Shape and topology sensitivity analysis for cracks in elastic bodies on boundaries of rigid inclusions

Khludnev, A. M.; Novotny, Antônio André; Sokołowski, Jan; Żochowski, Antoni

doi:10.1016/j.jmps.2009.07.003

Cited by 50 publications

(50 citation statements)

References 22 publications

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“…See also applications of the topological derivative in the context of multiscale constitutive modeling ; Giusti et al (2010aGiusti et al ( , 2009a; Novotny et al (2010)), fracture mechanics sensitivity analysis (Ammari et al (2014); Van Goethem and Novotny (2010)) and damage evolution modeling (Allaire et al (2011)). Regarding the theoretical development of the topological asymptotic analysis, see for instance (Amstutz (2006(Amstutz ( , 2010 ;Feijóo et al (2003); Garreau et al (2001); Hlaváček et al (2009); Khludnev et al (2009); Lewinski and Sokołowski (2003); Nazarov and Sokołowski (2003a,b, 2005, 2006, 2011; Żochowski (2003, 2005)), as well as the book by Novotny and Sokołowski (2013).…”

Section: Introductionmentioning

confidence: 99%

Topological derivative-based topology optimization of structures subject to multiple load-cases

Lopes

Santos

Novotny

2015

Lat. Am. j. solids struct.

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The topological derivative measures the sensitivity of a shape functional with respect to an infinitesimal singular domain perturbation, such as the insertion of holes, inclusions or source-terms. The topological derivative has been successfully applied in obtaining the optimal topology for a large class of physics and engineering problems. In this paper the topological derivative is applied in the context of topology optimization of structures subject to multiple load-cases. In particular, the structural compliance under plane stress or plane strain assumptions is minimized under volume constraint. For the sake of completeness, the topological asymptotic analysis of the total potential energy with respect to the nucleation of a small circular inclusion is developed in all details. Since we are dealing with multiple load-cases, a multi-objective optimization problem is proposed and the topological sensitivity is obtained as a sum of the topological derivatives associated with each load-case. The volume constraint is imposed through the Augmented Lagrangian Method. The obtained result is used to devise a topology optimization algorithm based on the topological derivative together with a level-set domain representation method. Finally, several finite element-based examples of structural optimization are presented. Keywords

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Section: Introductionmentioning

confidence: 99%

Topological derivative-based topology optimization of structures subject to multiple load-cases

Lopes

Santos

Novotny

2015

Lat. Am. j. solids struct.

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“…The difference encountered is that instead of a scalar wave equation one should consider dynamic system of elasticity. There are several works [3,10,35,47] which furnish the same kind of approximation for the energy functional, with the explicit expressions for the first order term, which can be used in our framework. The only difficulty is that instead of scalar problem, vectorial system of elasticity should be considered.…”

Section: Discussionmentioning

confidence: 99%

Sensitivity analysis of hyperbolic optimal control problems

2010

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The aim of this paper is to perform sensitivity analysis of optimal control problems defined for the wave equation. The small parameter describes the size of an imperfection in the form of a small hole or cavity in the geometrical domain of integration. The initial state equation in the singularly perturbed domain is replaced by the equation in a smooth domain. The imperfection is replaced by its approximation defined by a suitable Steklov's type differential operator. For approximate optimal control problems the well-posedness is shown. One term asymptotics of optimal control are derived and justified for the approximate model. The key role in the arguments is played by the so called "hidden regularity" of boundary traces generated by hyperbolic solutions.

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“…Based on the sensitivity analysis, the designer can carry out a systematic trade-off analysis [32], and resigning a system can be processed [31]. J Jang and Han devise a way to conduct dynamic sensitivity analysis for studying state sensitive information with respect to changes in the design variables [34].…”

Section: The Sensitivity Analysis Of the Critical Speed Of A High-spementioning

confidence: 99%

Improving the critical speeds of high-speed trains using magnetorheological technology

Sun

Deng

et al. 2013

Smart Mater. Struct.

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With the rapid development of high-speed railways, vibration control for maintaining stability, passenger comfort, and safety has become an important area of research. In order to investigate the mechanism of train vibration, the critical speeds of various DOFs with respect to suspension stiffness and damping are first calculated and analyzed based on its dynamic equations. Then, the sensitivity of the critical speed is studied by analyzing the influence of different suspension parameters. On the basis of these analyses, a conclusion is drawn that secondary lateral damping is the most sensitive suspension damper. Subsequently, the secondary lateral dampers are replaced with magnetorheological fluid (MRF) dampers. Finally, a high-speed train model with MRF dampers is simulated by a combined ADAMS and MATLAB simulation and tested in a roller rig test platform to investigate the mechanism of how the MRF damper affects the train's stability and critical speed. The results show that the semi-active suspension installed with MRF dampers substantially improves the stability and critical speed of the train. AbstractWith the rapid development of high-speed railways, vibration control for maintaining stability, passenger comfort, and safety has become an important area of research. In order to investigate the mechanism of train vibration, the critical speeds of various DOF with respect to suspension stiffness and damping are first calculated and analyzed based on its dynamics equations. Then, the sensitivity of critical speed is studied by analyzing the influence of different suspension parameters. Upon on these analyses, conclusion is drawn that secondary lateral damping is the most sensitive suspension damper. Subsequently, the secondary lateral dampers are replaced with magnetorheological fluid (MRF) dampers. At last, a high-speed train model with MRF dampers is simulated by a combination simulation of ADAMS and MATLAB and tested in a roller rig test platform to investigate the mechanism of how the MRF damper affects the train's stability and critical speed. The results show that the semi-active suspension installed with MRF damper substantially improves the stability and critical speed of the train.

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Shape and topology sensitivity analysis for cracks in elastic bodies on boundaries of rigid inclusions

Cited by 50 publications

References 22 publications

Topological derivative-based topology optimization of structures subject to multiple load-cases

Topological derivative-based topology optimization of structures subject to multiple load-cases

Sensitivity analysis of hyperbolic optimal control problems

Improving the critical speeds of high-speed trains using magnetorheological technology

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