Abstract
A conservative time integration algorithm based on a convected set of orthonormal base vectors is presented. The equations of motion are derived from an extended Hamiltonian formulation, combining the components of the three base vectors with a set of orthonormality constraints. The particular form of the kinetic energy used in the present formulation is deliberately chosen to correspond to a rigid body rotation, and the orthonormality constraints are introduced via the equivalent Green strain components of the base vectors. The particular form of the extended inertia tensor used here implies a set of orthogonality relations between the base vector components and their conjugate momentum components. These orthogonality relations permit explicit elimination of the Lagrange multipliers associated with the constraints, leading to a projected form of the dynamic equation without explicit algebraic constraints. The differential equations of motion are recast into discrete form using a suitable combination of mean values and increments, which is identified by considering a finite increment of the Hamiltonian. Examples illustrate the accuracy and conservation properties of the algorithm.
Original language | English |
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Title of host publication | COMPDYN 2013. 4th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering |
Editors | M. Papadrakakis, V. Papadopoulos, V. Plevris |
Number of pages | 9 |
Publication date | 2013 |
Publication status | Published - 2013 |
Event | 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering - Kos Island, Greece Duration: 12 Jun 2013 → 14 Jun 2013 http://www.compdyn2013.org/ |
Conference
Conference | 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering |
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Country/Territory | Greece |
City | Kos Island |
Period | 12/06/2013 → 14/06/2013 |
Internet address |
Keywords
- Conservative Time Integration
- Rigid Body Rotations
- Implicit Constraints
- Structural Dynamics