Abstract
Optimization of solid structures lead to better engineering designs and thus to a longer life time of e.g. technical components, engines and buildings. In an optimization process as well material parameters as shapes can be improved. However the computations needed to find optimal solutions are quite complex. Here a proper sensitivity analysis provides an efficient tool in order to compute complex derivations that are needed in the associated algorithms which finally leads to faster convergence of the underlying iterative procedures. Another applications where sensitivity analysis is needed is related to multi-scale analysis of coplex structures. Especially the so called FE\({}^2\)-schemes need an accurate computation of sensitivities. Here micro and macro levels are combined in the computations to account for complex material behaviour at micro level.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The index \(n + 1\) is in general omitted in order to simplify the notation.
References
Choi, K.K., and N.H. Kim. 2005a. Structural sensitivity analysis and optimization 1, Linear systems. New York: Springer Science+Business Media.
Choi, K.K., and N.H. Kim. 2005b. Structural sensitivity analysis and optimization 2, Nonlinear systems and applications. New York: Springer Science+Business Media.
Hudobivnik, B., and J. Korelc. 2016. Closed-form representation of matrix functions in the formulation of nonlinear material models. Finite Elements in Analysis and Design 111: 19–32.
Keulen, F., R. Haftka, and N. Kim. 2005. Review of options for structural design sensitivity analysis. part 1: Linear systems. Computer Methods in Applied Mechanics and Engineering 194: 3213–3243.
Kleiber, M., H. Antunez, T. Hien, and P. Kowalczyk. 1997. Parameter sensitivity in nonlinear mechanics. New York: Wiley.
Korelc, J. 2009. Automation of primal and sensitivity analysis of transient coupled problems. Computational Mechanics 44: 631–649.
Korelc, J. 2011b. Semi-analytical solution of path-independed nonlinear finite element models. Finite Elements in Analysis and Design 47: 281–287.
Korelc, J., and S. Stupkiewicz. 2014. Closed-form matrix exponential and its application in finite-strain plasticity. International Journal for Numerical Methods in Engineering 98: 960–987.
Kristanic, N., and J. Korelc. 2008. Optimization method for the determination of the most unfavorable imperfection of structures. Computational Mechanics 42: 859–872.
Melink, T., and J. Korelc. 2014. Stability of karhunen-love expansion for the simulation of gaussian stochastic fields using galerkin scheme. Probabilistic Engineering Mechanics 37: 7–15.
Michaleris, P., D. Tortorelli, and C. Vidal. 1994. Tangent operators and design sensitivity formulations for transient non-linear coupled problems with applications to elastoplasticity. International Journal for Numerical Methods in Engineering 37: 2471–2499.
Solinc, U., and J. Korelc. 2015. A simple way to improved formulation of fe2 analysis. Computational Mechanics 56: 905–915.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Korelc, J., Wriggers, P. (2016). Automation of Sensitivity Analysis. In: Automation of Finite Element Methods. Springer, Cham. https://doi.org/10.1007/978-3-319-39005-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-39005-5_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-39003-1
Online ISBN: 978-3-319-39005-5
eBook Packages: EngineeringEngineering (R0)