• Title/Summary/Keyword: Plate theory

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Finite Element Modal Analysis of a Spinning Flexible Disk-Spindle System Supported by Hydro Dynamic Bearings and Flexible Supporting Structures In a HDD (유연한 지지 구조와 유체 동압 베어링으로 지지되는 HDD의 회전 유연 디스크-스핀들 시스템에 대한 유한 요소 고유 진동 해석)

  • 한재혁;장건희
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.11a
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    • pp.572-578
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    • 2003
  • The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings in a HDD is analyzed by FEM. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Raynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigenvalue problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

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Design of 3-component Force/Moment Sensor with Force/Moment Ratio of Wide Range (넓은 범위의 힘/모멘트비를 갖는 3분력 힘/모멘트 센서 설계)

  • Kim, Gap-Sun
    • Journal of the Korean Society for Precision Engineering
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    • v.18 no.2
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    • pp.214-221
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    • 2001
  • This paper describes the design of 3-component force/moment sensor with the force and moment ratio of wide range. It can measure the x-direction force Fx, y-direction force Fy and z-direction moment Mz simultaneously. In order to accurately measure forces and moment using 3-component force/moment sensor, it should get suitable force and moment ratio(the ratio of force Fx=200 N and moment Mz=20 Nm is ten to one), and small interference error. In this paper, in order to design the 3-component force/moment sensor with the force and moment ratio of wide range, the procedures are performed as follow : 1) the derivation of the equations to predict the bending strains on the surfaces of the plate-beams under the force or the moments, 2) the determination of the size of the sensing elements of the force/moment sensor by using the derived equations, 3) the Finite Element Method(FEM) analysis and the characteristic test for confirming the strains from the theory analysis, 4) the selection of the attachment locations of the strain gages of each sensor, 5) the analysis of the rated strain and the interference error at the attachment location of strain gages. It reveals that the rated strains calculated from the derived equations make a good agreement with the results from the Finite Element Method analysis and the characteristic test.

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Shear Stress Effect on Isothermal Crystallization Behavior of Semicrystalline Polymer (고분자수지의 등온 결정화거동에 미치는 전단응력의 영향)

  • 박헌진
    • The Korean Journal of Rheology
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    • v.9 no.4
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    • pp.174-182
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    • 1997
  • 결정성 고분자수지는 가공조건에 의해 결정되는 미세구조의 변화에 따라 최종물성 이 현저히 달라지므로 최종 성형품의 물성을 극대화하기 위해서는 성형가공 중에 필연적으 로 부가되는 열이력 뿐만 아니라 전단이력이 결정화 거동에 미치는 영향을 규명하고 가공조 건의 최적화를 통하여 미세구조를 적절히 제어하는 것이 요구된다. 따라서 본 연구에서 in-situ 상태로 전단유도 결정화거동을 조사할수 있는 rheo-kinetic 실험 방법을 개발하고 결정화 거동에 미치는 열이력과 전단이력의 영향을 규명하고자 하였다. 이를 위해 비교적 결정화 속도가 빠른 폴리 부틸렌 테레프탈레이트 수지를 대상으로 냉각조건, 전단부가시간, 전단속도등을 다양하게 변화시키면서 plate-plate 레오미터로 시간에 따른 전단응력의 변화 를 조사하는 rheo-kinetic 연구를 수행하였다. 아울러 실험 중에 액체 질소로 급냉하여 얻은 시료를 대상으로 등온 및 비등온의 열분석 실험을 수행하고 JMA식과 Hoffman-Lauritzentlr 을 사용하여 분석한 다음, 그 결과를 rheo-kinetic 해석결과와 비교함으로써 결정화 거동에 미치는 전단응력의 영향을 규명하였다. 일정전단속동하에서 수행한 rheo-kinetic 실험결과, 시간에 따른 저난응력의 증가와 용융열이 증가하는 경향이 매우 유사한 거동을 보이므로 전 단응력의 증가는 결정화가 일어남에 기인한 결과임을 확인할수 있었으며 고분자수지가 전단 이력을 받게 되면 분자배향의 결과로 결정화 유도시간이 짧아지고 결정화속도가 증가할 뿐 만 아니라 보다 더 높은 온도에서 결정화가 일어나게 됨을 알수 있었다. 또 결정화 반가기 시간과 Hoffman-Lauritzen 식의 매개변수들이 전단속도, 전단부가시간, 결정화 온도 등의 이력에 무관하게 전단응력에 따라 선형적으로 변하고 있으므로 전단유도 결정화거동은 수지 에 부가되는 전단응력에 직접적인 영향을 받음을 알수 있었다. 이상과같은 전단유도 결정화 거동에 관한 결과를 가공공정상의 열전달 현상과 결합하여 해서하면 성형품 내부의모폴로지 의 예측이 가능하므로 성형품 물성의 극대화 방안의 수립에 이용될수 있을것으로 사료된다.

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Analysis on the Elastic Shear Buckling Characteristics of Corrugated Steel Plate in Accordance with Corrugation Shape (형상에 따른 주름강판의 탄성전단좌굴 특성 및 경향성 분석 연구)

  • Shon, Su-Deok;Yoo, Mi-Na;Lee, Seung-Jae
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.18 no.6
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    • pp.11-20
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    • 2014
  • This paper aims at comparing and analyzing shear buckling characteristics between sinusoidal corrugation shape and trapezoidal one. For this, I adopted the equal-length trapezoidal corrugation and sinusoidal one for the analytical models, and analyzed their shear buckling characteristics through linear buckling analysis and on its theory. Generally, the shear buckling shapes of corrugated steel plates are classified into local buckling, global buckling, and interactive buckling from the two buckling modes. Sinusoidal corrugation shape, unlike trapezoidal corrugation, does not have flat sides, which causes another tendency in shear buckling mode. Especially, the changes and different aspects of shear buckling on the boundary between local buckling and global buckling appear in different corrugation shapes. According to the analysis results, interactive buckling mode appeared on the boundary of local buckling and global bucking in trapezoidal corrugation. However, in the case of corrugated steel plates with sinusoidal configuration, interactive buckling mode appeared in the part where global bucking takes place. Besides, trapezoidal shapes are of advantages on shear buckling resistance in the local buckling section, and so are sinusoidal shapes in the global buckling section.

Analysis of Corugated Surface Wave Antenna Using Hybrid MOM/UTD Method (하이브리드 MOM/UTD 방법을 이용한 주름진 표면파 안테나의 해석)

  • Kim, Joong-Pyo;Lee, Chang-Won;Son, Hyon
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.10 no.3
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    • pp.359-367
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    • 1999
  • The analysis of a surface wave antenna with the corrugated ground plane fed by a parallel-plate waveguide is considered. An equivalent theorem Is employed to subdivide the original problem into three regions for the simple analysis : one concerning the geometry inside the shorted parallel-plate(Internal region 1), one concerning the geometry of the corrugation(Internal region 2), and one concerning the geometry of the conducting wedge(External region). The hybrid method of moment(MOM)/uniform geometrical theory of diffraction(UTD) method is applied to analyze a corrugated surface wave antenna with the end-fire radiation. Our numerical results are very well matched with those of the previous experiment, better results are obtained when compared with those of the previous simple equivalent current approach. Also, we can obtain the parameters to design an effective end-fire corrugated surface wave antenna.

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Formulation of Optimal Design Parameters and Failure Map for Metallic Sandwich Plates with Inner Dimpled Shell Structure Subject to Bending Moment (굽힘 하중을 받는 딤플형 내부구조 금속 샌드위치 판재의 최적설계변수의 수식화 및 파손선도)

  • Seong Dae-Yong;Jung Chang-Gyun;Yoon Seok-Joon;Ahn Dong-Gyu;Yang Dong-Yol
    • Journal of the Korean Society for Precision Engineering
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    • v.23 no.8 s.185
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    • pp.127-136
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    • 2006
  • Metallic sandwich plates with inner dimpled shell subject to 3-point bending have been analyzed and then optimized for minimum weight. Inner dimpled shells can be easily fabricated by press or roll with high precision and bonded with same material skin sheets by resistance welding or adhesive bonding. Metallic sandwich plates with inner dimpled shell structure can be optimally designed for minimum weight subject to prescribed combination of bending and transverse shear loads. Fundamental findings for lightweight design are presented through constrained optimization. Failure responses of sandwich plates are predicted and formulated with an assumption of narrow sandwich beam theory. Failure is attributed to four kinds of mechanisms: face yielding, face buckling, dimple buckling and dimple collapse. Optimized shape of inner dimpled shell structure is a hemispherical shell to minimize weight without failure. It is demonstrated that bending stiffness of sandwich plate is 2 or 3 times larger than solid plates with the same strength. Failure mode boundaries and iso-strength lines dependent upon the geometry and yield strain of the material are plotted with respect to geometric parameters on the failure map. Because optimal parameters of maximum strength for given material weight can be selected from the map, analytic solutions for maximum strength are expressed as a function of only material property and proposed strength. These optimal parameters match well with numerical optimal parameters.

Finite element based dynamic analysis of multilayer fibre composite sandwich plates with interlayer delaminations

  • Jayatilake, Indunil N.;Karunasena, Warna;Lokuge, Weena
    • Advances in aircraft and spacecraft science
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    • v.3 no.1
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    • pp.15-28
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    • 2016
  • Although the aircraft industry was the first to use fibre composites, now they are increasingly used in a range of structural applications such as flooring, decking, platforms and roofs. Interlayer delamination is a major failure mode which threatens the reliability of composite structures. Delamination can grow in size under increasing loads with time and hence leads to severe loss of structural integrity and stiffness reduction. Delamination reduces the natural frequency and as a consequence may result in resonance. Hence, the study of the effects of delamination on the free vibration behaviour of multilayer composite structures is imperative. The focus of this paper is to develop a 3D FE model and investigate the free vibration behaviour of fibre composite multilayer sandwich panels with interlayer delaminations. A series of parametric studies are conducted to assess the influence of various parameters of concern, using a commercially available finite element package. Additionally, selected points in the delaminated region are connected appropriately to simulate bolting as a remedial measure to fasten the delamination region in the aim of reducing the effects of delamination. First order shear deformation theory based plate elements have been used to model each sandwich layer. The findings suggest that the delamination size and the end fixity of the plate are the most important factors responsible for stiffness reduction due to delamination damage in composite laminates. It is also revealed that bolting the delaminated region can significantly reduce the natural frequency variation due to delamination thereby improving the dynamic performance.

Domain decomposition technique to simulate crack in nonlinear analysis of initially imperfect laminates

  • Ghannadpour, S. Amir M.;Karimi, Mona
    • Structural Engineering and Mechanics
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    • v.68 no.5
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    • pp.603-619
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    • 2018
  • In this research, an effective computational technique is carried out for nonlinear and post-buckling analyses of cracked imperfect composite plates. The laminated plates are assumed to be moderately thick so that the analysis can be carried out based on the first-order shear deformation theory. Geometric non-linearity is introduced in the way of von-Karman assumptions for the strain-displacement equations. The Ritz technique is applied using Legendre polynomials for the primary variable approximations. The crack is modeled by partitioning the entire domain of the plates into several sub-plates and therefore the plate decomposition technique is implemented in this research. The penalty technique is used for imposing the interface continuity between the sub-plates. Different out-of-plane essential boundary conditions such as clamp, simply support or free conditions will be assumed in this research by defining the relevant displacement functions. For in-plane boundary conditions, lateral expansions of the unloaded edges are completely free while the loaded edges are assumed to move straight but restricted to move laterally. With the formulation presented here, the plates can be subjected to biaxial compressive loads, therefore a sensitivity analysis is performed with respect to the applied load direction, along the parallel or perpendicular to the crack axis. The integrals of potential energy are numerically computed using Gauss-Lobatto quadrature formulas to get adequate accuracy. Then, the obtained non-linear system of equations is solved by the Newton-Raphson method. Finally, the results are presented to show the influence of crack length, various locations of crack, load direction, boundary conditions and different values of initial imperfection on nonlinear and post-buckling behavior of laminates.

Bending analysis of functionally graded plates with arbitrary shapes and boundary conditions

  • Panyatong, Monchai;Chinnaboon, Boonme;Chucheepsakul, Somchai
    • Structural Engineering and Mechanics
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    • v.71 no.6
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    • pp.627-641
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    • 2019
  • The paper focuses on bending analysis of the functionally graded (FG) plates with arbitrary shapes and boundary conditions. The material property of FG plates is modelled by using the power law distribution. Based on the first order shear deformation plate theory (FSDT), the governing equations as well as boundary conditions are formulated and obtained by using the principle of virtual work. The coupled Boundary Element-Radial Basis Function (BE-RBF) method is established to solve the complex FG plates. The proposed methodology is developed by applying the concept of the analog equation method (AEM). According to the AEM, the original governing differential equations are replaced by three Poisson equations with fictitious sources under the same boundary conditions. Then, the fictitious sources are established by the application of a technique based on the boundary element method and approximated by using the radial basis functions. The solution of the actual problem is attained from the known integral representations of the potential problem. Therefore, the kernels of the boundary integral equations are conveniently evaluated and readily determined, so that the complex FG plates can be easily computed. The reliability of the proposed method is evaluated by comparing the present results with those from analytical solutions. The effects of the power index, the length to thickness ratio and the modulus ratio on the bending responses are investigated. Finally, many interesting features and results obtained from the analysis of the FG plates with arbitrary shapes and boundary conditions are demonstrated.

Ultimate strength estimation of composite plates under combined in-plane and lateral pressure loads using two different numerical methods

  • Ghannadpour, S.A.M.;Shakeri, M.;Barvaj, A. Kurkaani
    • Steel and Composite Structures
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    • v.29 no.6
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    • pp.785-802
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    • 2018
  • In this paper, two different computational methods, called Rayleigh-Ritz and collocation are developed to estimate the ultimate strength of composite plates. Progressive damage behavior of moderately thick composite laminated plates is studied under in-plane compressive load and uniform lateral pressure. The formulations of both methods are based on the concept of the principle of minimum potential energy. First order shear deformation theory and the assumption of large deflections are used to develop the equilibrium equations of laminated plates. Therefore, Newton-Raphson technique will be used to solve the obtained system of nonlinear algebraic equations. In Rayleigh-Ritz method, two degradation models called complete and region degradation models are used to estimate the degradation zone around the failure location. In the second method, a new energy based collocation technique is introduced in which the domain of the plate is discretized into the Legendre-Gauss-Lobatto points. In this new method, in addition to the two previous models, the new model named node degradation model will also be used in which the material properties of the area just around the failed node are reduced. To predict the failure location, Hashin failure criteria have been used and the corresponding material properties of the failed zone are reduced instantaneously. Approximation of the displacement fields is performed by suitable harmonic functions in the Rayleigh-Ritz method and by Legendre basis functions (LBFs) in the second method. Finally, the results will be calculated and discussions will be conducted on the methods.