On the Modeling of Shells in Multibody Dynamics

Energy preserving/decaying schemes are presented for the simulation ofthe nonlinear multibody systems involving shell components. Theproposed schemes are designed to meet four specific requirements:unconditional nonlinear stability of the scheme, a rigorous treatmentof both geometric and material nonlinearities, exact satisfaction ofthe constraints, and the presence of high frequency numericaldissipation. The kinematic nonlinearities associated with arbitrarilylarge displacements and rotations of shells are treated in a rigorousmanner, and the material nonlinearities can be handled when theconstitutive laws stem from the existence of a strain energy densityfunction. The efficiency and robustness of the proposed approach isillustrated with specific numerical examples that also demonstrate theneed for integration schemes possessing high frequency numericaldissipation.     

A non-linear beam space-time finite element formulation using quaternion algebra: interpolation of the Lagrange multipliers and the appearance of spurious modes

In this work a three-field space-time beam finite element formulation is expressed in quaternion algebra. The unitary quaternion condition is enforced by means of an extension of the augmented Lagrangian method.The continuity requirements implied by the constrained energy principle obtained in this way lead to interpolations of the Lagrange multipliers which prove to be inappropriate when the beam is subject to certain boundary conditions. In particular, the tangent matrix becomes singular and the eigenvector of the multiplier degrees of freedom associated with the zero eigenvalue presents a checkerboard pattern. It is shown that this pathological behavior can be avoided if continuous-multiplier elements are employed.     

Anisotropic mesh adaption by metric‐driven optimization

We describe a Gauss–Seidel algorithm for optimizing a three‐dimensional unstructured grid so as to conform to a given metric. The objective function for the optimization process is based on the maximum value of an elemental residual measuring the distance of any simplex in the grid to the local target metric. We analyse different possible choices for the objective function, and we highlight their relative merits and deficiencies. Alternative strategies for conducting the optimization are compared and contrasted in terms of resulting grid quality and computational costs. Numerical simulations are used for demonstrating the features of the proposed methodology, and for studying some of its characteristics. Copyright © 2004 John Wiley & Sons, Ltd.     

Power curve tracking in the presence of a tip speed constraint

This paper considers the problem of power regulation for a variable speed wind turbine in the presence of a blade tip speed constraint, for example to limit noise emissions. The main contribution of the paper is the formulation of a policy for the regulation of the machine in the transition region between the classical regions II and III that accommodates the tip speed constraint, and the derivation of associated wind schedules for the rotor speed, blade pitch and aerodynamic torque. To exemplify the possible use of such wind schedules in the design of control laws, model-based controllers are formulated in this paper that are capable of performing power curve tracking throughout all wind speeds, in contrast with commonly adopted approaches that use switching controllers to cover the various operating regimes of the machine. The proposed regulation policies and control laws are demonstrated in a high fidelity simulation environment for a representative 3 MW machine.     

An Attempt at the Classification of Energy Decaying Schemes for Structural and Multibody Dynamics

This paper analyzes the formulation of energy preserving/decaying schemes for dynamics problems. We argue that any energy preserving/decaying scheme can always be seen as composed of an underlying temporal discretization, that is then slightly modified in order to prove a discrete energy bound within a time step. While the details of the modified scheme depend in a critical way on the governing equations, the underlying discretization can in principle be applied to a variety of models. We review some of the temporal underlying schemes recently proposed in the literature, presenting them with a common notation. We show their similarities and highlight their differences.     

Metric-driven mesh optimization using a local simulated annealing algorithm

We report on results obtained with a metric-driven mesh optimization procedure for simplicial meshes based on the simulated annealing (SA) method. The use of SA improves the chances of removing pathological clusters of bad elements, that have the tendency to lock into frozen configurations in difficult regions of the model such as corners and complex face intersections, prejudicing the overall quality of the final grid. A local version of the algorithm is developed that significantly lowers the computational cost. Numerical examples illustrate the effectiveness of the proposed methodology, which is compared to a classical greedy Gauss–Seidel optimization. Substantial improvement in the quality of the worst elements of the grid is observed for the local simulated annealing optimization. Furthermore, the method appears to be robust to the choice of the algorithmic parameters. Copyright © 2006 John Wiley & Sons, Ltd.