Equilibrium Paths for von Mises Trusses in Finite Elasticity
- 27 Downloads
This paper deals with the equilibrium problem of von Mises trusses in nonlinear elasticity. A general loading condition is considered and the rods are regarded as hyperelastic bodies composed of a homogeneous isotropic material. Under the hypothesis of homogeneous deformations, the finite displacement fields and deformation gradients are derived. Consequently, the Piola-Kirchhoff and Cauchy stress tensors are computed by formulating the boundary-value problem. The equilibrium in the deformed configuration is then written and the stability of the equilibrium paths is assessed through the energy criterion. An application assuming a compressible Mooney-Rivlin material is performed. The equilibrium solutions for the case of vertical load present primary and secondary branches. Although, the stability analysis reveals that the only form of instability is the snap-through phenomenon. Finally, the finite theory is linearized by introducing the hypotheses of small displacement and strain fields. By doing so, the classical solution of the two-bar truss in linear elasticity is recovered.
KeywordsFinite elasticity Equilibrium von Mises truss Stability Snap-through
Mathematics Subject Classification74B20 74G05
The authors acknowledge funding from the Italian Ministry MIUR-PRIN voce COAN 5.50.16.01 code 2015JW9NJT.
Compliance with Ethical Standards
Conflict of Interest: The authors declare that they have no conflict of interest.
- 5.Faa di Bruno, F.: Sullo sviluppo delle funzioni. Ann Sci. Mat. Fis. 6, 479–480 (1855) Google Scholar
- 19.Ogden, R.W.: Large deformation isotropic elasticity: on the correlation of theory and experiment for compressible rubberlike solids. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci., 567–583 (1972) Google Scholar
- 21.Psotny, M., Ravinger, J.: Von Mises truss with imperfection. Slov. J. Civ. Eng. 11, 1–7 (2003) Google Scholar
- 32.Ziegler, H.: Principles of Structural Stability, vol. 35. Birkhäuser, Basel (2013) Google Scholar