Semi-implicit numerical simulations of geometrically nonlinear beam, plate, and shell dynamical systems

Alexeev, Timur; Hafez, Mohammed M.

doi:10.1080/15502287.2016.1247121

Cited by 1 publication

(2 citation statements)

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“…Imposing boundary and symmetry constraints on the shape function power series results in dependencies among the coefficients a n . We first enforce the boundary conditions (15) and ( 16) which considered at = 0 impose the vanishing of the constant and linear terms and considered at = 1 impose the relations These relations can be solved for the first two non-vanishing coefficients yielding and The symmetry constraint (17) similarly imposes the relations (30)…”

Section: General Methods and Resultsmentioning

confidence: 99%

“…A similar approach was previously used to derive a nonlinear model of microcantilever actuators [14] and its extension to a nonlinear modal analysis was considered in [15,16]. Furthermore, the approach utilized in the derivation of our model has been successfully applied on numerous occasions in the form of a Galerkin method used to model geometrical nonlinearities in the context of efficient full spatio-temporal numerical simulations of MEMS structures [17,18]. However, to the best of our knowledge, the model presented in the present paper is the first lumped model of the piezoelectric bridge system accounting for geometrical nonlinearities and incorporating their effect on the shape of the bridge.…”

Section: Introductionmentioning

confidence: 99%

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Geometrical nonlinearities and shape effects in electromechanical models of piezoelectric bridge structures

Ohlsson

Johannisson

Rusu

2021

Int J Energy Environ Eng

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We consider nonlinear shape effects appearing in the lumped electromechanical model of a bimorph piezoelectric bridge structure due to the interaction between the electromechanical constitutive model and the geometry of the structure. At finite proof-mass displacement and electrode voltage, the shape of the beams is no longer given by Euler-Bernoulli theory which implies that shape effects enter in both the electrical and mechanical domains and in the coupling between them. Accounting for such effects is important for the accurate modelling of, e.g., piezoelectrical energy harvesters and actuators in the regime of large deflections and voltages. We present a general method, based on a variational approach minimizing the Gibbs enthalpy of the system, for computing corrections to the nominal shape function and the associated corrections to the lumped model. The lowest order correction is derived explicitly and is shown to produce significant improvements in model accuracy, both in terms of the Gibbs enthalpy and the shape function itself, over a large range of displacements and voltages. Furthermore, we validate the theoretical model using large deflection finite element simulations of the bridge structure and conclude that the lowest order correction substantially improve the model, obtaining a level of accuracy expected to be sufficient for most applications. Finally, we derive the equations of motion for the lowest order corrected model and show how the coupling between the electromechanical properties and the geometry of the bridge structure introduces nonlinear interaction terms.

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Section: General Methods and Resultsmentioning

confidence: 99%