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Shock and Vibration
Volume 19 (2012), Issue 6, Pages 1445-1461

Optimization Design of Structures Subjected to Transient Loads Using First and Second Derivatives of Dynamic Displacement and Stress

Qimao Liu,1 Jing Zhang,3 and Liubin Yan2

1Department of Civil and Structural Engineering, Aalto University, Espoo, Finland
2College of Civil and Architecture Engineering, Guangxi University, Nanning, China
3Department of Mechanical Engineering, Indiana University-Purdue University Indianapolis, Indianapolis, IN, USA

Received 16 September 2010; Revised 19 July 2011

Copyright © 2012 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.


This paper developed an effective optimization method, i.e., gradient-Hessian matrix-based method or second order method, of frame structures subjected to the transient loads. An algorithm of first and second derivatives of dynamic displacement and stress with respect to design variables is formulated based on the Newmark method. The inequality time-dependent constraint problem is converted into a sequence of appropriately formed time-independent unconstrained problems using the integral interior point penalty function method. The gradient and Hessian matrixes of the integral interior point penalty functions are also computed. Then the Marquardt's method is employed to solve unconstrained problems. The numerical results show that the optimal design method proposed in this paper can obtain the local optimum design of frame structures and sometimes is more efficient than the augmented Lagrange multiplier method.