Ionic polymer metal composites (IPMCs) are a class of soft electroactive polymers. IPMCs comprise a soft ionic polymer core, on which two stiff metal electrodes are plated. These active materials exhibit large bend- ing upon the application of a small driving voltage across their electrodes, in air or in aqueous environments. In a recent work, we presented compelling theoretical and numerical evidence suggesting that ionic polymer membranes exhibit complex multiaxial deformations neglected by reduced-order structural models. Where most beam theories (including Euler-Bernoulli, Timoshenko, and most higher-order shear deformation models) would suggest vanishing through-the-thickness deformation, we discover the onset of localized deformation that rever- berates into axial stretching. Building upon this effort, here we investigate the role of the electrodes and shear on multiaxial deformations of IPMCs. We establish a novel structural theory for IPMCs, based on the Euler- Bernoulli kinematics enriched with the through-the-thickness deformation in the ionic polymer, computed from a Saint-Venant-like problem for uniform bending. While considering boundary conditions that elicit non-uniform bending, we compare the results of this model against classical Euler-Bernoulli beam theory without enrichment and finite element simulations, encapsulating the nonlinear response of the material. We demonstrate that our theory can predict the macroscopic displacement of the IPMC, along with the localized deformation in the ionic polymer at the interface with the electrodes, which are not captured by the classical Euler-Bernoulli beam theory. This work paves the way to the development of more sophisticated structural theories for IPMCs and analogous active materials, affording an accurate description of deformations at a limited computational cost.
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Topology optimization of structural frames based on a nonlinear Timoshenko beam finite element considering full interaction
This article presents an approach for the topology optimization of frame structures composed of nonlinear Timoshenko beam finite elements (FEs) under time‐varying excitation. Material nonlinearity is considered with a nonlinear Timoshenko beam FE model that accounts for distributed plasticity and axial–shear–moment interactions through appropriate hysteretic interpolation functions and a yield/capacity function, respectively. Hysteretic variables for curvature, shear, and axial deformations represent the nonlinearities and evolve according to first‐order nonlinear ordinary differential equations (ODEs). Owing to the first‐order representation, the governing dynamic equilibrium equations, and hysteretic evolution equations can thus be concisely presented as a combined system of first‐order nonlinear ODEs that can be solved using a general ODE solver. This avoids divergence due to an ill‐conditioned stiffness matrix that can commonly occur with Newmark–Newton solution schemes that rely upon linearization. The approach is illustrated for a volume minimization design problem, subject to dynamic excitation where an approximation for the maximum displacement at specified nodes is constrained to a given limit, that is, a drift ratio. The maximum displacement is approximated using the p‐norm, thus facilitating the derivation of the analytical sensitivities for gradient‐based optimization. The proposed approach is demonstrated through several numerical examples for the design of structural frames subjected to sinusoidal base excitation.
more » « less- PAR ID:
- 10370649
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- International Journal for Numerical Methods in Engineering
- Volume:
- 123
- Issue:
- 19
- ISSN:
- 0029-5981
- Page Range / eLocation ID:
- p. 4562-4585
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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