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  • Open AccessOpen Access

    EDITORIAL

    Advances in Finite Rotations in Structural Mechanics

    M. Iura, S. N. Atluri
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 213-216, 2003, DOI:10.3970/cmes.2003.004.213
    Abstract This article has no abstract. More >

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    1308

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    923

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    ARTICLE

    Finite Rotations and large Strains in Finite Element Shell Analysis

    Y. Başar, O. Kintzel1
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 217-230, 2003, DOI:10.3970/cmes.2003.004.217
    Abstract The objective of this contribution is the development of a finite element model for finite rotation and large strain analysis of thin walled shells involving geometry intersections. The shell configuration is described by a linear polynomial in the thickness coordinate. The director of the shell is multiplicatively decomposed into a stretching parameter and an inextensible unit vector whose rotation is accomplished by an updated-rotation formulation. A rotation vector with three independent components is used throughout the shell which permits advantageously to consider smooth shells and compound shells by a unified procedure. This formulation is introduced into an isoparametric four-node element.… More >

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    1337

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    1385

  • Open AccessOpen Access

    ARTICLE

    On Deformation of an Euler-Bernolli Beam Under Terminal Force and Couple

    P.B. Béda1
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 231-238, 2003, DOI:10.3970/cmes.2003.004.231
    Abstract The paper studies the behavior of a spatial Euler-Bernoulli beam loaded by a terminal thrusting force and a couple. The classical Clebsch-Kirchhoff equilibrium equations are written by using appropriate angular coordinates describing the finite rotations of the local frames attached to each cross-sections of the beam with respect to a fixed system. When we have geometric boundary conditions at one end and dynamic boundary conditions (a force and a couple) at the other the set of equilibrium equations form and initial value probem which can easily be solved with standard Runge-Kutta method. More >

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    921

  • Open AccessOpen Access

    ARTICLE

    Element Coordinates and the Utility in Large Displacement Analysis of a Space Frame

    K. Ijima1, H. Obiya1, S. Iguchi2, S. Goto2
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 239-248, 2003, DOI:10.3970/cmes.2003.004.239
    Abstract Defining element coordinates in space frame, element end deformations become statically clear from the energy principle. Therefore, the deformations can be expressed by nodal displacement without any approximation. The paper indicates that the exact expressions of the deformations and the geometrical stiffness strictly based on the equations makes large displacement analysis of space frame possible with robustness on the computation. More >

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    1107

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    925

  • Open AccessOpen Access

    ARTICLE

    Accuracy of Co-rotational Formulation for 3-D Timoshenko's Beam

    M. Iura1, Y. Suetake2, S. N. Atluri3
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 249-258, 2003, DOI:10.3970/cmes.2003.004.249
    Abstract An accuracy of finite element solutions for 3-D Timoshenko's beams, obtained using a co-rotational formulation, is discussed. The co-rotational formulation has often been used with an assumption that the relative deformations are small. A fundamental question, therefore, has been raised as to whether or not the numerical solutions obtained approach the solutions of the exact theory. In this paper, from theoretical point of view, we investigate the accuracy of the co-rotational formulation for 3-D Timoshenko's beam undergoing finite strains and finite rotations. It is shown that the use of the conventional secant coordinates fails to give satisfactory numerical solutions. We… More >

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    1212

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    1029

  • Open AccessOpen Access

    ARTICLE

    A Buckling and Postbuckling Analysis of Rods Under End Torque and Compressive Load

    Wen Yi Lin1, Kuo Mo Hsiao2
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 259-272, 2003, DOI:10.3970/cmes.2003.004.259
    Abstract The buckling and postbuckling behavior of spatial rods under different types of end torque and compressive axial force is investigated using finite element method. All coupling among bending, twisting, and stretching deformations for beam element is considered by consistent second-order linearization of the fully geometrically nonlinear beam theory. However, the third order term of the twist rate is also considered. An incremental-iterative method based on the Newton-Raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations. The zero value of the tangent stiffness matrix determinant of the structure is used… More >

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    1287

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    1117

  • Open AccessOpen Access

    ARTICLE

    A Conservative Time Integration Scheme for Dynamics of Elasto-damaged Thin Shells

    L. Briseghella1, C. Majorana1, P. Pavan1
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 273-286, 2003, DOI:10.3970/cmes.2003.004.273
    Abstract Some aspects of the application of a conservative time integration scheme to the non-linear dynamics of elasto-damaged thin shells are presented. The main characteristic of the scheme is to be conservative, in the sense that it allows the time-discrete system to preserve the basic laws of continuum, namely the balance of the linear and angular momenta as well as the fulfilment of the second law of thermodynamic. Here the method is applied to thin shells under large displacements and rotations. The constitutive model adopted is built coupling the linear elastic model of De Saint Venant-Kirchhoff with a scalar damage function… More >

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    1193

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    904

  • Open AccessOpen Access

    ARTICLE

    Finite-Element Nonlinear Dynamics of Flexible Structures in Three Dimensions

    S. Okamoto1, Y. Omura1
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 287-300, 2003, DOI:10.3970/cmes.2003.004.287
    Abstract The purpose of this study is to develop a procedure for performing a dynamic analysis in the case that a structure undergoes large translational and rotational displacements when moving along a nonlinear trajectory at variable velocity. Finite-element equations of motion that include the inertial force of the structure's motion have been derived. The equations also account for the geometric nonlinearity that has to be considered in a problem of finite translational and rotational displacements. A finite rotational matrix was used to transfer vectors or matrices measured in a certain coordinate frame to those measured in another coordinate frame. The computational… More >

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    1382

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    954

  • Open AccessOpen Access

    ARTICLE

    A new finite element formulation of three-dimensional beam theory based on interpolation of curvature

    D. Zupan1, M. Saje1
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 301-318, 2003, DOI:10.3970/cmes.2003.004.301
    Abstract A new finite element formulation of the `kinematically exact finite-strain beam theory' is presented. The finite element formulation employs the generalized virtual work in which the main role is played by the pseudo-curvature vector. The solution of the governing equations is found by using a combined Galerkin-collocation algorithm. More >

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    1320

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    949

  • Open AccessOpen Access

    ARTICLE

    Finite Displacement Analysis Using Rotational Degrees of Freedom about Three Right-angled Axes

    Humihiko Gotou1, Takashi Kuwataka1, Terumasa Nishihara1, Tetsuo Iwakuma1
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 319-328, 2003, DOI:10.3970/cmes.2003.004.319
    Abstract The stiffness equation in finite displacement problems is often derived from the virtual work equation, partly in order to avoid the complicated formulation based on the potential functional. Describing the virtual rotational angles by infinitesimal rotational angles about three axes of the right-angled Cartesian coordinate system, we formulate tangent stiffness equations whose rotational degrees of freedom are described by rotational angles about the three axes. The rotational degrees of freedom are useful to treat three rotational components in nodal displacement vectors as vector components for coordinate transformation, when non-vector components like Euler's angles are used to describe finite rotations. In… More >

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    1179

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    1043

  • Open AccessOpen Access

    ARTICLE

    Variational Formulation and Symmetric Tangent Operator for Shells with Finite Rotation Field

    Yoshitaka Suetake1, Masashi Iura2, S. N. Atluri3
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 329-336, 2003, DOI:10.3970/cmes.2003.004.329
    Abstract The objective of this paper is to examine the symmetry of the tangent operator for nonlinear shell theories with the finite rotation field. As well known, it has been stated that since the rotation field carries the Lie group structure, not a vector space one, the tangent operator incorporating the rotation field does not become symmetric. In this paper, however, it is shown that by adopting a rotation vector as a variable, the symmetry can be achieved in the Lagrangean (material) description. First, we present a general concept for the problem. Next, we adopt the finitely deformed thick shell problem… More >

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    1178

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    882

  • Open AccessOpen Access

    ARTICLE

    Shape Optimization of Elastic Structural Systems Undergoing Large Rotations: Simultaneous Solution Procedure

    Adnan Ibrahimbegovic1, Catherine Knopf-Lenoir2
    CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 337-344, 2003, DOI:10.3970/cmes.2003.004.337
    Abstract In this work we present an unconventional procedure for combining the optimal shape design and nonlinear analysis in mechanics. The main goal of the presented procedure is to enhance computational efficiency for nonlinear problems with respect to the conventional, sequential approach by solving the analysis and design phases simultaneously. A detailed development is presented for the chosen model problem, the 3d rod undergoing large rotations. More >

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    923

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