• 제목/요약/키워드: Element Stiffness Matrix

검색결과 498건 처리시간 0.028초

단면변형의 효과를 포함한 강상자형 거더의 엄밀한 해석 (An Exact Analysis of Steel Box Girders with the Effects of Distortional Deformation of Sections)

  • 진만식;이병주;김문영
    • 한국전산구조공학회논문집
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    • 제17권1호
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    • pp.11-20
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    • 2004
  • 본 연구에서는 직선 강상자형 거더의 단면변형에 의한 변형 및 응력계산을 위한 Matlab 해석프로그램을 개발하고자 한다. 이를 위하여 단면변형이론을 요약하고 빔유사이론을 제시한다. 이후 탄성지반위의 보-기둥부재의 지배방정식을 제시하고, 일반화된 고유치해석을 통하여 집중 및 분포하중을 받는 보요소의 엄밀한 강성행렬을 계산한다. 본 연구의 효율성과 정확성을 입증하기 위하여 격벽을 갖는 상자형 거더의 뒤틀림응력을 계산하고 유한요소해와 비교한다.

An analytical-numerical procedure for cracking and time-dependent effects in continuous composite beams under service load

  • Chaudhary, Sandeep;Pendharkar, Umesh;Nagpal, A.K.
    • Steel and Composite Structures
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    • 제7권3호
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    • pp.219-240
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    • 2007
  • An analytical-numerical procedure has been presented in this paper to take into account the nonlinear effects of concrete cracking and time-dependent effects of creep and shrinkage in the concrete portion of the continuous composite beams under service load. The procedure is analytical at the element level and numerical at the structural level. The cracked span length beam element consisting of uncracked zone in middle and cracked zones near the ends has been proposed to reduce the computational effort. The progressive nature of cracking of concrete has been taken into account by division of the time into a number of time intervals. Closed form expressions for stiffness matrix, load vector, crack lengths and mid-span deflection of the beam element have been presented in order to reduce the computational effort and bookkeeping. The procedure has been validated by comparison with the experimental and analytical results reported elsewhere and with FEM. The procedure can be readily extended for the analysis of composite building frames where saving in computational effort would be very considerable.

유한요소 다결정 모델을 이용한 마그네슘 합금 AZ31B 판재의 압연 집합 조직 예측 (Prediction of Rolling Texture for Mg Alloy AZ31B Sheet using Finite Element Polycrystal Model)

  • 원성연;김영석;나경환
    • 한국소성가공학회:학술대회논문집
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    • 한국소성가공학회 2004년도 제5회 압연심포지엄 신 시장 개척을 위한 압연기술
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    • pp.72-82
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    • 2004
  • The deformation mechanism of hexagonal close-packed materials is quite complicate including slips and twins. A deformation mechanism, which accounts for both slip and twinning, was investigated for polycrystalline hop materials. The model was developed in a finite element polycrystal model formulated with initial strain method where the stiffness matrix in FEM is based on the elastic modulus. We predicted numerically the texture of Mg alloy(AZ31B) sheet by using FEM based on crystal plasticity theory. Also, we introduced the recrystallized texture employed the maximum energy release theory after rolling. From the numerical study, it was clarified that the shrink twin could not be the main mechanism for shortening of c-axis, because the lattice rotation due to twin rejects fur c-axis to become parallel to ND(normal direction of plate). It was showed that the deformation texture with the pyramidal slip gives the ring type pole figure having hole in the center.

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편심(偏心) 보강평판(補强平板)의 강도(强度) 해석(解析) (Strength Analysis of Eccentrically Stiffened Plates by Finte Element Method)

  • 김창렬;김재복
    • 대한조선학회지
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    • 제17권4호
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    • pp.1-11
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    • 1980
  • Stiffened plates are commonly used as a component of ship's structures. Most frequently symmetrically stiffened plates are used, but some of stern structures and any specified parts are often constructed with eccentrically stiffened plates. The problems of these eccentrically stiffened plates have been studied rarely, and the results of eccentricity effect of eccentrically stiffened plates are not available. This paper deals with the analysis of eccentrically stiffened plates in the linear elastic range. The derivation of the stiffness matrix was carried out by finite element method for which the isoparametric element was adopted. To show the effect of eccentricity, the deflection at the center under the uniformly distributed and the concentrated load of simply supported and clamped plate models are computed respectively in accordance with the eccentricity of the stiffener. As shown in the results of computations, the eccentricity effect of concentrated load case is greater than that of distributed load case and that of simply supported boundary condition is greater than that of clamped boundary condition. The higher eccentricity of stiffener is, the smaller the effect of stiffener becomes, therefore scantling of eccentrically stiffened plates should be considerably greater than those of symmetrically stiffened plates.

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응력량을 이용한 요소제거법의 위상최적화 (Topology Optimization of Element Removal Method Using Stress Density)

  • 임오강;이진식;김창식
    • 한국전산구조공학회논문집
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    • 제16권1호
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    • pp.1-8
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    • 2003
  • 위상최적설계는 개념설계에 적합하며, 제품의 설계에서 사용되어지고 있다. 전통적인 위상최적화는 균질화법과 최적조건법을 사용해 왔다. 균질화법은 구멍으로 구성된 구조물과 강성행렬사이의 관계를 연결해주는데 사용되며, 최적조건법은 부피분율을 유지하며 설계변수의 개선에 사용되어진다. 전통적인 위상최적설계는 수렴성이 좋은 장점은 있지만 수렴시간이 많이 걸린다는 단점이 있었다. 이 문제를 해결하는 하나의 방법으로 평균 응력량을 기준으로 요소를 제거하는 요소제거법을 제시하였다. 예제에서 수렴속도가 향상됨을 알 수 있었다.

전단변형을 고려한 적층복합 I형 박벽보의 C유한요소 (A C Finite Element of Thin-Walled Laminated Composite I-Beams Including Shear Deformation)

  • 백성용;이승식
    • 한국강구조학회 논문집
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    • 제18권3호
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    • pp.349-359
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    • 2006
  • 본 연구에서는 직교좌표계에 근거한 적층복합 I형 박벽보의 유한요소 해석을 위한 새로운 블록 강도행렬을 제안한다. 변위장은1차 전단변형을 고려한 보 이론을 사용하여 정의되었다. 축방향 변위는 Timoshenko 보이론과 수정된 Vlasov 박벽보 이론을 결합하여 투영단면의 면 변형과 면외 변형의 합으로 나타낸다. 유도된 강성행렬은 휨 전단변형과 뒴 비틂에 의한 영향을 고려한다. 본 유한요소 에서는 2절점, 3절점, 4절점의 세 가지 보요소를 제안하였다. 3절점과 4절점 보 요소는 적층복합 보의 휨 해석에 효과적이었다. 다른 연구자의 수치해석 결과와 비교 검토를 통하여 새로운 유한요소의 활용성과 정확성을 입증하였다.

DDM Rotordynamic Design Sensitivity Analysis of an APU Turbogenerator Having a Spline Shaft Connection

  • Lee, An-Sung;Ha, Jin-Woong
    • Journal of Mechanical Science and Technology
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    • 제17권1호
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    • pp.57-63
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    • 2003
  • An eigenvalue design sensitivity formulation of a general nonsymmetric-matrix rotor-bearing system is devised. using the DDM (direct differential method). Then, investigations on the design sensitivities of critical speeds are carried out for an APU turbogenerator with a spline shaft connection. Results show that the dependence of the rate of change of the critical speed on the stiffness changes of bearing models of spline shaft connection points is negligible, and thereby their modeling uncertainty does not present any problem. And the passing critical speeds up to the 4th critical speed are not sensitive to the design stiffness coefficients of four main bearings. Further, the dependence of the rate of change of the critical speed on the shaft-element length changes shows quantitatively that the spline shaft has some limited influence on the 4th critical speed but no influence on the 1st to 3rd critical speeds. With no adverse effect from the spline shaft, the APU system achieves a critical speed separation margin of more than 40% at a rated speed of 60,000 rpm.

절점 강성을 고려한 공간 구조물의 비선형 불안정 거동에 관한 연구 (A Study of Nonlinear Unstable Phenomenon of Framed Space Structures Considering Joint Rigidity)

  • 손수덕;김승덕;황경주;강문명
    • 한국공간구조학회논문집
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    • 제3권1호
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    • pp.87-97
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    • 2003
  • The structural system that discreterized from continuous shells is frequently used to make a large space structures. As well these structures show the unstable phenomena when a load level over the limit load, and snap-through and bifurcation are most well known of it. For the collapse mechanism, rise-span ratio, element stiffness and load mode are main factor, which it give an effect to unstable behavior. In our real situation, most structures have semi-rigid joint that has middle characteristic between pin and rigid joint. So the knowledge of semi-rigid joint is very important problem of stable large space structure. And the instability phenemena of framed space structures show a strong non-linearity and very sensitive behavior according to the joint rigidity For this reason In this study, we are investigating to unstable problem of framed structure with semi-rigidity and to grasp the nonlinear instability behavior that make the fundamental collapse mechanism of the large space frame structures with semi-rigid joint, by proposed the numerical analysis method. Using the incremental stiffness matrix in chapter 2, we study instability of space structures.

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Experimental and numerical analysis of the punching behavior of RC isolated footings

  • Walid, Mansour;Sabry, Fayed;Ali, Basha
    • Steel and Composite Structures
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    • 제45권5호
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    • pp.665-682
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    • 2022
  • In the current study, punching behavior of Reinforced concrete (RC) isolated footings was experimentally and numerically investigated. The experimental program consisted of four half-scale RC isolated footing specimens. The test matrix was proposed to show effect of footing area, reinforcement mesh ratio, adding internal longitudinal reinforcement bars and stirrups on the punching response of RC isolated footings. Footings area varied from 1200×1200 mm2 to 1500×1500 mm2 while the mesh reinforcement ratio was in the range from 0.36 to 0.45%. On the other hand, a 3D non-linear finite element model was constructed using ABAQUS/standard program and verified against the experimental program. The numerical results agreed well with the experimental records. The validated numerical model was used to study effect of concrete compressive strength; longitudinal reinforcement bars ratio and stirrups concentration along one or two directions on the ultimate load, deflection, stiffness and failure patterns of RC isolated footings. Results concluded that adding longitudinal reinforcement bars did not significantly affect the punching response of RC isolated footings even high steel ratios were used. On the contrary, as the stirrups ratio increased, the ultimate load of RC isolated footings increased. Footing with stirrups ratio of 1.5% had ultimate load equal to 1331 kN, 19.6% higher than the bare footing. Moreover, adding stirrups along two directions with lower ratio (0.5 and 0.7%) significantly enhanced the ultimate load of RC isolated footings compared to their counterparts with higher stirrups ratio (1.0 and 1.5%).

유동계산을 위한 다단계 부분 구조법에 대한 연구 (A STUDY ON A MULTI-LEVEL SUBSTRUCTURING METHOD FOR COMPUTATIONS OF FLUID FLOW)

  • 김진환
    • 한국전산유체공학회지
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    • 제10권2호
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    • pp.38-47
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    • 2005
  • Substructuring methods are often used in finite element structural analyses. In this study a multi-level substructuring(MLSS) algorithm is developed and proposed as a possible candidate for finite element fluid solvers. The present algorithm consists of four stages such as a gathering, a condensing, a solving and a scattering stage. At each level, a predetermined number of elements are gathered and condensed to form an element of higher level. At the highest level, each sub-domain consists of only one super-element. Thus, the inversion process of a stiffness matrix associated with internal degrees of freedom of each sub-domain has been replaced by a sequential static condensation of gathered element matrices. The global algebraic system arising from the assembly of each sub-domain matrices is solved using a well-known iterative solver such as the conjugare gradient(CG) or the conjugate gradient squared(CGS) method. A time comparison with CG has been performed on a 2-D Poisson problem. With one domain the computing time by MLSS is comparable with that by CG up to about 260,000 d.o.f. For 263,169 d.o.f using 8 x 8 sub-domains, the time by MLSS is reduced to a value less than $30\%$ of that by CG. The lid-driven cavity problem has been solved for Re = 3200 using the element interpolation degree(Deg.) up to cubic. in this case, preconditioning techniques usually accompanied by iterative solvers are not needed. Finite element formulation for the incompressible flow has been stabilized by a modified residual procedure proposed by Ilinca et al.[9].