Details
| Original language | English |
|---|---|
| Article number | 105008 |
| Journal | Smart materials and structures |
| Volume | 30 |
| Issue number | 10 |
| Early online date | 24 Jul 2021 |
| Publication status | Published - Oct 2021 |
Abstract
Most existing semi-analytical models to analyse multistable structures are based on the principle of minimum potential energy, which inherently does not satisfy the in-plane equilibrium equations in a strong sense. Although such models predict the multistable shapes with reasonable accuracy, there is a significant discrepancy in predicting the snap-through behaviour when compared to the finite element (FE) or experimental results. In this work, a refined analytical model is derived to analyse a bistable cross-ply elliptical disc using Föppl von Kármán kinematics. The Rayleigh-Ritz approach with a decoupled energy formulation is used, where the stretching and bending energies are separated using the semi-inverse constitutive equation. The in-plane stress resultants are expressed in terms of curvatures using the compatibility and the in-plane equilibrium equations. A closed-form solution for the curvatures is derived to predict the cured bistable shapes of elliptical laminates. A layer of macro fibre composite actuator is added to trigger the snap-through between the stable shapes. Consequently, the critical voltage at which the snap-through occurs is predicted using the analytical model. The model is further extended to square plates, where the solutions of the differential equations emanating from the compatibility and in-plane equilibrium equations are obtained by converting the resulting differential equations into the form of standard FE elasticity problem. The in-plane stress resultants for the square plates are calculated by numerically solving the resulting elasticity problem using a standard FE discretization approach. The solutions are further compared with previous experimental studies and the results from a fully geometrically non-linear FE model.
Keywords
- MFC actuators, morphing, Rayleigh method, semi-analytical model, snap-through
ASJC Scopus subject areas
- Computer Science(all)
- Signal Processing
- Engineering(all)
- Civil and Structural Engineering
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
- Materials Science(all)
- Physics and Astronomy(all)
- Condensed Matter Physics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Electrical and Electronic Engineering
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In: Smart materials and structures, Vol. 30, No. 10, 105008, 10.2021.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Semi-analytical investigations on bistable cross-ply laminates with MFC actuators
AU - Haldar, A.
AU - Anilkumar, P. M.
AU - Jansen, E. L.
AU - Rao, B. N.
AU - Rolfes, R.
PY - 2021/10
Y1 - 2021/10
N2 - Most existing semi-analytical models to analyse multistable structures are based on the principle of minimum potential energy, which inherently does not satisfy the in-plane equilibrium equations in a strong sense. Although such models predict the multistable shapes with reasonable accuracy, there is a significant discrepancy in predicting the snap-through behaviour when compared to the finite element (FE) or experimental results. In this work, a refined analytical model is derived to analyse a bistable cross-ply elliptical disc using Föppl von Kármán kinematics. The Rayleigh-Ritz approach with a decoupled energy formulation is used, where the stretching and bending energies are separated using the semi-inverse constitutive equation. The in-plane stress resultants are expressed in terms of curvatures using the compatibility and the in-plane equilibrium equations. A closed-form solution for the curvatures is derived to predict the cured bistable shapes of elliptical laminates. A layer of macro fibre composite actuator is added to trigger the snap-through between the stable shapes. Consequently, the critical voltage at which the snap-through occurs is predicted using the analytical model. The model is further extended to square plates, where the solutions of the differential equations emanating from the compatibility and in-plane equilibrium equations are obtained by converting the resulting differential equations into the form of standard FE elasticity problem. The in-plane stress resultants for the square plates are calculated by numerically solving the resulting elasticity problem using a standard FE discretization approach. The solutions are further compared with previous experimental studies and the results from a fully geometrically non-linear FE model.
AB - Most existing semi-analytical models to analyse multistable structures are based on the principle of minimum potential energy, which inherently does not satisfy the in-plane equilibrium equations in a strong sense. Although such models predict the multistable shapes with reasonable accuracy, there is a significant discrepancy in predicting the snap-through behaviour when compared to the finite element (FE) or experimental results. In this work, a refined analytical model is derived to analyse a bistable cross-ply elliptical disc using Föppl von Kármán kinematics. The Rayleigh-Ritz approach with a decoupled energy formulation is used, where the stretching and bending energies are separated using the semi-inverse constitutive equation. The in-plane stress resultants are expressed in terms of curvatures using the compatibility and the in-plane equilibrium equations. A closed-form solution for the curvatures is derived to predict the cured bistable shapes of elliptical laminates. A layer of macro fibre composite actuator is added to trigger the snap-through between the stable shapes. Consequently, the critical voltage at which the snap-through occurs is predicted using the analytical model. The model is further extended to square plates, where the solutions of the differential equations emanating from the compatibility and in-plane equilibrium equations are obtained by converting the resulting differential equations into the form of standard FE elasticity problem. The in-plane stress resultants for the square plates are calculated by numerically solving the resulting elasticity problem using a standard FE discretization approach. The solutions are further compared with previous experimental studies and the results from a fully geometrically non-linear FE model.
KW - MFC actuators
KW - morphing
KW - Rayleigh method
KW - semi-analytical model
KW - snap-through
UR - http://www.scopus.com/inward/record.url?scp=85112847710&partnerID=8YFLogxK
U2 - 10.1088/1361-665X/ac1736
DO - 10.1088/1361-665X/ac1736
M3 - Article
AN - SCOPUS:85112847710
VL - 30
JO - Smart materials and structures
JF - Smart materials and structures
SN - 0964-1726
IS - 10
M1 - 105008
ER -