, Volume 47, Issue 4, pp 877–891 | Cite as

Sensitivity, probabilistic and stochastic analysis of the thermo-piezoelectric phenomena in solids by the stochastic perturbation technique

  • Marcin Kamiński
  • Alberto Corigliano
Open Access


The main aim here is to present the application of the generalized stochastic perturbation technique to thermo-piezoelectric analysis of solid continua. The general nth order Taylor series representation for all random input parameters and the state functions is employed to formulate the coupled thermo-electro-elasticity equilibrium equations of the additional order; a determination of any probabilistic moments and characteristics is described; the discretization of the problem in terms of the Stochastic perturbation-based Finite Element Method is also provided. Since this expansion includes the lowest order partial derivatives, the structural sensitivity analysis using direct differentiation is performed at the same time with probabilistic modeling contrasted with the Monte-Carlo simulation results. The probabilistic approach is extended here towards an accounting for the stochastic ageing processes, which appear frequently in aggressive external environments and under dynamic excitation. The two parametric stochastic process with Gaussian initial value and ageing velocity is tested for this purpose. The entire procedure is tested on the example of the thermo-electro-elastic pulsation of the beam modeled analytically using the symbolic software MAPLE, where polynomial approximations, design sensitivities, probabilistic moments and their histories are computed and visualized.


Coupled field problems Stochastic perturbation method Thermo-piezoelectricity Reliability analysis MEMS devices Monte-Carlo simulation 


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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Faculty of Civil Engineering, Architecture and Environmental EngineeringTechnical University of ŁódźŁódźPoland
  2. 2.Dipartimento di Ingegneria StrutturalePolitecnico di Milano, Piazza Leonardo da Vinci, 32MilanoItaly

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