Local Co-ordinate System (local + co-ordinate_system)

Distribution by Scientific Domains


Selected Abstracts


A quadrilateral thin shell element based on area co-ordinate for explicit dynamic analysis

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2003
Zhu Yaqun
Abstract The mechanism of explicit dynamic finite element method for shell deformation analysis and the key influential factors on computation precision and efficiency are briefly described. A new area co-ordinate-based quadrilateral thin shell element is put forward and combined with the co-rotational theory and velocity strain formulation in the shell stress and strain analysis. A new local co-ordinate system is constructed in which normal vector is much closer to the material axis. The more accurate integration can be obtained and the hourglass control is avoided. Therefore simulation precision and efficiency of thin shells are improved. Copyright 2003 John Wiley & Sons, Ltd. [source]


Accurate eight-node hexahedral element

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2007
Magnus Fredriksson
Abstract Based on the assumed strain method, an eight-node hexahedral element is proposed. Consistent choice of the fundamental element stiffness guarantees convergence and fulfillment of the patch test a priori. In conjunction with a ,-projection operator, the higher order strain field becomes orthogonal to rigid body and linear displacement fields. The higher order strain field in question is carefully selected to preserve correct rank for the element stiffness matrix, also for distorted elements. Volumetric locking is also removed effectively. By considerations of the bending energy, improved accuracy is obtained even for coarse element meshes. The choice of local co-ordinate system aligned with the principal axes of inertia makes it possible to improve the performance even for distorted elements. The strain-driven format obtained is well suited for materials with non-linear stress,strain relations. Several numerical examples are presented where the excellent performance of the proposed eight-node hexahedral is verified. Copyright 2007 John Wiley & Sons, Ltd. [source]


Moving least-square interpolants in the hybrid particle method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2005
H. Huang
Abstract The hybrid particle method (HPM) is a particle-based method for the solution of high-speed dynamic structural problems. In the current formulation of the HPM, a moving least-squares (MLS) interpolant is used to compute the derivatives of stress and velocity components. Compared with the use of the MLS interpolant at interior particles, the boundary particles require two additional treatments in order to compute the derivatives accurately. These are the rotation of the local co-ordinate system and the imposition of boundary constraints, respectively. In this paper, it is first shown that the derivatives found by the MLS interpolant based on a complete polynomial are indifferent to the orientation of the co-ordinate system. Secondly, it is shown that imposing boundary constraints is equivalent to employing ghost particles with proper values assigned at these particles. The latter can further be viewed as placing the boundary particle in the centre of a neighbourhood that is formed jointly by the original neighbouring particles and the ghost particles. The benefit of providing a symmetric or a full circle of neighbouring points is revealed by examining the error terms generated in approximating the derivatives of a Taylor polynomial by using a linear-polynomial-based MLS interpolant. Symmetric boundaries have mostly been treated by using ghost particles in various versions of the available particle methods that are based on the strong form of the conservation equations. In light of the equivalence of the respective treatments of imposing boundary constraints and adding ghost particles, an alternative treatment for symmetry boundaries is proposed that involves imposing only the symmetry boundary constraints for the HPM. Numerical results are presented to demonstrate the validity of the proposed approach for symmetric boundaries in an axisymmetric impact problem. Copyright 2005 John Wiley & Sons, Ltd. [source]


Spherical harmonics in a non-polar co-ordinate system and application to Fourier series in 2-sphere,

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2007
H. M. Nasir
Abstract A new non-polar spherical co-ordinate system for the three-dimensional space is introduced. The co-ordinate system is composed of six local co-ordinate systems mapped from six faces of a cube on to the 2-sphere. Weakly orthogonal and orthogonal spherical harmonics are constructed in this co-ordinate system. The spherical harmonics are easily computable functions consisting of polynomials and square root of polynomials. Examples of finite Fourier series computations are given in terms of the new spherical harmonics to demonstrate their immediate applicability. Copyright 2007 John Wiley & Sons, Ltd. [source]