A novel advanced model for an isotropic electro-thermo-elastic bar with a variable cross-section is developed using a reformulated strain gradient theory. This theory incorporates strain gradient effects, electric quadrupoles, and flexoelectric phenomena. The governing equations and boundary conditions are derived via a variational formulation based on Hamilton’s principle. The static one-dimensional problem of a stretched slender bar with one fixed end is solved. The influence of the temperature gradient on the behavior of an isotropic microbar with a non-uniform cross-sectional area is analyzed. A differential quadrature method (DQM) is employed to solve the obtained coupled system of governing equations with variable coefficients. The impact of small-scale factor, flexoelectric material properties, microbar geometry, and thermal loading on the coupled fields in the thermoelastic structure is studied. The results underscore the importance of considering non-uniform bar geometry, flexoelectricity, and size effect in micro-scale analyses and applications.

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Some Aspects of Coupled Electro-Thermo-Mechanical Effects in Flexoelectric Microbar

  • Olha Hrytsyna,
  • Maryan Hrytsyna

摘要

A novel advanced model for an isotropic electro-thermo-elastic bar with a variable cross-section is developed using a reformulated strain gradient theory. This theory incorporates strain gradient effects, electric quadrupoles, and flexoelectric phenomena. The governing equations and boundary conditions are derived via a variational formulation based on Hamilton’s principle. The static one-dimensional problem of a stretched slender bar with one fixed end is solved. The influence of the temperature gradient on the behavior of an isotropic microbar with a non-uniform cross-sectional area is analyzed. A differential quadrature method (DQM) is employed to solve the obtained coupled system of governing equations with variable coefficients. The impact of small-scale factor, flexoelectric material properties, microbar geometry, and thermal loading on the coupled fields in the thermoelastic structure is studied. The results underscore the importance of considering non-uniform bar geometry, flexoelectricity, and size effect in micro-scale analyses and applications.