Time dependent response of impact induced functionally graded conical shell considering porosity
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Sådhanå (2020)45:219 https://doi.org/10.1007/s12046-020-01455-6
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Time dependent response of impact induced functionally graded conical shell considering porosity APURBA DAS1,3,* , MRUTYUNJAY ROUT2
and AMIT KARMAKAR3
1
Mechanical Engineering Department, Netaji Subhash Engineering College, Kolkata 700152, India Mechanical Engineering Department, Government College of Engineering, Bhawanipatna, India 3 Mechanical Engineering Department, Jadavpur University, Kolkata 700032, India e-mail: [email protected]; [email protected]; [email protected] 2
MS received 14 April 2018; accepted 13 July 2020 Abstract. Time dependent low-velocity single and multiple impact response of functionally graded (FG) untwisted and pretwisted conical shells are analysed considering porosity factor. A modified Hertzian contact law which accounts for permanent indentation is considered for the low velocity impact problem. An eightnoded isoparametric shell element is used for the finite element formulation while Newmark’s time integration algorithm is used to solve the time dependent equations. The effects of porosity considering even and uneven porosity factor, initial velocity of impactor (VOI), mass of the impactor and twist angle of FG conical shell on the transient impact response of the conical shell are examined and analyzed. The contact force and indentation increase with increase of VOI and mass of the impactor while the contact duration decreases for both the occasions. Twist angle has a significant effect on contact force but has marginal effect on contact duration. Contact force for perfect (porosity free) FG conical shells is higher than that of porous FG conical shells. Lower contact force is observed for higher porosity factor. Even porous FG conical shell predicts lower contact force and higher shell displacement than that of an uneven porous FG conical for a given porosity factor. Keywords. angle.
Functionally graded material; porosity; finite element; low velocity impact; conical shell; twist
1. Introduction A new variant of composite materials named as Functionally graded materials (FGMs), where the microstructures are spatially graded to achieve specific mechanical and/or thermal properties to fit the functionality of the structure has become popular in the energy, nuclear and aviation industries. Functionally graded (FG) shallow conical shells can be idealized as turbo-machinery blades under rotation that can be employed in aviation, energy, nuclear and mechanical industries. The impact response of such conical shells by elastic spherical mass impactor is an important phenomenon in terms of impact load, damage and design aspect. FGMs do not contain well distinguished boundaries or interfaces between their different regions as in the case of conventional composite materials due to these FGMs have many advantages, which facilitates them to use in
This paper is a revised and expanded version of an article presented in ‘‘First International Conference on Mec
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