase of plastic shear strain, the sandstone cohesion decreases first and then tends to be stable, while the internal friction angle increases first, then decreases, and finally maintains unchanged. The evolution of sandstone shear strength parameters is closely related to the whole process of crack formation, propagation and coalescence. When the internal micro-cracks are less and distributed randomly and dispersedly, and the rock shear strength parameters (cohesion, internal friction angle) are considered to have not been fully mobilized. As the directional development of the internal micro-fractures as well as the gradual formation of macroscopic shear plane, the rock cohesion reduces continuously and the internal friction angle is in the rise stage. As the formation of the macroscopic shear plane, both the rock cohesion and internal friction angle continuously decrease to a certain residual level.

A Finite Element Nonlinear Formulation for Large Deformations of Plane Frames (평면 뼈대구조물의 큰 변형에 대한 비선형 유한요소의 정식화)

  • 윤영묵;박문호
    • Computational Structural Engineering
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    • v.7 no.4
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    • pp.69-83
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    • 1994
  • An explicit finite element nonlinear formulation for very large deformations of plane frame structures is developed. The formulation is based on an updated material reference frame and hence a true stress-strain relationship can be directly applied to characterize the properties of material which is subjected to very large deformations. In the formulation, a co-rotational approach is applied to deal with the large rotations but small strain problems. Straight beam element is considered when the strain of an element is large. The element formulation is based on the small deflection beam theory but with the inclusion of the effect of axial force. The element equations are constructed in an element local coordinate system which rotates and translates with the element, and then transformed to the global coordinate system. Several numerical examples are analyzed to validate the presented formulation.

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A Study on Crack Initiation of 2-Phase Composite with Through Notch (貫通노치를 가진 二相接合材의 龜裂發생에 대한 硏究)

  • ;;Shimada, Heihachi
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.13 no.4
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    • pp.636-642
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    • 1989
  • In this paper, 3-dimensional fracture phenomena in the local area near the notch tip between the surface and the center of a composite bar which is consisted of two different materials were investigated by using embedded dyeing grids with the pitch of 50.8.mu. It was confirmed that the maximum strain near the notch tip occurred not at the notch front but at the curvature beginning point of the notch which is in the interior of z/W = 0.3 - 0.35 from the surface and a notch was initiated from that point. And that the strain near the notch front between the center and z/W = 0.65 - 0.7 toward the surface was in a state of compression.

An exact solution for mechanical behavior of BFRP Nano-thin films embedded in NEMS

  • Altabey, Wael A.
    • Advances in nano research
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    • v.5 no.4
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    • pp.337-357
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    • 2017
  • Knowledge of thin films mechanical properties is strongly associated to the reliability and the performances of Nano Electro Mechanical Systems (NEMS). In the literature, there are several methods for micro materials characterization. Bulge test is an established nondestructive technique for studying the mechanical properties of thin films. This study improve the performances of NEMS by investigating the mechanical behavior of Nano rectangular thin film (NRTF) made of new material embedded in Nano Electro Mechanical Systems (NEMS) by developing the bulge test technique. The NRTF built from adhesively-bonded layers of basalt fiber reinforced polymer (BFRP) laminate composite materials in Nano size at room temperature and were used for plane-strain bulging. The NRTF is first pre-stressed to ensure that is no initial deflection before applied the loads on NRTF and then clamped between two plates. A differential pressure is applying to a deformation of the laminated composite NRTF. This makes the plane-strain bulge test idea for studying the mechanical behavior of laminated composite NRTF in both the elastic and plastic regimes. An exact solution of governing equations for symmetric cross-ply BFRP laminated composite NRTF was established with taking in-to account the effect of the residual strength from pre-stressed loading. The stress-strain relationship of the BFRP laminated composite NRTF was determined by hydraulic bulging test. The NRTF thickness gradation in different points of hemisphere formed in bulge test was analysed.

Free-strain solutions for two-dimensional consolidation with sand blankets under multi-ramp loading

  • Zan Li;Songyu Liu;Cuiwei Fu
    • Geomechanics and Engineering
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    • v.35 no.4
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    • pp.385-393
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    • 2023
  • To analyze the consolidation with horizontal sand drains, the plane strain consolidation model under multi-ramp loading is established, and its corresponding analytical solution is derived by using the separation of variables method. The proposed solution is verified by the field measurement data and finite element results. Then, the effects of the loading mode and stress distribution on consolidation and dissipation of pore pressure are investigated. At the same time, the influence of hydraulic conductivity and thickness of sand blankets on soil consolidation are also analyzed. The results show that the loading mode has a significant effect on both the soil consolidation rate and generation-dissipation process of pore water pressure. In contrast, the influence of stress distribution on pore pressure dissipation is obvious, while its influence on soil consolidation rate is negligible. To guarantee the fully drained condition of the sand blanket, the ratio of hydraulic conductivity of the sand blanket to that of clay layer kd/kv should range from 1.0×104 to 1.0×106 with soil width varying from 100 m to 1000 m. A larger soil width correspondingly needs a greater value of kd/kv to make sure that the pore water can flow through the sand blanket smoothly with little resistance. When the soil width is relatively small (e.g., less than 100 m), the effect of thickness of the sand blanket on soil consolidation is insignificant. And its influence appears obvious gradually with the increase of the soil width.

Natural Vibration Analysis of Thick Rings (두꺼운 링의 고유진동 해석)

  • Park, Jung-Woo;Kim, Sehee;Kim, Chang-Boo
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.15 no.10 s.103
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    • pp.1186-1194
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    • 2005
  • In this paper, we have systematically formulated the equations concerned to the in-plane and out-of-plane motions and deformations of a thick circular beam by using the kinetic and strain energies in order to analyse natural frequencies of a thick ring. The effects of variation of radius of curvature across the cross-section and also the effects of bending shear, extension and twist are considered. The equations of motion for natural vibration analysis of a ring are obtained utilizing the cyclic symmetry of vibration modes of the ring. The frequencies calculated using thick ring model and thin ring model are compared and discussed with the ones obtained from finite element analysis using the method of cyclic symmetry with 20-node hexahedral solid elements for rings with the different ratio of radial thickness to mean radius.