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.
Compdyn 2013. 4th Eccomas Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, 2013
Conservative Time Integration; Rigid Body Rotations; Implicit Constraints; Structural Dynamics
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4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, 2013