• Title/Summary/Keyword: finite-deflections

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Post-buckling analysis of Timoshenko beams with various boundary conditions under non-uniform thermal loading

  • Kocaturk, Turgut;Akbas, Seref Doguscan
    • Structural Engineering and Mechanics
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    • v.40 no.3
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    • pp.347-371
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    • 2011
  • This paper focuses on post-buckling analysis of Timoshenko beams with various boundary conditions subjected to a non-uniform thermal loading by using the total Lagrangian Timoshenko beam element approximation. Six types of support conditions for the beams are considered. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. As far as the authors know, there is no study on the post-buckling analysis of Timoshenko beams under uniform and non-uniform thermal loading considering full geometric non-linearity investigated by using finite element method. The convergence studies are made and the obtained results are compared with the published results. In the study, the relationships between deflections, end rotational angles, end constraint forces, thermal buckling configuration, stress distributions through the thickness of the beams and temperature rising are illustrated in detail in post-buckling case.

Secondary buckling analysis of spherical caps

  • Kato, Shiro;Chiba, Yoshinao;Mutoh, Itaru
    • Structural Engineering and Mechanics
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    • v.5 no.6
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    • pp.715-728
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    • 1997
  • The aim of this paper is to investigate the secondary buckling behaviour and mode-coupling of spherical caps under uniformly external pressure. The analysis makes use of a rotational finite shell element on the basis of strain-displacement relations according to Koiter's shell theory (Small Finite Deflections). The post-buckling behaviours after a bifurcation point are analyzed precisely by considering multi-mode coupling between several higher order harmonic wave numbers: and on the way of post-buckling path the positive definiteness of incremental stiffness matrix of uncoupled modes is examined step by step. The secondary buckling point that has zero eigen-value of incremental stiffness matrix and the corresponding secondary mode are obtained, moreover, the secondary post-buckling path is traced.

Convergence studies on static and dynamic analysis of beams by using the U-transformation method and finite difference method

  • Yang, Y.;Cai, M.;Liu, J.K.
    • Structural Engineering and Mechanics
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    • v.31 no.4
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    • pp.383-392
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    • 2009
  • The static and dynamic analyses of simply supported beams are studied by using the U-transformation method and the finite difference method. When the beam is divided into the mesh of equal elements, the mesh may be treated as a periodic structure. After an equivalent cyclic periodic system is established, the difference governing equation for such an equivalent system can be uncoupled by applying the U-transformation. Therefore, a set of single-degree-of-freedom equations is formed. These equations can be used to obtain exact analytical solutions of the deflections, bending moments, buckling loads, natural frequencies and dynamic responses of the beam subjected to particular loads or excitations. When the number of elements approaches to infinity, the exact error expression and the exact convergence rates of the difference solutions are obtained. These exact results cannot be easily derived if other methods are used instead.

Post-buckling analysis of Timoshenko beams made of functionally graded material under thermal loading

  • Kocaturk, Turgut;Akbas, Seref Doguscan
    • Structural Engineering and Mechanics
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    • v.41 no.6
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    • pp.775-789
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    • 2012
  • This paper focuses on post-buckling analysis of functionally graded Timoshenko beam subjected to thermal loading by using the total Lagrangian Timoshenko beam element approximation. Material properties of the beam change in the thickness direction according to a power-law function. The beam is clamped at both ends. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. As far as the authors know, there is no study on the post-buckling analysis of functionally graded Timoshenko beams under thermal loading considering full geometric non-linearity investigated by using finite element method. The convergence studies are made and the obtained results are compared with the published results. In the study, with the effects of material gradient property and thermal load, the relationships between deflections, end constraint forces, thermal buckling configuration and stress distributions through the thickness of the beams are illustrated in detail in post-buckling case.

Strengthening Effect of Reinforced Concrete Beam at Different Loading Stages (재하상태에 따른 철근콘크리트 보의 보강효과)

  • 이차돈;이학주
    • Proceedings of the Korea Concrete Institute Conference
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    • 1999.04a
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    • pp.733-739
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    • 1999
  • A theoretical model for flexural behavior of strengthened reinforced concrete beam is developed based on displacement controlled nonlinear finite element method in this study. The developed model is shown to reasonably reproducing the experimental results of variously strengthened reinforced concrete beam. Parametric studies for the strengthened reinforced concrete beam at different loading stages are then performed using this model in order to assess the effect of loading stages at the time of strengthening on characteristic values of strengthened beam under flexure. It was found that depending on loading stages of a beam, deflections at yielding and at ultimate loads are more influenced than corresponding load capacities.

Analysis of Nonlinear Forced Vibrations by Ritz Vectors for a Stepped Beam (Ritz벡터를 이용한 변단면 보의 비선형 강제진동 해석)

  • 심재수;박명균
    • Computational Structural Engineering
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    • v.6 no.1
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    • pp.99-105
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    • 1993
  • A Stepped beam with immovable ends under forced vibrations with large amplitude is investigated by using the finite element method and the Ritz vectors. Unlike the Eigen vectors, the Ritz vectors are generated by a simple recurrence relation. Moreover the Ritz vectors yield much faster convergence with respect to the number of vectors used than the use of Eigen vectors. The computer program is developed for nonlinear analysis using Ritz vectors instead of Eigen vectors and numerical examples are analysed for deflections and natural frequencies of stepped beam under various support conditions. Results show that the proposed method is valid and efficient.

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Variability of Deflections for Reinforced Concrete Flat Plate (철근 콘크리트 플랫 플레이트 처짐의 변동성 평가)

  • Kim, Min Sook;Jo, Eunsun;Lee, Young Hak
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.27 no.6
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    • pp.543-549
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    • 2014
  • The deflection of reinforced concrete members can be highly variable, due to uncertainties in the characteristics of the concrete. However, current standards do not take this problem into account, instead recommending only the minimum thickness and maximum allowable deflections based on empirical data. This paper is aimed at evaluation deflection variabilities by applying a probabilistic analysis model to a finite element analysis model. To evaluate the variabilities of deflections, a Monte Carlo simulation, which incorporated the eight parameters related to concrete, reinforcement, member size, and tension stiffening. The results showed that lager spans were more sensitive to the deflection due to loads and that as the applied live loads were increases and the slab thickness were decreased, the deflection variability increased.

Design of Subsea Manifold Protective Structure against Dropped Object Impacts (낙하체 충돌을 고려한 심해저 매니폴드 보호 구조물 설계)

  • Woo, Sun-Hong;Lee, Kangsu;Choung, Joonmo
    • Journal of Ocean Engineering and Technology
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    • v.31 no.3
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    • pp.233-240
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    • 2017
  • Subsea structures are always vulnerable to accidental risks induced by fishing gear, dropped objects, etc. This paper presents the design of a subsea manifold protective structure that protects against dropped object impacts. Probable dropped object scenarios were established considering the shapes and masses of the dropped objects. A design layout for the manifold protective structure was proposed, with detailed scantlings and material specifications. A method applicable to the pipelines specified in DNV-RP-F107(DNV, 2010) was applied to calculate the annual probabilities of dropped objects hitting the subsea manifold. Nonlinear finite element analyses provided the structural consequences due to the dropped object impacts such as the maximum deflections of the protective structure and the local fracture occurrences. A user-subroutine to implement the three-dimensional fracture strain surface was used to determine whether local fractures occur. The proposed protective structure was shown to withstand the dropped object impact loads in terms of the maximum deflections, even though local fractures could induce accelerated corrosion.

Bending of a cracked functionally graded nanobeam

  • Akbas, Seref Doguscan
    • Advances in nano research
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    • v.6 no.3
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    • pp.219-242
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    • 2018
  • In this study, static bending of an edge cracked cantilever nanobeam composed of functionally graded material (FGM) subjected to transversal point load at the free end of the beam is investigated based on modified couple stress theory. Material properties of the beam change in the height direction according to exponential distributions. The cracked nanobeam is modelled using a proper modification of the classical cracked-beam theory consisting of two sub-nanobeams connected through a massless elastic rotational spring. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new non-classical beam model reduces to the classical beam model when the length scale parameter is set to zero. The considered problem is investigated within the Euler-Bernoulli beam theory by using finite element method. In order to establish the accuracy of the present formulation and results, the deflections are obtained, and compared with the published results available in the literature. Good agreement is observed. In the numerical study, the static deflections of the edge cracked FGM nanobeams are calculated and discussed for different crack positions, different lengths of the beam, different length scale parameter, different crack depths, and different material distributions. Also, the difference between the classical beam theory and modified couple stress theory is investigated for static bending of edge cracked FGM nanobeams. It is believed that the tabulated results will be a reference with which other researchers can compare their results.

Large deflection analysis of orthotropic, elliptic membranes

  • Chucheepsakul, Somchai;Kaewunruen, Sakdirat;Suwanarat, Apiwat
    • Structural Engineering and Mechanics
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    • v.31 no.6
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    • pp.625-638
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    • 2009
  • Applications of membrane mechanisms are widely found in nano-devices and nano-sensor technologies nowadays. An alternative approach for large deflection analysis of the orthotropic, elliptic membranes - subject to gravitational, uniform pressures often found in nano-sensors - is described in this paper. The material properties of membranes are assumed to be orthogonally isotropic and linearly elastic, while the principal directions of elasticity are parallel to the coordinate axes. Formulating the potential energy functional of the orthotropic, elliptic membranes involves the strain energy that is attributed to inplane stress resultant and the potential energy due to applied pressures. In the solution method, Rayleigh-Ritz method can be used successfully to minimize the resulting total potential energy generated. The set of equilibrium equations was solved subsequently by Newton-Raphson. The unparalleled model formulation capable of analyzing the large deflections of both circular and elliptic membranes is verified by making numerical comparisons with existing results of circular membranes as well as finite element solutions. The results are found in excellent agreements at all cases. Then, the parametric investigations are given to delineate the impacts of the aspect ratios and orthotropic elasticity on large static tensions and deformations of the orthotropic, elliptic membranes.