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A TORSIONAL SPRING‐LIKE BEAM ELEMENT FOR THE DYNAMIC ANALYSIS OF FLEXIBLE MULTIBODY SYSTEMS
Author(s) -
WASFY T. M.
Publication year - 1996
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19960415)39:7<1079::aid-nme765>3.0.co;2-w
Subject(s) - finite element method , equations of motion , multibody system , beam (structure) , bending , rigid body , inertia , spring (device) , classical mechanics , degrees of freedom (physics and chemistry) , structural engineering , mathematical analysis , physics , mathematics , engineering , quantum mechanics
A new finite element beam formulation for modelling flexible multibody systems undergoing large rigid‐body motion and large deflections is developed. In this formulation, the motion of the ‘nodes’ is referred to a global inertial reference frame. Only Cartesian position co‐ordinates are used as degrees of freedom. The beam element is divided into two subelements. The first element is a truss element which gives the axial response. The second element is a torsional spring‐like bending element which gives the transverse bending response. D'Alembert principle is directly used to derive the system's equations of motion by invoking the equilibrium, at the nodes, of inertia forces, structural (internal) forces and externally applied forces. Structural forces on a node are calculated from the state of deformation of the elements surrounding that node. Each element has a convected frame which translates and rotates with it. This frame is used to determine the flexible deformations of the element and to extract those deformations from the total element motion. The equations of motion are solved along with constraint equations using a direct iterative integration scheme. Two numerical examples which were presented in earlier literature are solved to demonstrate the features and accuracy of the new method.