## Abstract

Nodal coordinates are referred to a fixed configuration in the conventional equations of equilibrium. Nodal coordinates are referred to the initial configuration in the total Lagrangian formulation and to the last calculated configuration in the updated Lagrangian formulation. This research proposes to use the relative nodal coordinates in representing the position and orientation for a node. Since the nodal coordinates are measured relative to its adjacent nodal reference frame, they are still small for a structure undergoing large deformations if the element sizes are small. As a consequence, many element formulations developed under small deformation assumptions are still valid for structures undergoing large deformations, which significantly simplifies the equations of equilibrium. A structural system is represented by a graph to systematically develop the governing equations of equilibrium for general systems. A node and an element are represented by a node and an edge in graph form, respectively. Closed loops are opened to form a tree topology by cutting edges. Two computational sequences are defined in a graph. One is the forward path sequence that is used to recover the Cartesian nodal deformations from relative nodal displacements and traverses a graph from the base node towards the terminal nodes. The other is the backward path sequence that is used to recover the nodal forces in the relative coordinate system from the known nodal forces in the absolute coordinate system and traverses from the terminal nodes towards the base node. One open loop and one closed loop structure undergoing large displacements are analyzed to demonstrate the efficiency and validity of the proposed method.

Original language | English |
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Pages | 115-122 |

Number of pages | 8 |

Publication status | Published - 2001 |

Event | 18th Biennial Conference on Mechanical Vibration and Noise - Pittsburgh, PA, United States Duration: 9 Sept 2001 → 12 Sept 2001 |

### Conference

Conference | 18th Biennial Conference on Mechanical Vibration and Noise |
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Country/Territory | United States |

City | Pittsburgh, PA |

Period | 9/09/01 → 12/09/01 |

### Bibliographical note

Funding Information:This research was supported by Advanced Highway Research Center, Hanyang University, sponsored by KOSEF.