Application of optimal control method in buckling analysis of constrained elastica problems

Liakou, Anna

doi:10.1016/j.ijsolstr.2018.02.019

Cited by 13 publications

(13 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…which is composed by two nonlinear differential equations in the time variable and a nonlinear algebraic equation. The differential equations represent the Newton's second law, eqn (30), for the lumped mass, decomposed along the x and y directions. The algebraic equation represents the interfacial boundary condition, eqn (21), namely, the axial equilibrium at the sliding sleeve end in the presence of the configurational force.…”

Section: Closed-form Spatial Integration Of the Elasticamentioning

confidence: 99%

“…• the resultant components (30) acting on the lumped mass are modified into eqns (41) 1 and (41) 2 to account for viscous dissipation, through the non-constant parameter c(t) defining a linear damping, related to air drag and to the presence of lubricant in the sliding sleeve.…”

Section: Closed-form Spatial Integration Of the Elasticamentioning

confidence: 99%

“…Configurational forces, introduced in solid mechanics by Eshelby [15,16,17,18] to model interactions between dislocations or forces driving crack propagation, have been recently shown to be possible in structural mechanics too [6]. The action of configurational forces on structures have been exploited to provide unexpected quasi-static response [5,7,8] and propulsion [4,12], have been explained through a material force balance [25,35,36,41] and have been used to investigate constrained buckling problems [29,30,31]. It is also worth noting that the recent research on configurational forces in structural mechanics has eventually inspired a new interpretation of their action in solids [3].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Configurational forces and nonlinear structural dynamics

Armanini

Corso

Misseroni

et al. 2019

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

Configurational, or Eshelby-like, forces are shown to strongly influence the nonlinear dynamics of an elastic rod constrained with a frictionless sliding sleeve at one end and with an attached mass at the other end. The configurational force, generated at the sliding sleeve constraint and proportional to the square of the bending moment realized there, has been so far investigated only under quasi-static setting and is now confirmed (through a variational argument) to be present within a dynamic framework. The deep influence of configurational forces on the dynamics is shown both theoretically (through the development of a dynamic nonlinear model in which the rod is treated as a nonlinear spring, obeying the Euler elastica, with negligible inertia) and experimentally (through a specifically designed experimental setup). During the nonlinear dynamics, the elastic rod may slip alternatively in and out from the sliding sleeve, becoming a sort of nonlinear oscillator displaying a motion eventually ending with the rod completely injected into or completely ejected from the sleeve. The present results may find applications in the dynamics of compliant and extensible devices, for instance, to guide the movement of a retractable and flexible robot arm.

show abstract

Section: Closed-form Spatial Integration Of the Elasticamentioning

confidence: 99%

Section: Closed-form Spatial Integration Of the Elasticamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Configurational forces and nonlinear structural dynamics

Armanini

Corso

Misseroni

et al. 2019

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

show abstract

“…The scientific interest for the Elastica theory has never diminished, even today numerous papers can be found in the Literature (see, for example, [16], [17] and [18]). In addition, the Elastica has been used to simulate a wide range of new practical problems (see, for example, [19], [20], [21], [22], [23] and [24]). The state of the art of the Elastica theory can be found in the fundamental works by Bigoni [25] and O'Reilly [26].…”

Section: Introductionmentioning

confidence: 99%

Mechanics of High-Flexible Beams Under Live Loads

Lanzoni

Tarantino

2020

J Elast

View full text Add to dashboard Cite

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.

show abstract

“…In particular, the sliding of an elastic rod through a frictionless sleeve generates at both constraint ends an 'Eshelby-like' force of amount proportional to the square of the bending moment and direction parallel to that of sliding. Configurational forces may also be derived through an asymptotic approach [5,6] or a material force balance [7][8][9][10] and have been so far exploited in a series of novel applications [11][12][13][14][15][16][17][18][19][20]. The action of Eshelby-like forces was recently disclosed in a dynamic framework and the case of a falling mass attached to an end of an elastic rod investigated to reveal a complex and often counterintuitive motion [21].…”

Section: Introductionmentioning

confidence: 99%

Nested Bloch waves in elastic structures with configurational forces

Corso

Tallarico

Movchan

et al. 2019

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

Small axial and flexural oscillations are analyzed for a periodic and infinite structure, constrained by sliding sleeves and composed of elastic beams. A nested Bloch-Floquet technique is introduced to treat the non-linear coupling between longitudinal and transverse displacements induced by the configurational forces generated at the sliding sleeve ends. The action of configurational forces is shown to play an important role from two perspectives. First, the band gap structure for purely longitudinal vibration is broken so that axial propagation may occur at frequencies that are forbidden in the absence of a transverse oscillation and, second, a flexural oscillation may induce axial resonance, a situation in which the longitudinal vibrations tend to become unbounded. The presented results disclose the possibility of exploiting configurational forces in the design of mechanical devices towards longitudinal actuation from flexural vibrations of small amplitude at given frequency.

show abstract

Application of optimal control method in buckling analysis of constrained elastica problems

Cited by 13 publications

References 35 publications

Configurational forces and nonlinear structural dynamics

Configurational forces and nonlinear structural dynamics

Mechanics of High-Flexible Beams Under Live Loads

Nested Bloch waves in elastic structures with configurational forces

Contact Info

Product

Resources

About