A Locking-Free Approximation of Curved Rods by Straight Beam Elements
نویسنده
چکیده
We consider an elastic model for a curved rod with arbitrary threedimensional geometry, incorporating shear and membrane as well as bending and torsion effects. We define an approximation procedure based on a discretization by linear Timoshenko beam elements. Introducing an equivalent mixed problem, we establish optimal error estimates independent of the thickness, thereby proving that shear and membrane locking is avoided. The approximation scheme is tested on specific examples and the numerical results confirm the estimates obtained by theory.
منابع مشابه
Non Uniform Rational B Spline (NURBS) Based Non-Linear Analysis of Straight Beams with Mixed Formulations
Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, tota...
متن کاملNonlinear Finite Element Analysis of Bending of Straight Beams Using hp-Spectral Approximations
Displacement finite element models of various beam theories have been developed using traditional finite element interpolations (i.e., Hermite cubic or equi-spaced Lagrange functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation φ and/or shear strain γxz, or in the integral form u...
متن کاملA Linear Thick Curved Beam Element
Early attempts to derive curved beam and shell elements in a curvilinear system were dramatically unsuccessful. This was wrongly attributed to the failure of these elements to recover strain-free rigid body displacement modes in a curvilinear co-ordinate description. Recent evidence points to a ‘membrane locking’ phenomenon that arises when constrained strain fields corresponding to inextension...
متن کاملNumerical solution of base shear in high tensioned cable antenna
A finite element solution based on equevalent elements is proposed for the static and dynamic analysis of tallhigh tensioned cable antennas. To reduce high number of degrees of freedom in space frame body of a structure, a simple equivalent beam element is defined for each simulative substructure. This numerical procedure is applicable to analyze complex three dimensional assemblies of substruc...
متن کاملBeam & Shell Models for Composite Straight or Curved Bridge Decks with Intermediate Diaphragms & Assessment of Design Specifications
In this research effort, the generalized warping and distortional problem of straight or horizontally curved composite beams of arbitrary cross section, loading and boundary conditions is presented. An inclined plane of curvature is considered. Additionally, the stiffness of diaphragmatic plates has been introduced in the formulation in order to compare with the case where rigid diaphragms are ...
متن کامل