• 제목/요약/키워드: matrix stiffness method

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부분강절 뼈대구조의 비탄성 좌굴해석 (Inelastic Buckling Analysis of Frames with Semi-Rigid Joints)

  • 민병철
    • 한국강구조학회 논문집
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    • 제26권3호
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    • pp.143-154
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    • 2014
  • 본 연구에서는 부분강절 뼈대구조물의 비탄성 좌굴해석기법을 제시하기 위하여, 이전의 연구[16]에서 제시되었던 부분강절 뼈대구조의 엄밀한 강도행렬과 선형해석을 위한 탄성 및 기하학적 강도행렬을 도입하고 비탄성 좌굴해석을 위해 도로교시방서의 극한내하력 기준과 EF법을 이용하여 부분강절 뼈대구조의 비탄성 좌굴해석 프로그램을 새롭게 개발하였다. 본 연구에서 제시한 부분강절 뼈대구조의 접선강도행렬은 안정함수를 사용함에 따라 부재 당 하나의 요소만으로 정확한 비탄성 좌굴해석 결과를 얻을 수 있으며 고유벡터를 이용하여 비탄성 좌굴형상을 얻을 수 있는 장점을 갖는다. 또한, 엄밀한 접선강도행렬에 대해 Taylor 전개를 수행하여 4차항까지 고려함으로서 탄성 강도행렬과 기하학적 강도행렬을 유도하고 선형화된 좌굴해석기법을 제시하였다. 결국, 접선강도행렬을 이용한 비선형 해석프로그램(M1)과 탄성 및 기하학적 강도행렬을 이용한 선형 해석프로그램(M2)이 개발되었으며 이를 이용하여 부분강절로 연결된 뼈대구조물의 비탄성좌굴에 대한 시스템 좌굴하중과 개별부재의 유효좌굴계수를 제시함에 따라 부분강절이 전체 구조계의 좌굴과 개별부재의 유효좌굴길이에 미치는 영향을 다양한 해석예제를 통해 조사하였다.

Buckling analysis of laminated composite cylindrical shell subjected to lateral displacement-dependent pressure using semi-analytical finite strip method

  • Khayat, Majid;Poorveis, Davood;Moradi, Shapour
    • Steel and Composite Structures
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    • 제22권2호
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    • pp.301-321
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    • 2016
  • The objective of this paper is to investigate buckling behavior of composite laminated cylinders by using semi-analytical finite strip method. The shell is subjected to deformation-dependent loads which remain normal to the shell middle surface throughout the deformation process. The load stiffness matrix, which is responsible for variation of load direction, is also throughout the deformation process. The shell is divided into several closed strips with alignment of their nodal lines in the circumferential direction. The governing equations are derived based on the first-order shear deformation theory with Sanders-type of kinematic nonlinearity. Displacements and rotations of the shell middle surface are approximated by combining polynomial functions in the meridional direction and truncated Fourier series along with an appropriate number of harmonic terms in the circumferential direction. The load stiffness matrix, which is responsible for variation of load direction, is also derived for each strip and after assembling, global load stiffness matrix of the shell is formed. The numerical illustrations concern the pressure stiffness effect on buckling pressure under various conditions. The results indicate that considering pressure stiffness causes buckling pressure reduction which in turn depends on various parameters such as geometry and lay-ups of the shell.

Analysis Of the Joint Structure of the Vehicle Body by Condensed Joint Matrix Method

  • Suh, Myung-Won;Yang, Won-Ho;Jonghwan Suhr
    • Journal of Mechanical Science and Technology
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    • 제15권12호
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    • pp.1639-1646
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    • 2001
  • It is often necessary that the joints characteristics should be determined in the early stage of the vehicle body design. The researches on identification of joints in a vehicle body have been performed until the recent year. In this study, the joint characteristics of vehicle structure were expressed as the condensed matrix forms from the full joint stiffness matrix. The condensed joint stiffness matrix was applied to typical T-type and Edge-type joints, and the usefulness was confirmed. In addition, it was applied to the real center pillar model and the full vehicle body in order to validate the practical application.

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축약 행렬법을 적용한 차체 결합부 해석 (Application of Condensed Joint Matrix Method to the Joint Structure of Vehicle Body)

  • 서종환;서명원;양원호
    • 한국자동차공학회논문집
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    • 제6권4호
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    • pp.9-16
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    • 1998
  • The joint characteristics are necessary to be determined in the early stage of the vehicle body design. Researches on identification of joints in a vehicle body have been performed until the recent year. In this study, the joint characteristics of vehicle struct- ure were expressed as condensed forms from the full joint stiffness and mass matrix. The condensed joint stiffness and mass matrix were applied to typical T-type and Edge-type joints, and the usefulness was confirmed. In addition, those were applied to center pillar and full vehicle body to validate the practical application.

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Dynamic stiffness matrix of composite box beams

  • Kim, Nam-Il
    • Steel and Composite Structures
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    • 제9권5호
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    • pp.473-497
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    • 2009
  • For the spatially coupled free vibration analysis of composite box beams resting on elastic foundation under the axial force, the exact solutions are presented by using the power series method based on the homogeneous form of simultaneous ordinary differential equations. The general vibrational theory for the composite box beam with arbitrary lamination is developed by introducing Vlasov°Øs assumption. Next, the equations of motion and force-displacement relationships are derived from the energy principle and explicit expressions for displacement parameters are presented based on power series expansions of displacement components. Finally, the dynamic stiffness matrix is calculated using force-displacement relationships. In addition, the finite element model based on the classical Hermitian interpolation polynomial is presented. To show the performances of the proposed dynamic stiffness matrix of composite box beam, the numerical solutions are presented and compared with the finite element solutions using the Hermitian beam elements and the results from other researchers. Particularly, the effects of the fiber orientation, the axial force, the elastic foundation, and the boundary condition on the vibrational behavior of composite box beam are investigated parametrically. Also the emphasis is given in showing the phenomenon of vibration mode change.

Numerical modelling of nonlinear behaviour of prestressed concrete continuous beams

  • Lou, Tiejiong;Lopes, Sergio M.R.;Lopes, Adelino V.
    • Computers and Concrete
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    • 제15권3호
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    • pp.373-389
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    • 2015
  • The development of a finite element model for the geometric and material nonlinear analysis of bonded prestressed concrete continuous beams is presented. The nonlinear geometric effect is introduced by the coupling of axial and flexural fields. A layered approach is applied so as to consider different material properties across the depth of a cross section. The proposed method of analysis is formulated based on the Euler-Bernoulli beam theory. According to the total Lagrangian description, the constructed stiffness matrix consists of three components, namely, the material stiffness matrix reflecting the nonlinear material effect, the geometric stiffness matrix reflecting the nonlinear geometric effect and the large displacement stiffness matrix reflecting the large displacement effect. The analysis is capable of predicting the nonlinear behaviour of bonded prestressed concrete continuous beams over the entire loading stage up to failure. Some numerical examples are presented to demonstrate the validity and applicability of the proposed model.

배영계의 진동해소를 위한 주파수종속 요표행렬 (Frequency-Dependent Element Matrices for Vibration Analysis of Piping Systems)

  • 양보석;안영홍;최원호
    • 한국해양공학회지
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    • 제6권2호
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    • pp.125-132
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    • 1992
  • This paper presents an approach for the derivation of frequency-dependent element matrices for vibration analysis of piping systems containing a moving medium. The dynamic stiffness matrix is deduced from transfer matrix, and, in turn, the frequency-dependent element matrices are derived. Numerical examples show that method gives more accurate results than those obtained using the conventional static shape function based element matrices.

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측정 모달 데이터를 이용한 골조의 강성행렬 및 질량행렬 추정에 관한 연구 (A Study on Estimated Stiffness and Mass Matrices from Modal Data at Measured Points)

  • 한동호;이치형;윤성기
    • 한국공간구조학회논문집
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    • 제2권2호
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    • pp.59-67
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    • 2002
  • In this study, a method that estimates stiffness and mass matrices of shear building from modal test data is presented. This method applied of building depends on the number of measurement points that are less in number than the total structural degrees of freedom, and on the first two orders of structural mode measured. By means of this method it is possible to use modal data of unmeasurable points to estimate total stiffness and mass matrices of structure. Some examples are studied in this paper, and its result shows that this method is reliable.

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Damage assessment in periodic structures from measured natural frequencies by a sensitivity and transfer matrix-based method

  • Zhu, Hongping;Li, Lin;Wang, Dansheng
    • Structural Engineering and Mechanics
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    • 제16권1호
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    • pp.17-34
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    • 2003
  • This paper presents a damage assessment procedure applied to periodic spring mass systems using an eigenvalue sensitivity-based method. The damage is directly related to the stiffness reduction of the damage element. The natural frequencies of periodic structures with one single disorder are found by adopting the transfer matrix approach, consequently, the first order approximation of the natural frequencies with respect to the disordered stiffness in different elements is used to form the sensitivity matrix. The analysis shows that the sensitivity of natural frequencies to damage in different locations depends only on the mode number and the location of damage. The stiffness changes due to damage can be identified by solving a set of underdetermined equations based on the sensitivity matrix. The issues associated with many possible damage locations in large structural systems are addressed, and a means of improving the computational efficiency of damage detection while maintaining the accuracy for large periodic structures with limited available measured natural frequencies, is also introduced in this paper. The incomplete measurements and the effect of random error in terms of measurement noise in the natural frequencies are considered. Numerical results of a periodic spring-mass system of 20 degrees of freedom illustrate that the proposed method is simple and robust in locating single or multiple damages in a large periodic structure with a high computational efficiency.

등방성 및 복합재 플레이트용 16절점 요소의 강성행렬 계산 (Evaluation of Stiffness Matrix of 3-Dimensional Elements for Isotropic and Composite Plates)

  • 윤태혁;김정운;이재복
    • 대한기계학회논문집
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    • 제18권10호
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    • pp.2640-2652
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    • 1994
  • The stiffness of 6-node isotropic element is stiffer than that of 8-node isotropic element of same configuration. This phenomenon was called 'Relative Stiffness Stiffening Phenomenon'. In this paper, an equation of sampling point modification which correct this phenomenon was derived for the composite plate, as well as an equation for an isotropic plate. The relative stiffness stiffening phenomena of an isotropic plate element could be corrected by modifying Gauss sampling points in the numerical integration of stiffness matrix. This technique could also be successfully applied to the static analyses of composite plate modeled by the 3-dimensional 16-node elements. We predicted theoretical errors of stiffness versus the number of layers that result from the reduction of numerical integration order. These errors coincide very well with the actual errors of stiffness. Therefore, we can choose full integration of reduced integration based upon the permissible error criterion and the number of layers by using the thoretically predicted error.