Dynamic effects in lattice structures produced by additive technologies
https://doi.org/10.22405/2226-8383-2019-20-2-512-522
Abstract
The influence of lattice structures on the propagation of elastic waves in these structures is analyzed. The statement of problem is formulated within the framework of linear elasticity under small strains. To solve this problem, the finite element method and the Fidesys CAEsystem were used. Different variants of plane lattice structures are modeled: the classical lattice and the lattice with uniformly curved strips across the plane: elevator and star-shaped lattices. The relation between the structure of lattice structures and the propagation of perturbations in these structures is analyzed. The dependence of wave velocity in curved lattice structures on the frequency of the emitted waves is analyzed. The applied conceptual model of the device for measuring the frequency of waves is developed.
About the Authors
Vladimir Anatolyevich LevinRussian Federation
Konstasntin Moiseevich Zingerman
Russian Federation
Anatolij Victorovich Vershinin
Russian Federation
Ivan Andreevich Podpruzhnikov
Russian Federation
References
1. Vendik I. B., Vendik O. G. Metamaterials and their application in ultrahigh-frequency engineering // Journal of technical physics. V. 83, No. 1. P. 3-28.
2. Cheng L., Liang X., Bai J., Chen Q., Lemon J., To A. On utilizing topology optimization to design support structure to prevent residual stress induced build failure in laser powder bed metal additive manufacturing // Additive Manufacturing. 2019. V. 27. P. 290–304.
3. Phani A.S., Woodhouse J., Fleck N. Wave propagation in two-dimensional periodic lattices. J. Acoust. Soc. Am. 2006. V. 119 (4). P. 1995–2005.
4. Cheng L., Liang X., Bai J., Chen Q., Lemon J., To A. On utilizing topology optimization to design support structure to prevent residual stress induced build failure in laser powder bed metal additive manufacturing // Additive Manufacturing. 2019. V. 27. P. 290–304.
5. Sedov L.I. Continuum Mechanics. V. 2. Moscow: Nauka, 1970. 568 p.
6. Pobedrya B. E., Georgievskii D. V. Fundamentals of continuum mechanics. Course of lectures. – Moscow: FIZMATLIT, 2006. 272 p.
7. Eglit M. E. Lectures on continuum mechanics. - Moscow: Publishing House of Moscow University, 2008. - 318 p.
8. Andreev V. B. Lectures on the finite element method (textbook). Moscow: MAX Press, 2010. – 262 p.
9. Morozov E. M., Levin V. A., Vershinin A.V. Strength analysis. Fidesys in the hands of an engineer. – Moscow: URSS, 2015. – 408 p.
10. Levin V. A., Vershinin A. V. Industrial package for engineering strength analysis // Proceedings of XI all-Russian Congress on fundamental problems of theoretical and applied mechanics. Kazan, August 20-24, 2015. P. 2281–2283.
11. Brovko G.L., Ilyushin A.A. On a plane model of perforated plates. Moscow University Mechanics Bulletin. 1993. No. 2. P. 83–91.
12. Levin V.A., Zingermann K.M. Effective Constitutive Equations for Porous Elastic Materials at Finite Strains and Superimposed Finite Strains // Journal of Applied Mechanics, Transactions ASME. 2003. V. 70, No. 6. P. 809–816.
13. Levin V.A., Zingerman K.M., Vershinin A.V., Yakovlev M. Numerical analysis of effective mechanical properties of rubber-cord composites under finite strains // Composite Structures. 2015. V. 131. P. 25–36.
14. Vershinin A.V., Levin V.A., Zingerman, K.M., Sboychakov A.M., Yakovlev M.Y. Software for estimation of second order effective material properties of porous samples with geometrical and physical nonlinearity accounted for // Advances in Engineering Software. 2015. V.86. P. 80–84.
15. Roehling J.D., Smith W.L., Roehling T.T., Vrancken B., Guss G.M., McKeown J.T., Hill M.R., Matthews M.J. Reducing residual stress by selective large-area diode surface heating during laser powder bed fusion additive manufacturing // Additive Manufacturing. 2019. V. 28. P. 228–235.
16. Protasov C.E., Safronov V.A., Kotoban D.V., Gusarov A.V. Experimental study of residual stresses in metal parts obtained by selective laser melting // Physics Procedia. 2016. V. 83. P. 825–832.
17. Robinson J., Ashton I., Fox P., Jones E., Sutcliffe C. Determination of the effect of scan strategy on residual stress in laser powder bed fusion additive manufacturing // Additive Manufacturing. 2018. V. 23. P. 13–24.
18. Levin V.A. Theory of repeated superposition of large deformations: Elastic and viscoelastic bodies // International Journal of Solids and Structures, 1998. V. 35(20) P. 2585-2600.
19. Levin V.A., Zubov L.M., Zingerman K.M. The torsion of a composite, nonlinear-elastic cylinder with an inclusion having initial large strains // International Journal of Solids and Structures. 2014. V. 51. No. 6. P. 1403–1409.
20. Levin V.A., Zubov L.M., Zingerman K.M. An exact solution for the problem of flexure of a composite beam with preliminarily strained layers under large strains // International Journal of Solids and Structures. 2015. V. 67–68. P. 244–249.
21. Levin V.A, Zubov L.M., Zingerman K.M. Multiple joined prestressed orthotropic layers under large strains// International Journal of Engineering Science. 2018. V. 133. P. 47–59.
Review
For citations:
Levin V.A., Zingerman K.M., Vershinin A.V., Podpruzhnikov I.A. Dynamic effects in lattice structures produced by additive technologies. Chebyshevskii Sbornik. 2019;20(2):512-522. (In Russ.) https://doi.org/10.22405/2226-8383-2019-20-2-512-522
Views:
575
Email this article 