The Effect of Own Weight on Dynamic Analysis of a Pre-Stretched Composite Plate-Strip Containing Twin Circular Inclusions Under Bending Using Finite Element Method

Abstract

This manuscript describes how the weight of a simply supported composite plate-strip (containing twin circular inclusions) affects its dynamic behaviors when exposed to bending load as analyzed via the finite element method (FEM). The centers of the twin circular inclusions are on a line parallel to the free surface, and the materials of both inclusions are the same. First, the effects of body forces (the plate-strip’s own weight) and surface forces (pre-stretching load) on the plate-strip (both are considered to be initial stresses) are identified using the classical linear theory of elasticity. Next, the consequences of these stressors (identified in the first step) under additional time harmonic bending load on the forced vibration around the inclusions are determined using the three-dimensional linearized theory of elasticity (TDLTE) under the plane-strain state. The data herein suggest that the plate-strip’s weight can significantly effect dynamic characteristics of the considered plate-strip.

Keywords

• initial stress,own weight,circular inclusions,forced vibration,fundamental frequency

References

1. [1] T. Mura, “Inclusion Problems”, Appl. Mech. Rev., vol. 41, no 1, pp. 15-20,1988.
2. [2] T. Mura, H.M. Shodja and Y. Hirose, “Inclusion Problems”, Appl. Mech. Rev., vol. 49, no 10S, pp. 118-127, 1996.
3. [3] K. Zhou, H.J. Hoh, X. Wang, L.M. Keer, J.H.L. Pang, B. Song and Q.J. Wang, “A review of recent works on inclusions”, Mech. Mater., vol. 60, pp. 144-158, 2013.
4. [4] W. Hufenbach and B. Zhou, “Solutions for an anisotropic finite plate with an elastic inclusion and a loaded boundary”, Compos. Struct., vol. 52, no 2, pp. 161-166, 2001.
5. [5] J.H. Huang, “Vibration response of laminated plates containing spheroidal inclusions”, Compos. Struct., vol. 50, no 3, pp. 269-277, 2000.
6. [6] U. Babuscu Yesil, “Forced Vibration Analysis of Pre-stretched Plates With Twin Circular Inclusions”, J. Eng. Mech., vol. 141, no 1, pp. 04014099-1-04014099-16, 2015.
7. [7] S.D. Akbarov, Dynamics of Pre-Strained Bi-Material Elastic Systems Linearized Three-Dimensional Approach, Springer-Heidelberg, New York, 2015.
8. [8] H. Takabatake, “Effects of dead loads in dynamic plates”, J. Struct. Eng.-ASCE, vol. 118, no 1, pp. 34-51,1992.

9. [9] H. Takabatake, “Effects of dead loads on dynamic analyses of beams subject to moving loads”, Earthq. Struct., vol. 5, no 5, pp. 589-605, 2013.
10. [10] H. Takabatake, “Effect of dead loads on natural frequencies on beams”, J. Struct. Eng.-ASCE, vol. 117, no 4, pp. 1039-1052, 1991.
11. [11] H. Takabatake, “Effects of dead loads on dynamic analyses of beams”, Earthq. Struct., vol. 1, no 4, pp. 411-425, 2010.
12. [12] U. Babuscu Yesil, “The Effect of Own Weight On The Static Analysis of A Prestretched Plate-Strip With A Circular Hole In Bending”, Mech. Compos. Mater., vol. 53, no 2, pp. 243-252, 2017.
13. [13] S.J. Zhou and X. Zhu, “Analysis of effect of dead loads on natural frequencies of beams using finite-element techniques”, J. Struct. Eng. -ASCE, vol. 122, no 5, pp. 512-516, 1996.
14. [14] S.J. Zhou, “Load-induced stiffness matrix of plates”, Can. J. Civ. Eng., vol. 29, no 1, 181-184, 2002.
15. [15] S.D. Akbarov, Stability Loss and Buckling Delamination: Three-Dimensional Linearized Approach for Elastic and Viscoelastic Composites, Springer-Heidelberg, New York, 2013.
16. [16] A.N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin, 1999.
17. [17] A.N. Guz, Elastic Waves in Bodies with Initial (Residual) Stresses [in Russian], Kiev, 2004.
18. [18] O.C. Zienkiewicz and R.L. Taylor, The Finite Element Methods: Basic Formulation and Linear Problems (Vol. 1, 4th Edition). Mc Graw-Hill Book Company, Oxford, 1989.
19. [19] S.P. Timoshenko and J.N. Goodier, Theory of Elasticity, Third Edition, McGraw-Hill International Editions, London, 1970.