Basic criteria to design and produce multistable shells

Hamouche, Walid; Maurini, Corrado; Vincenti, Angela; Vidoli, Stefano

doi:10.1007/s11012-016-0375-5

Cited by 31 publications

(20 citation statements)

References 24 publications

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“…For an almost neutrally stable shell, the stiffness with respect to c is much higher than the one with respect to φ . As far as the inextensible shell model is pertinent, this stiffness ratio is vanishing independently of the shell thickness and Young modulus, see [17,18]. Hence, we will study the coupled fluid–structure interaction under the further approximation that c is constant, and φ is the only structural degree of freedom left to describe the shell deformation.…”

Section: Stokes Flow and Forces From The Fluid To The Structurementioning

confidence: 99%

A neutrally stable shell in a Stokes flow: a rotational Taylor's sheet

et al. 2019

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In a seminal paper published in 1951, Taylor studied the interactions between a viscous fluid and an immersed flat sheet which is subjected to a travelling wave of transversal displacement. The net reaction of the fluid over the sheet turned out to be a force in the direction of the wave phase-speed. This effect is a key mechanism for the swimming of micro-organisms in viscous fluids. Here, we study the interaction between a viscous fluid and a special class of nonlinear morphing shells. We consider pre-stressed shells showing a one-dimensional set of neutrally stable equilibria with almost cylindrical configurations. Their shape can be effectively controlled through embedded active materials, generating a large-amplitude shape-wave associated with precession of the axis of maximal curvature. We show that this shape-wave constitutes the rotational analogue of a Taylor's sheet, where the translational swimming velocity is replaced by an angular velocity. Despite the net force acting on the shell vanishes, the resultant torque does not. A similar mechanism can be used to manoeuver in viscous fluids.

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Section: Stokes Flow and Forces From The Fluid To The Structurementioning

confidence: 99%

A neutrally stable shell in a Stokes flow: a rotational Taylor's sheet

et al. 2019

Self Cite

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“…Then, a formal treatment performs a partinversion of the Jacobian matrix in Eqs. (24)- (26), giving first a one-matrix eigenproblem of size N u for the displacement components…”

Section: The Case B = 0 With Non-singular Bmentioning

confidence: 99%

“…Rafsanjani, Akbarzadeh and Pasini show how a meta-material with selected properties can be designed from geometrically non-linear effects in a non-homogeneous material [37]. Hamouche and co-workers derive closed-form expressions for bi-or tri-stability of thin shallow shells, and show how the shape of a structure can be controlled by active materials [25,26]. Emam and Inman give an extensive review of the morphing and energy harvesting potential in bi-stable composite laminates, where morphing is an "interesting feature of modern structures that enables them to change shape according to environmental or operational conditions" [14].…”

Section: Introductionmentioning

confidence: 99%

Constrained stability of conservative static equilibrium

Eriksson

Nordmark

2019

Comput Mech

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Modelling of static structural stability problems is considered. Focus is set on problems where passive physical constraints affect the response to applied forces, and where more than one free parameter describes the setting. The existence of vibration frequencies at equilibrium states is investigated, as an indication of stability. The relevant Jacobian matrix is developed, with an emphasis on the necessity to formulate the constraint equations from an energy form in a conservative problem. The corresponding mass matrix is introduced, with zero mass contribution from constraint equations. Three different forms of the relevant Jacobians are considered, and alternative methods for the eigenvalue extraction given. Stability is discussed in a context of generalized equilibrium problems, where auxiliary parameters and equations can be included in a continuation setting. Examples show the formulation, implementation and interpretation of stability.

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“…Stress induced by geometrical frustration is known to affect the mechanical equilibria of complex rods [23][24][25], sheets [26] and shells [27][28][29]. To explore similar effects of incompatible curvature on the stability of conical frusta, we fabricate elastic RCF with controlled overcurvature by redesigning the negative mold (# 1, Fig.…”

Section: Effect Of Overcurvature On Multistability Of a Pop Toobmentioning

confidence: 99%

Overcurvature induced multistability of linked conical frusta: how a ‘bendy straw’ holds its shape

Bende

Corbin

et al. 2018

Soft Matter

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We study the origins of multiple mechanically stable states exhibited by an elastic shell comprising multiple conical frusta, a geometry common to reconfigurable corrugated structures such as 'bendy straws'. This multistability is characterized by mechanical stability of axially extended and collapsed states, as well as a partially inverted 'bent' state that exhibits stability in any azimuthal direction. To understand the origin of this behavior, we study how geometry and internal stress affect the stability of linked conical frusta. We find that tuning geometrical parameters such as the frustum heights and cone angles can provide axial bistability, whereas stability in the bent state requires a sufficient amount of internal pre-stress, resulting from a mismatch between the natural and geometric curvatures of the shell. We analyze the latter effect through curvature analysis during deformation using X-ray computed tomography (CT), and with a simple mechanical model that captures the qualitative behavior of these highly reconfigurable systems.

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Basic criteria to design and produce multistable shells

Cited by 31 publications

References 24 publications

A neutrally stable shell in a Stokes flow: a rotational Taylor's sheet

A neutrally stable shell in a Stokes flow: a rotational Taylor's sheet

Constrained stability of conservative static equilibrium

Overcurvature induced multistability of linked conical frusta: how a ‘bendy straw’ holds its shape

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