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Structural topology synthesis with dynamics and nonlinearities using equivalent linear systems

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Abstract

Topology optimization for nonlinear and dynamic problems is expensive because of the necessity to solve the equations of motion at every optimization iteration in order to evaluate the objective function and constraints. In this work, an iterative methodology is developed using the concept of an equivalent linear system for the topology synthesis of structures undergoing nonlinear and dynamic response, using minimal nonlinear response evaluations. The approach uses equivalent loads obtained from nonlinear dynamic analysis to perform optimization iterations, during the course of which the nonlinear and dynamic system is continuously approximated. In this process, the optimization is decoupled from the nonlinear dynamic analysis. Results are presented for various kinds of nonlinear and dynamic problems showing the effectiveness of the developed approach.

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Acknowledgements

The authors are thankful to Dr. Prakash D. Mangalgiri and Dr. Narendran Balan of General Motors, India Science Lab., Bangalore, India, for reviewing the manuscript and providing important suggestions.

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Authors and Affiliations

  1. India Science Lab., General Motors Global Research and Development, GM Technical Centre India Pvt. Ltd., Creator Building, International Tech Park Ltd., Whitefield Road, Bangalore, 560 066, India

    Phani Motamarri, Anand Ramani & Anshul Kaushik

  2. Department of Mechanical Engineering, University of Michigan, 3812 EECS Building, Ann Arbor, MI, 48109, USA

    Phani Motamarri

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  1. Phani Motamarri
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  2. Anand Ramani
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  3. Anshul Kaushik
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Correspondence to Anand Ramani.

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Motamarri, P., Ramani, A. & Kaushik, A. Structural topology synthesis with dynamics and nonlinearities using equivalent linear systems. Struct Multidisc Optim 45, 545–558 (2012). https://doi.org/10.1007/s00158-011-0713-0

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  • DOI: https://doi.org/10.1007/s00158-011-0713-0

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