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Shock and Vibration
Volume 17, Issue 4-5, Pages 641-649

Multicriteria Optimization of Injury Prevention Systems to Impact

J.B. Cardoso,1 P.P. Moita,2 and A.J. Valido2

1Instituto Superior Técnico, Departamento de Engenharia Mecânica, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
2Escola Superior de Tecnologia de Setúbal, Campus do IPS, 2914-508 Setúbal, Portugal

Received 18 June 2010; Accepted 18 June 2010

Copyright © 2010 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A sensitivity analysis and multicriteria control optimization formulation is derived for mechanical systems. This formulation is implemented into an interactive optimum design code and it is applied to optimize protection systems for the prevention of injuries. The limiting isolation capabilities of the systems are determined. The effect of pre-acting control is investigated. Control forces as well as the time at which the control should act before the instant of impact are considered as design variables. The same idea used by the authors in previous articles for minimum time control problems is applied here to find the preview time. Dynamic response index, maximum acceleration, rattlespace, or maximum power of the resisting force among others can be used as performance criteria. In order to handle the multicriteria problem, both the reduced feasible region method and a min-max upper bound method are utilized. The adjoint system approach is used to calculate the sensitivities. The dynamic response of the systems and its sensitivity are discretized via space-time finite elements. The equations of motion and the sensitivity equations are integrated at-once as it is typical for the static response. This way, displacement, velocity or acceleration control conditions can be imposed easily at any point in time. Also, adjoint system response is obtained without needing primary response memorization. Mathematical programming is used for the optimal control process.