Equilibrium Paths for von Mises Trusses in Finite Elasticity

Pelliciari, Matteo; Tarantino, Angelo Marcello

doi:10.1007/s10659-019-09731-1

Cited by 29 publications

(22 citation statements)

References 27 publications

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“…This paper extends the nonlinear formulation developed in Pelliciari and Tarantino [11] to the case of the three-bar truss depicted in Figure 1. Based on the formulation provided by Kwasniewski [9], Rezaiee-Pajand and Naghavi [12] derived an analytical solution of this problem for the vertical load case.…”

Section: Introductionmentioning

confidence: 75%

“…The constitutive relation (equation ( 9)) along with the boundary conditions (equation ( 14)) provide the following equations governing the equilibrium of the dth body (see also Pelliciari and Tarantino [11] and Lanzoni and Tarantino [28]):…”

Section: Equilibrium Configurations Of the Three-bar Trussmentioning

confidence: 99%

“…Their values depend on the material analyzed and are determined experimentally. Values commonly adopted in the literature [11,28] are…”

Section: Vertical Loadmentioning

confidence: 99%

“…Although the aforementioned hypotheses allow relevant simplifications of the equilibrium problem, they do not reflect the actual behavior of solids subjected to large deformations. Hence, Pelliciari and Tarantino [11] provided a fully nonlinear solution of the problem, where both displacements and deformations are large and the rods are regarded as hyperelastic bodies composed of a general homogeneous compressible isotropic material. The constitutive law is thus defined through a stored energy function that can be different from the harmonic potential employed in the case of linear materials.…”

Section: Introductionmentioning

confidence: 99%

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Equilibrium paths of a three-bar truss in finite elasticity with an application to graphene

Pelliciari

Tarantino

2019

Mathematics and Mechanics of Solids

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This paper presents the formulation of the equilibrium problem of a three-bar truss in the nonlinear context of finite elasticity. The bars are composed of a homogeneous, isotropic, and compressible hyperelastic material. The equilibrium equations in the deformed configuration are derived under the assumption of homogeneous deformations and the stability of the solutions is assessed through the energy criterion. The general formulation is then specialized for a compressible Mooney–Rivlin material. The results for both vertical and horizontal load cases show unexpected post-critical behaviors involving several branches, stable asymmetrical configurations, bifurcation, and snap-through. The three-bar truss studied here is not only a benchmark test for the numerical analysis of nonlinear truss structures, but also a representative system for the unit cell of the graphene hexagonal lattice. Therefore, an application to graphene is performed by simulating the covalent bonds between carbon atoms as the bars of the truss, characterized by the modified Morse potential. The results provide insights on the internal mechanisms that take place when graphene undergoes large in-plane deformations, whose influence should be considered when developing molecular mechanics and continuum models in nonlinear elasticity.

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Section: Introductionmentioning

confidence: 75%

Section: Equilibrium Configurations Of the Three-bar Trussmentioning

confidence: 99%

“…Their values depend on the material analyzed and are determined experimentally. Values commonly adopted in the literature [11,28] are…”

Section: Vertical Loadmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Equilibrium paths of a three-bar truss in finite elasticity with an application to graphene

Pelliciari

Tarantino

2019

Mathematics and Mechanics of Solids

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“…This last condition has been determined by imposing that when the stretches are unitary the stresses are null (see, e.g., [34], [35] and [36]). Other details on the above stored energy function can be found in [37] and [38].…”

Section: Basic Equationsmentioning

confidence: 99%

Mechanics of High-Flexible Beams Under Live Loads

Lanzoni

Tarantino

2020

J Elast

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In this paper the mathematical formulation of the equilibrium problem of high-flexible beams in the framework of fully nonlinear structural mechanics is presented. The analysis is based on the recent model proposed by L. Lanzoni and A.M. Tarantino: The bending of beams in finite elasticity. [1]. In this model the complete three-dimensional kinematics of the beam is taken into account, both deformations and displacements are considered large and a nonlinear constitutive law in assumed. After having illustrated and discussed the peculiar mechanical aspects of this special class of structures, the criteria and methods of analysis have been addressed. A classification of the structures based on the degree of kinematic constraints has been proposed, distinguishing between isogeometric and hypergeometric structures. External static loads dependent on deformation (live loads) are also considered. The governing equations are derived on the basis of a moment-curvature relationship obtained in [1]. The governing equations take the form of a highly nonlinear coupled system of equations in integral form, which is solved through an iterative numerical procedure. Finally, the proposed analysis is applied to some popular structural systems subjected to dead and live loads. The results are compared and discussed.

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Equilibrium of the von Mises Truss in Nonlinear Elasticity

Pelliciari

Tarantino

2020

Lecture Notes in Mechanical Engineering

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Equilibrium Paths for von Mises Trusses in Finite Elasticity

Cited by 29 publications

References 27 publications

Equilibrium paths of a three-bar truss in finite elasticity with an application to graphene

Equilibrium paths of a three-bar truss in finite elasticity with an application to graphene

Mechanics of High-Flexible Beams Under Live Loads

Equilibrium of the von Mises Truss in Nonlinear Elasticity

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