Electroelastic high-order computational continuum strategy for critical voltage and frequency of piezoelectric NEMS via modified multi-physical couple stress theory

2022 ◽  
Vol 165 ◽  
pp. 108373
Author(s):  
Xiaomo Yu ◽  
Allam Maalla ◽  
Zohre Moradi
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
High Order ◽  
Critical Voltage ◽  
Stress Theory

scholarly journals Couple stress theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

2017 ◽  
Vol 4 (1) ◽  
pp. 119-133 ◽  
Author(s):  
V.V. Zozulya
Keyword(s):  
Fourier Series ◽  
Couple Stress ◽  
Legendre Polynomials ◽  
Fourier Coefficients ◽  
Couple Stress Theory ◽  
Order Theory ◽  
Theory Of Elasticity ◽  
High Order ◽  
Stress Theory ◽  
Curved Rods

AbstractNew models for plane curved rods based on linear couple stress theory of elasticity have been developed.2-D theory is developed from general 2-D equations of linear couple stress elasticity using a special curvilinear system of coordinates related to the middle line of the rod as well as special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and rotation along with body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby, all equations of elasticity including Hooke’s law have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of elasticity, a system of differential equations in terms of displacements and boundary conditions for Fourier coefficients have been obtained. Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear couple stress theory of elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scales when taking into account couple stress and rotation effects.

A non-classical theory of elastic dielectrics incorporating couple stress and quadrupole effects: part I – reconsideration of curvature-based flexoelectricity theory

2021 ◽  
pp. 108128652110015
Author(s):  
YL Qu ◽  
GY Zhang ◽  
YM Fan ◽  
F Jin
Keyword(s):  
Classical Theory ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Constitutive Relations ◽  
Stress Theory ◽  
Isotropic Materials ◽  
Flexoelectric Effect ◽  
Beam Bending ◽  
Gradient Theories ◽  
Anisotropic And Isotropic Materials

A new non-classical theory of elastic dielectrics is developed using the couple stress and electric field gradient theories that incorporates the couple stress, quadrupole and curvature-based flexoelectric effects. The couple stress theory and an extended Gauss’s law for elastic dielectrics with quadrupole polarization are applied to derive the constitutive relations of this new theory through energy conservation. The governing equations and the complete boundary conditions are simultaneously obtained through a variational formulation based on the Gibbs-type variational principle. The constitutive relations of general anisotropic and isotropic materials with the corresponding independent material constants are also provided, respectively. To illustrate the newly proposed theory and to show the flexoelectric effect in isotropic materials, one pure bending problem of a simply supported beam is analytically solved by directly applying the formulas derived. The analytical results reveal that the flexoelectric effect is present in isotropic materials. In addition, the incorporation of both the couple stress and flexoelectric effects always leads to increased values of the beam bending stiffness.

A size-dependent model for shear deformable laminated micro-nano plates based on couple stress theory

2021 ◽  
Vol 259 ◽  
pp. 113457
Author(s):  
Zanhang He ◽  
Jianghong Xue ◽  
Sishi Yao ◽  
Yongfu Wu ◽  
Fei Xia
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Stress Theory ◽  
Size Dependent ◽  
Dependent Model ◽  
Shear Deformable
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