Z. D. Han¹, A. M. Rajendran², S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 1-12, 2005, DOI:10.3970/cmes.2005.010.001

Abstract A nonlinear formulation of the Meshless Local Petrov-Galerkin (MLPG) finite-volume mixed method is developed for the large deformation analysis of static and dynamic problems. In the present MLPG large deformation formulation, the velocity gradients are interpolated independently, to avoid the time consuming differentiations of the shape functions at all integration points. The nodal values of velocity gradients are expressed in terms of the independently interpolated nodal values of displacements (or velocities), by enforcing the compatibility conditions directly at the nodal points. For validating the present large deformation MLPG formulation, two example problems are considered: 1) large deformations and rotations of… More >

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 >

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 >

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 >

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 >

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 >

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 >

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 >

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 >

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 >