A novel boundary element approach to time-harmonic dynamics of incremental nonlinear elasticity: The role of pre-stress on structural vibrations and dynamic shear banding

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 41-44, 2007, Pages 4222-4249

  Bigoni, D ^a   Capuani, D ^b   Bonetti, P ^a   Colli, S ^a  

^a UNIVERSITY OF TRENTO   (Italy)

^b UNIVERSITY OF FERRARA   (Italy)

Author keywords

Non linear elasticity; Time harmonic dynamics; Vibrations

Indexed keywords

BOUNDARY ELEMENT METHOD; BOUNDARY VALUE PROBLEMS; DEFORMATION; ELASTICITY; GREEN'S FUNCTION; SHEAR BANDS; STRUCTURAL DYNAMICS; VIBRATIONS (MECHANICAL);

ELASTIC STRUCTURES; NONLINEAR ELASTICITY; TIME-HARMONIC DYNAMICS;

STRESS ANALYSIS;

BOUNDARY ELEMENT METHOD; BOUNDARY VALUE PROBLEMS; DEFORMATION; ELASTICITY; GREEN'S FUNCTION; SHEAR BANDS; STRESS ANALYSIS; STRUCTURAL DYNAMICS; VIBRATIONS (MECHANICAL);

EID: 34547604128     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.04.013     Document Type: Article

References (51)

1. Ariza M.P., and Dominguez J. Dynamic BE analysis of 3-D cracks in transversely isotropic solids. Comput. Methods Appl. Mech. Engrg. 193 (2004) 765-779
2. Balas J., Sladek J., and Sladek V. Stress Analysis by Boundary Element Methods (1989), Elsevier, Amsterdam
3. Beskos D.E. Boundary element methods in dynamic analysis: Part II (1986-1996). Appl. Mech. Rev. 50 (1997) 149-197
4. Besnainou C. From wood mechanical measurements to composite material for musical instruments - new technology for instrument makers. Mrs Bull 20 3 (1995) 34-36
5. Bigoni D., and Capuani D. Green's function for incremental nonlinear elasticity: shear bands and boundary integral formulation. J. Mech. Phys. Solids 50 (2002) 471-500
6. Bigoni D., and Capuani D. Time-harmonic Green's function and boundary integral formulation for incremental nonlinear elasticity: dynamic of wave patterns and shear bands. J. Mech. Phys. Solids 53 (2005) 1163-1187
7. Bigoni D., Gei M., and Franceschini G. Thermoelastic small-amplitude wave propagation in nonlinear elastic multilayers. Math. Mech. Solids 9 (2004) 555-568 (special issue dedicated to Prof. R.W. Ogden)
8. Biot M.A. Mechanics of incremental deformations (1965), J. Wiley and Sons, New York
9. Bissinger G. Modern vibration measurement techniques for bowed string instruments - testing of acoustic stringed musical instruments. Exp. Techniques 25 4 (2001) 43-46
10. Bonnet M. Boundary Integral Equation Methods for Solids and Fluids (1995), Wiley & Sons, New York
11. Brun M., Capuani D., and Bigoni D. A boundary element technique for incremental, nonlinear elasticity. Part I: Formulation. Comput. Methods Appl. Mech. Engrg. 192 (2003) 2461-2479
12. Brun M., Capuani D., and Bigoni D. A boundary element technique for incremental, nonlinear elasticity. Part II: Bifurcation and shear bands. Comput. Methods Appl. Mech. Engrg. 192 (2003) 2481-2499
13. Brunelle E.J., and Robertson S.R. Vibrations of an initially stressed thick plate. J. Sound Vibr. 45 (1976) 405-416
14. Cruse T.A. Boundary Element Analysis in Computational Fracture Mechanics (1988), Kluver, Dordrecht
15. Cruse T.A., and Rizzo F.J. A direct formulation and numerical solution of the general transient elastodynamic problem I. J. Math. Anal. Appl. 22 (1968) 244-259
16. Denda M., Wang C.Y., and Yong Y.K. 2-D time-harmonic BEM for solids of general anisotropy with application to eigenvalue problems. J. Sound Vibr. 261 (2003) 247-276
17. Dominguez J. Boundary Elements in Dynamics (1993), Computational Mechanics Publications co-published with Elsevier Applied Science
18. Dowaikh M.A., and Ogden R.W. On surface waves and deformations in a pre-stressed incompressible elastic solids. IMA J. Appl. Math. 44 (1990) 261-284
19. Dowaikh M.A., and Ogden R.W. Interfacial waves and deformations in pre-stressed elastic media. Proc. R. Soc. Lond. A 443 (1991) 313-328
20. Drescher-Krasicka E., and Willis J.R. Mapping stress with ultrasound. Nature 384 (1996) 52-55
21. Gaul L., Kögl M., and Wagner M. Boundary Element Methods for Engineers and Scientists. An Introductory Course with Advanced Topics (2003), Springer
22. Graff K.F. Wave Motion in Elastic Solids (1991), OSU Press
23. Herrmann G., and Armenakas A.E. Vibrations and stability of plates under initial stress. J. Mech. Division ASCE 86 (1960) 458-487
24. Hirose S., and Kitahara M. Elastic wave scattering by inhomogeneous and anisotropic bodies in a half space. Earthquake Engrg. Struct. Dyn. 18 (1989) 285-297
25. Jha A.K., and Inman D.J. Importance of geometric non-linearity and follower pressure load in the dynamic analysis of a gossamer structure. J. Sound Vibr. 278 (2004) 207-231
26. Kame N., Rice J.R., and Dmowska R. Effects of pre-stress state and rupture velocity on dynamic fault branching. J. Geophys. Res. 108 (2003) 1-19
27. Kari L. On the dynamic stiffness of preloaded vibration isolators in the audible frequency range: Modeling and experiments. J. Acous. Soc. Am. 113 (2003) 1909-1921
28. Kausel F., and Roësset J.M. Semianalytic hyperelement for layered strata. J. Engrg. Mech. Div. ASCE 103 EM4 (1977) 569-589
29. Kim J.T., Yun C.B., Ryu Y.S., and Cho H.M. Identification of prestress-loss in PSC beams using modal information. Struct. Engrg. Mech. 17 (2004) 467-482
30. Kogl M., and Gaul L. A 3-D boundary element method for dynamic analysis of anisotropic elastic solids. CMES-Comput. Modelling Engrg. Sciences 1 (2000) 27-43
31. Lachat J.C., and Watson J.O. Effective numerical treatment of boundary integral equations: a formulation for elastostatics. Int. J. Numer. Methods Engrg. 10 (1976) 991-1005
32. Manolis G.D., and Beskos D.E. Boundary Element Methods in Elastodynamics (1988), Unwin Hyman Ltd, London
33. Mantic V. A new formula for the C-matrix in the Somigliana identity. J. Elasticity 33 (1993) 191-201
34. Mantic V., and Paris F. Integral kernels in the 2D Somigliana displacement and stress identities for anisotropic materials. Computational Mechanics 22 (1998) 77-87
35. Medina F., and Penzien J. Infinite elements for elastodynamics. Earthquake Engrg. Struct. Dyn. 10 (1982) 699-709
36. Murphy K.D., Virgin L.N., and Rizzi S.A. The effect of thermal prestress on the free vibration characteristics of clamped plates: theory and experiment. J. Vibrat. Acoust. ASME 119 (1997) 243-249
37. Nardini D., and Brebbia C.A. A new approach to free vibration analysis using boundary elements. In: Brebbia C.A. (Ed). Boundary Element Methods in Engineering (1982), Springer, Berlin 312-326
38. Ogden R.W., and Sotiropulos D.A. On interfacial waves in pre-stressed layered incompressible elastic solid. Proc. Roy. Soc. Lond. A 450 (1995) 319-341
39. Paul O., and Baltes H. Mechanical behavior and sound generation efficiency of prestressed, elastically clamped and thermomechanically driven thin film. J. Micromech. Microengrg. 9 (1999) 19-29
40. Polyzos D., Tsinopoulos S.V., and Beskos D.E. Static and dynamic element analysis in incompressible linear elasticity. Eur. J. Mech., A/Solids 17 (1998) 515-536
41. Przybylski J., Tomski L., and Golebiowska-Rozanow M. Free vibration of an axially loaded prestressed planar frame. J. Sound Vibr. 189 (1996) 609-624
42. Radi E., Bigoni D., and Capuani D. Effects of pre-stress on crack-tip fields in elastic, incompressible solids. Int. J. Solids Structures 39 (2002) 3971-3996
43. Roxburgh D.G., and Ogden R.W. Stability and vibration of pre-stressed compressible elastic plates. Int. J. Engrg. Sci. 32 (1994) 427-454
44. Ryzhak E.I. On stable deformation of "unstable materials in a rigid triaxial testing machine. J. Mech. Phys. Solids 41 (1993) 1345-1356
45. Ryzhak E.I. On stability of homogeneous elastic bodies under boundary-conditions weaker than displacement conditions. Quart. J. Mech. Appl. Math. 47 (1994) 663-672
46. Sjöberg M., and Kari L. Nonlinear isolator dynamics at finite deformations: an effective hyperelastic, fractional derivative, generalized friction model. Nonlinear Dynamics 33 (2003) 323-336
47. Sultan C., and Skelton R. A force and torque tensegrity sensor. Sensors Actuators A-Physical 112 (2004) 220-231
48. Tanaka M., Sladek V., and Sladek J. Regularization techniques applied to boundary element methods. ASME Appl. Mech. Rev. 47 (1994) 457-499
49. S.M. Vogel, F.J. Rizzo, An integral equation formulation of three dimensional anisotropic elastostatic boundary value problems, J. Elasticity 3, 1-14.
50. White W., Valliappan S., and Lee I.K. Unified boundary for finite dynamics models. J. Engrg. Mech. Div. ASCE 103 (1977) 949-964
51. Zhao C., and Liu T. Non-reflecting artificial boundaries for modelling scalar wave propagation problems in two-dimensional half space. Comput. Meth. Appl. Mech. Engrg. 191 (2002) 4569-4585