• 제목/요약/키워드: displacement formulation

검색결과 446건 처리시간 0.032초

고속선(高速船) 선체고유상하진동(船體固有上下振動)의 초기추정(初期推定) 방법(方法) (A Method for the Preliminary Estimation of Vertical Natural Vibations of High Speed Boats)

  • 김극천;김학빈
    • 대한조선학회지
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    • 제17권1호
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    • pp.25-29
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    • 1980
  • For the preliminary estimation of the vertical hull natural frequency, the Schlick's or Schlick-type formulae have been traditional ones and are still in common use today. Some investigators have made their efforts, based on statistical data of ships' system parameters, to extend the applicability of Schlick-type formulae to higher modes, or to utilize the Rayleigh method. For instance, the work done by Dinsenbacher et al.[5] belongs to the former and that of Nagamoto et al.[6] to the latter. In a part of his previous paper[7], the author, investigating the case of a cargo ship of medium size, suggested that provided statistically simplified curves such as trapezoid of system parameter distributions are available in hands, direct utlization of an ordinary computer program can be also an another convenient method by which we can obtain both natural frequencies and normal mode shapes. In this paper, to confirm the feasibility of the above suggestion, four high speed boats are investigated. The system parameters of them are originally given in [5]. The computer program used here is one confiled based on a calculation method derived from Myklestal-Prohl modeling of hull, transfer matrix formulation and an extended Gumbel's initial value method for solving frequency equation. The results of the investigation show that the direct calculation based on statistically oriented and reasonably assumed trapezoidal mean curves of system parameter distributions can give us natural frequencies within about 5% deviation up to several-noded modes and normal mode shapes serviceable at least up to 4- or 5-noded modes in comparision with those based on actual distributions of system parameters. For this simplified method the actual data required for input are only of ship length, displacement, total added mass, bending and shear rigidity at amidship. They are available at the early stage of design. By this method we can also easily trace variations of vibration characteristics in the course of ship design cycles.

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합성보의 부착슬립 효과를 고려한 유한요소 기반의 수치해석모델 (FE Based Numerical Model to Consider Bond-slip Effect in Composite Beams)

  • 곽효경;황진욱
    • 한국전산구조공학회논문집
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    • 제23권1호
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    • pp.95-110
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    • 2010
  • 본 논문에서는 합성보의 부착슬립 효과를 고려할 수 있는 유한요소 수치모델을 제안하고자 한다. 전단연결재가 설치된 슬래브와 거더 경계에서 선형 전단력-슬립 관계를 가정하여, 부착슬립 거동을 해석할 수 있는 수치모델이 구현되었다. 본 수치모델을 통하여 축 방향의 자유도를 부가하지 않고 2절점의 보 요소를 적용하여 합성보 경계에서의 슬립 거동을 고려하는 것이 가능하다. 선형 부분전단 연결이론을 토대로 한 슬립 거동의 지배방정식은 슬래브와 거더 경계에서 힘의 평형상태와 단면 내에서 상수로 가정된 곡률을 바탕으로 결정된다. 또한, 지배방정식 구성에 있어서 요소 양 절점에서의 휨 모멘트 값을 필요로 하기 때문에 유한요소 해석으로 도출되는 상수 모멘트를 요소 내에서 선형으로 분포시켰다. 제안된 수치모델을 적용한 해석결과를 기존 연구의 수치해석 결과 및 실험결과와 비교하였으며, 하중-처짐 곡선의 비교를 통하여 본 모델의 성능을 검증하였다.

Bending of steel fibers on partly supported elastic foundation

  • Hu, Xiao Dong;Day, Robert;Dux, Peter
    • Structural Engineering and Mechanics
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    • 제12권6호
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    • pp.657-668
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    • 2001
  • Fiber reinforced cementitious composites are nowadays widely applied in civil engineering. The postcracking performance of this material depends on the interaction between a steel fiber, which is obliquely across a crack, and its surrounding matrix. While the partly debonded steel fiber is subjected to pulling out from the matrix and simultaneously subjected to transverse force, it may be modelled as a Bernoulli-Euler beam partly supported on an elastic foundation with non-linearly varying modulus. The fiber bridging the crack may be cut into two parts to simplify the problem (Leung and Li 1992). To obtain the transverse displacement at the cut end of the fiber (Fig. 1), it is convenient to directly solve the corresponding differential equation. At the first glance, it is a classical beam on foundation problem. However, the differential equation is not analytically solvable due to the non-linear distribution of the foundation stiffness. Moreover, since the second order deformation effect is included, the boundary conditions become complex and hence conventional numerical tools such as the spline or difference methods may not be sufficient. In this study, moment equilibrium is the basis for formulation of the fundamental differential equation for the beam (Timoshenko 1956). For the cantilever part of the beam, direct integration is performed. For the non-linearly supported part, a transformation is carried out to reduce the higher order differential equation into one order simultaneous equations. The Runge-Kutta technique is employed for the solution within the boundary domain. Finally, multi-dimensional optimization approaches are carefully tested and applied to find the boundary values that are of interest. The numerical solution procedure is demonstrated to be stable and convergent.

An efficient shear deformation theory for wave propagation of functionally graded material plates

  • Boukhari, Ahmed;Atmane, Hassen Ait;Tounsi, Abdelouahed;Adda Bedia, E.A.;Mahmoud, S.R.
    • Structural Engineering and Mechanics
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    • 제57권5호
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    • pp.837-859
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    • 2016
  • An efficient shear deformation theory is developed for wave propagation analysis of an infinite functionally graded plate in the presence of thermal environments. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The thermal effects and temperature-dependent material properties are both taken into account. The temperature field is assumed to be a uniform distribution over the plate surface and varied in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle and the physical neutral surface concept. There is no stretching.bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The analytic dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions and temperature on wave propagation of functionally graded plate are discussed in detail. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded plate. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.

Effects of macroporosity and double porosity on noise control of acoustic cavity

  • Sujatha, C.;Kore, Shantanu S.
    • Advances in aircraft and spacecraft science
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    • 제3권3호
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    • pp.351-366
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    • 2016
  • Macroperforations improve the sound absorption performance of porous materials in acoustic cavities and in waveguides. In an acoustic cavity, enhanced noise reduction is achieved using porous materials having macroperforations. Double porosity materials are obtained by filling these macroperforations with different poroelastic materials having distinct physical properties. The locations of macroperforations in porous layers can be chosen based on cavity mode shapes. In this paper, the effect of variation of macroporosity and double porosity in porous materials on noise reduction in an acoustic cavity is presented. This analysis is done keeping each perforation size constant. Macroporosity of a porous material is the fraction of area covered by macro holes over the entire porous layer. The number of macroperforations decides macroporosity value. The system under investigation is an acoustic cavity having a layer of poroelastic material rigidly attached on one side and excited by an internal point source. The overall sound pressure level (SPL) inside the cavity coupled with porous layer is calculated using mixed displacement-pressure finite element formulation based on Biot-Allard theory. A 32 node, cubic polynomial brick element is used for discretization of both the cavity and the porous layer. The overall SPL in the cavity lined with porous layer is calculated for various macroporosities ranging from 0.05 to 0.4. The results show that variation in macroporosity of the porous layer affects the overall SPL inside the cavity. This variation in macroporosity is based on the cavity mode shapes. The optimum range of macroporosities in poroelastic layer is determined from this analysis. Next, SPL is calculated considering periodic and nodal line based optimum macroporosity. The corresponding results show that locations of macroperforations based on mode shapes of the acoustic cavity yield better noise reduction compared to those based on nodal lines or periodic macroperforations in poroelastic material layer. Finally, the effectiveness of double porosity materials in terms of overall sound pressure level, compared to equivolume double layer poroelastic materials is investigated; for this the double porosity material is obtained by filling the macroperforations based on mode shapes of the acoustic cavity.

HC-DSSE 조합 파단 변형률 정식화에 기반한 선박해양 구조물용 강재의 연성 파단 예측 (Ductile Fracture of a Marine Structural Steel based on HC-DSSE Combined Fracture Strain Formulation)

  • 박성주;이강수;부락 잔 체릭;김영훈;정준모
    • 대한조선학회논문집
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    • 제56권1호
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    • pp.82-93
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    • 2019
  • In this paper, the ductile fracture criteria for a marine structural steel (EH36) are presented and validated. The theoretical background of the recently developed Hosford-Coulomb (HC) fracture strain model and the DSSE fracture strain model which was developed to apply to the shell elements is described. In order to accurately estimate the flow stress in the large strain range up to the fracture, the material constants for the combined Swift-Voce constitutive equation were derived by the numerical analyses of the smooth and notched specimens made from the EH36 steel. As a result of applying the Swift-Voce flow stress to the other notched specimen model, a very accurate load - displacement curve could be derived. The material constants of the HC fracture strain and DSSE fracture strain models were independently calibrated based on the numerical analyses for the smooth and notch specimen tests. The user subroutine (VUMAT of Abaqus) was developed to verify the accuracy of the combined HC-DSSE fracture strain model. An asymmetric notch specimen was used as verification model. It was confirmed that the fracture of the asymmetric specimen can be accurately predicted when a very small solid elements are used together with the HC fracture strain model. On the other hand, the combined HC-DSSE fracture strain model can predict accurately the fracture of shell element model while the shell element size effect becomes less sensitive.

Investigation of wave propagation in anisotropic plates via quasi 3D HSDT

  • Bouanati, Soumia;Benrahou, Kouider Halim;Atmane, Hassen Ait;Yahia, Sihame Ait;Bernard, Fabrice;Tounsi, Abdelouahed;Bedia, E.A. Adda
    • Geomechanics and Engineering
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    • 제18권1호
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    • pp.85-96
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    • 2019
  • A free vibration analysis and wave propagation of triclinic and orthotropic plate has been presented in this work using an efficient quasi 3D shear deformation theory. The novelty of this paper is to introducing this theory to minimize the number of unknowns which is three; instead four in other researches, to studying bulk waves in anisotropic plates, other than it can model plates with great thickness ratio, also. Another advantage of this theory is to permits us to show the effect of both bending and shear components and this is carried out by dividing the transverse displacement into the bending and shear parts. Hamilton's equations are a very potent formulation of the equations of analytic mechanics; it is used for the development of wave propagation equations in the anisotropic plates. The analytical dispersion relationship of this type of plate is obtained by solving an eigenvalue problem. The accuracy of the present model is verified by confronting our results with those available in open literature for anisotropic plates. Moreover Numerical examples are given to show the effects of wave number and thickness on free vibration and wave propagation in anisotropic plates.

Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position

  • Hachemi, Houari;Bousahla, Abdelmoumen Anis;Kaci, Abdelhakim;Bourada, Fouad;Tounsi, Abdeldjebbar;Benrahou, Kouider Halim;Tounsi, Abdelouahed;Al-Zahrani, Mesfer Mohammad;Mahmoud, S.R.
    • Steel and Composite Structures
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    • 제39권1호
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    • pp.51-64
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    • 2021
  • This paper presents a high-order shear and normal deformation theory for the bending of FGM plates. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. Based on the novel shear and normal deformation theory, the position of neutral surface is determined and the governing equilibrium equations based on neutral surface are derived. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Navier-type analytical solution is obtained for functionally graded plate subjected to transverse load for simply supported boundary conditions. The accuracy of the present theory is verified by comparing the obtained results with other quasi-3D higher-order theories reported in the literature. Other numerical examples are also presented to show the influences of the volume fraction distribution, geometrical parameters and power law index on the bending responses of the FGM plates are studied.

고인성 복합체로 보강한 조적부재의 휨 거동 평가 (Evaluation of Flexural Behavior of Masonry Members Reinforced with Engineered Cementitious Composite)

  • 양승현;김선웅;김재환;강석표;홍성욱
    • 한국구조물진단유지관리공학회 논문집
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    • 제25권4호
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    • pp.37-45
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    • 2021
  • 논문은 조적부재에 고인성 복합체를 보강하여 내진보강 가능성을 평가하기 위한 기초연구이다. 고인성 복합체의 섬유 혼입률에 따른 성능을 검토하기 위하여 배합설계에 따라 시험체를 제조하고 유동성능, 압축강도, 휨 강도, 길이변화율 및 직접인장변형률을 측정하였다. 또한, 무보강 조적부재, 고인성 복합체로 보강한 조적부재, 고인성 복합체에 유리섬유 및 와이어 메쉬를 별도 보강한 조적부재를 제작하고 휨 강도와 최대변위를 측정하였다. 고인성 복합체를 보강한 모든 실험체들은 무보강과 비교하여 최대내력이 16배 이상의 효과가 나타났으며 균열 형상을 검토한 결과 에너지소산능력이 우수한 것으로 나타나 내진보강 가능성을 확인하였다.

Buckling behaviors of FG porous sandwich plates with metallic foam cores resting on elastic foundation

  • Abdelkader, Tamrabet;Belgacem, Mamen;Abderrahmane, Menasria;Abdelhakim, Bouhadra;Abdelouahed, Tounsi;Mofareh Hassan, Ghazwani;Ali, Alnujaie;S.R., Mahmoud
    • Structural Engineering and Mechanics
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    • 제85권3호
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    • pp.289-304
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    • 2023
  • The main objective of this paper is to study the effect of porosity on the buckling behavior of thick functionally graded sandwich plate resting on various boundary conditions under different in-plane loads. The formulation is made for a newly developed sandwich plate using a functional gradient material based on a modified power law function of symmetric and asymmetric configuration. Four different porosity distribution are considered and varied in accordance with material propriety variation in the thickness direction of the face sheets of sandwich plate, metal foam also is considered in this study on the second model of sandwich which containing metal foam core and FGM face sheets. New quasi-3D high shear deformation theory is used here for this investigate; the present kinematic model introduces only six variables with stretching effect by adopting a new indeterminate integral variable in the displacement field. The stability equations are obtained by Hamilton's principle then solved by generalized solution. The effect of Pasternak and Winkler elastic foundations also including here. the present model validated with those found in the open literature, then the impact of different parameters: porosities index, foam cells distribution, boundary conditions, elastic foundation, power law index, ratio aspect, side-to-thickness ratio and different in-plane axial loads on the variation of the buckling behavior are demonstrated.