13 research outputs found
Shape-shifting and instabilities of plates and shells
Slender structures like plates and shells -- for which at least one dimension is much smaller than the others -- are lightweight, flexible, and offer considerable strength with little material. As such, these structures are abundant in nature (e.g. flower petals, eggshells, and blood vessels) and design (e.g. bridge decks, fuel tanks, and soda cans). However, with slenderness comes suceptibility to large and often sudden deformations, which can be wildly nonlinear, as bending is energetically preferable to stretching. Though once considered categorically undesirable, these instabilities are often coveted nowadays in the engineering community. They provide mechanical explanations for observations in nature like the wrinkled structure of the brain or the snapping mechanism of the Venus fly trap, and when precisely controlled, enable the design of functional devices like artificial muscles or self-propelling microswimmers. As a prerequisite, these achievements require a thorough understanding of how thin structures "shape-shift" in response to stimuli and confinement. Advancing this fundamental knowledge is the goal of this thesis.
In the first two chapters, we consider the shape-selection of shells and plates that are confined by their environment. The shells are made by residual swelling of silicone elastomers, a process that mimics differential growth, and causes initially flat structures to irreversibly morph into curved shapes. Flattening the central region forces further reconfiguration, and the confined shells display multi-lobed buckling patterns. These experiments, finite element (FE) simulations, and a scaling argument reveal that a single geometric confinement parameter predicts the general features of this shape-selection. Next, in experiments and molecular dynamics (MD) simulations, we constrain intrinsically flat sheets in the same manner, so that their center remains flat when we quasi-statically force them through a ring. In the absence of planar confinement, these sheets form a well-studied conical shape (the developable cone or d-cone). Our annular d-cone buckles circumferentially into patterns that are qualitatively similar to the confined shells, despite the distinct curvatures and loading methods. This is explained by the dominant role of confinement geometry in directing deformation, which we uncover via a scaling argument based on the elastic energy. There are also marked differences between the way plates and shells change shape, which we highlight when we investigate the rich dynamics of reconfiguration.
In the final two chapters, we demonstrate how mechanics, geometry, and materials can inform the design of structures that use instabilities to function. We observe in experiments that dynamic loading causes a spherical elastomer shell to buckle at ostensibly subcritical pressures, following a substantial time delay. To explain this, we show that viscoelastic creep deformation lowers the critical load in the same predictable, quantifiable way that a growing defect would in an elastic shell. This work offers a pathway to introduce tunable, time-controlled actuation to existing mechanical actuators, e.g. pneumatic grippers. The final chapter aims at reducing the energy input required for bistable actuators, wherein snap-through instability is typically induced by a stimulus applied to the entire shell. To do so, we combine theory with 1D finite element simulations of spherical caps with a non-homogeneous distribution of stimuli--responsive material. We demonstrate that restricting the active area to the shell boundary allows for a large reduction in its size, while preserving snap-through behavior. These results are stimulus-agnostic, which we demonstrate with two sets of experiments, using residual swelling of bilayer silicone elastomers as well as a magneto-active elastomer. Our findings elucidate the underlying mechanics, offering an intuitive route to optimal design for efficient snap-through.2022-05-06T00:00:00
Static and Free Vibration Analyses of Composite Shells Based on Different Shell Theories
Equations of motion with required boundary conditions for doubly curved deep and thick composite shells are shown using two formulations. The first is based upon the formulation that was presented initially by Rath and Das (1973, J. Sound and Vib.) and followed by Reddy (1984, J. Engng. Mech. ASCE). In this formulation, plate stiffness parameters are used for thick shells, which reduced the equations to those applicable for shallow shells. This formulation is widely used but its accuracy has not been completely tested. The second formulation is based upon that of Qatu (1995, Compos. Press. Vessl. Indust.; 1999, Int. J. Solids Struct.). In this formulation, the stiffness parameters are calculated by using exact integration of the stress resultant equations. In addition, Qatu considered the radius of twist in his formulation. In both formulations, first order polynomials for in-plane displacements in the z-direction are utilized allowing for the inclusion of shear deformation and rotary inertia effects (first order shear deformation theory or FSDT). Also, FSDTQ has been modified in this dissertation using the radii of each laminate instead of using the radii of mid-plane in the moment of inertias and stress resultants equations. Exact static and free vibration solutions for isotropic and symmetric and anti-symmetric cross-ply cylindrical shells for different length-to-thickness and length-to-radius ratios are obtained using the above theories. Finally, the equations of motion are put together with the equations of stress resultants to arrive at a system of seventeen first-order differential equations. These equations are solved numerically with the aid of General Differential Quadrature (GDQ) method for isotropic, cross-ply, angle-ply and general lay-up cylindrical shells with different boundary conditions using the above mentioned theories. Results obtained using all three theories (FSDT, FSDTQ and modified FSDTQ) are compared with the results available in literature and those obtained using a three-dimensional (3D) analysis. The latter (3D) is used here mainly to test the accuracy of the shell theories presented here
Static and Free Vibration Analyses of Composite Shells Based on Different Shell Theories
Equations of motion with required boundary conditions for doubly curved deep and thick composite shells are shown using two formulations. The first is based upon the formulation that was presented initially by Rath and Das (1973, J. Sound and Vib.) and followed by Reddy (1984, J. Engng. Mech. ASCE). In this formulation, plate stiffness parameters are used for thick shells, which reduced the equations to those applicable for shallow shells. This formulation is widely used but its accuracy has not been completely tested. The second formulation is based upon that of Qatu (1995, Compos. Press. Vessl. Indust.; 1999, Int. J. Solids Struct.). In this formulation, the stiffness parameters are calculated by using exact integration of the stress resultant equations. In addition, Qatu considered the radius of twist in his formulation. In both formulations, first order polynomials for in-plane displacements in the z-direction are utilized allowing for the inclusion of shear deformation and rotary inertia effects (first order shear deformation theory or FSDT). Also, FSDTQ has been modified in this dissertation using the radii of each laminate instead of using the radii of mid-plane in the moment of inertias and stress resultants equations. Exact static and free vibration solutions for isotropic and symmetric and anti-symmetric cross-ply cylindrical shells for different length-to-thickness and length-to-radius ratios are obtained using the above theories. Finally, the equations of motion are put together with the equations of stress resultants to arrive at a system of seventeen first-order differential equations. These equations are solved numerically with the aid of General Differential Quadrature (GDQ) method for isotropic, cross-ply, angle-ply and general lay-up cylindrical shells with different boundary conditions using the above mentioned theories. Results obtained using all three theories (FSDT, FSDTQ and modified FSDTQ) are compared with the results available in literature and those obtained using a three-dimensional (3D) analysis. The latter (3D) is used here mainly to test the accuracy of the shell theories presented here
Recent Advances in Theoretical and Computational Modeling of Composite Materials and Structures
The advancement in manufacturing technology and scientific research has improved the development of enhanced composite materials with tailored properties depending on their design requirements in many engineering fields, as well as in thermal and energy management. Some representative examples of advanced materials in many smart applications and complex structures rely on laminated composites, functionally graded materials (FGMs), and carbon-based constituents, primarily carbon nanotubes (CNTs), and graphene sheets or nanoplatelets, because of their remarkable mechanical properties, electrical conductivity and high permeability. For such materials, experimental tests usually require a large economical effort because of the complex nature of each constituent, together with many environmental, geometrical and or mechanical uncertainties of non-conventional specimens. At the same time, the theoretical and/or computational approaches represent a valid alternative for designing complex manufacts with more flexibility. In such a context, the development of advanced theoretical and computational models for composite materials and structures is a subject of active research, as explored here for a large variety of structural members, involving the static, dynamic, buckling, and damage/fracturing problems at different scales
A new mixed model based on the enhanced-Refined Zigzag Theory for the analysis of thick multilayered composite plates
The Refined Zigzag Theory (RZT) has been widely used in the numerical analysis of multilayered
and sandwich plates in the last decay. It has been demonstrated its high accuracy in predicting global quantities, such as maximum displacement, frequencies and buckling loads, and local quantities such
as through-the-thickness distribution of displacements and in-plane stresses [1,2]. Moreover, the C0
continuity conditions make this theory appealing to finite element formulations [3]. The standard RZT,
due to the derivation of the zigzag functions, cannot be used to investigate the structural behaviour
of angle-ply laminated plates. This drawback has been recently solved by introducing a new set of
generalized zigzag functions that allow the coupling effect between the local contribution of the zigzag
displacements [4]. The newly developed theory has been named enhanced Refined Zigzag Theory (en-
RZT) and has been demonstrated to be very accurate in the prediction of displacements, frequencies,
buckling loads and stresses. The predictive capabilities of standard RZT for transverse shear stress
distributions can be improved using the Reissner’s Mixed Variational Theorem (RMVT). In the mixed
RZT, named RZT(m) [5], the assumed transverse shear stresses are derived from the integration of local
three-dimensional equilibrium equations. Following the variational statement described by Auricchio
and Sacco [6], the purpose of this work is to implement a mixed variational formulation for the en-RZT,
in order to improve the accuracy of the predicted transverse stress distributions. The assumed kinematic
field is cubic for the in-plane displacements and parabolic for the transverse one. Using an appropriate
procedure enforcing the transverse shear stresses null on both the top and bottom surface, a new set
of enhanced piecewise cubic zigzag functions are obtained. The transverse normal stress is assumed as
a smeared cubic function along the laminate thickness. The assumed transverse shear stresses profile
is derived from the integration of local three-dimensional equilibrium equations. The variational functional
is the sum of three contributions: (1) one related to the membrane-bending deformation with a
full displacement formulation, (2) the Hellinger-Reissner functional for the transverse normal and shear
terms and (3) a penalty functional adopted to enforce the compatibility between the strains coming
from the displacement field and new “strain” independent variables. The entire formulation is developed
and the governing equations are derived for cases with existing analytical solutions. Finally, to assess
the proposed model’s predictive capabilities, results are compared with an exact three-dimensional solution,
when available, or high-fidelity finite elements 3D models. References: [1] Tessler A, Di Sciuva
M, Gherlone M. Refined Zigzag Theory for Laminated Composite and Sandwich Plates. NASA/TP-
2009-215561 2009:1–53. [2] Iurlaro L, Gherlone M, Di Sciuva M, Tessler A. Assessment of the Refined
Zigzag Theory for bending, vibration, and buckling of sandwich plates: a comparative study of different
theories. Composite Structures 2013;106:777–92. https://doi.org/10.1016/j.compstruct.2013.07.019.
[3] Di Sciuva M, Gherlone M, Iurlaro L, Tessler A. A class of higher-order C0 composite and sandwich
beam elements based on the Refined Zigzag Theory. Composite Structures 2015;132:784–803.
https://doi.org/10.1016/j.compstruct.2015.06.071. [4] Sorrenti M, Di Sciuva M. An enhancement
of the warping shear functions of Refined Zigzag Theory. Journal of Applied Mechanics 2021;88:7.
https://doi.org/10.1115/1.4050908. [5] Iurlaro L, Gherlone M, Di Sciuva M, Tessler A. A Multi-scale
Refined Zigzag Theory for Multilayered Composite and Sandwich Plates with Improved Transverse Shear
Stresses, Ibiza, Spain: 2013. [6] Auricchio F, Sacco E. Refined First-Order Shear Deformation Theory
Models for Composite Laminates. J Appl Mech 2003;70:381–90. https://doi.org/10.1115/1.1572901