Nonlinear dynamics of doubly curved shallow microshells

Ghayesh, Mergen H.; Farokhi, Hamed

doi:10.1007/s11071-018-4091-7

Cited by 28 publications

(5 citation statements)

References 53 publications

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“…Based on the modified couple stress theory, 14 a considerable amount of non-classical shell models has been successfully established in recent years. For instance, Zeighampour and Beni 15,16 developed the thin cylindrical shell and conical shell models respectively for free vibration analysis of the single-walled carbon nanotube and nanocone; Jouneghani et al 17 developed the first-order shear deformation shell model for orthotropic doubly curved micro shells; Ghayesh and Farokhi 18 studied the nonlinear mechanical behaviors of the doubly curved shallow micro shells; Hosseini-Hashemi et al 19 proposed the size-dependent model for the closed micro/nano spherical shells; Ghadiri and Safarpour 20 performed the analysis of the cylindrical nano shell considering the magneto-electro-thermoelastic coupling effects; Wang et al 21 investigated the vibration responses of the circular cylindrical polymeric shell reinforced by graphene platelet. Other contributions on micro/nano shell models based on the modified couple stress theory can be found in Beni et al, 22 Salehipour et al, 23 Wang et al 24 and the references therein.…”

Section: Introductionmentioning

confidence: 99%

An efficient 4‐node facet shell element for the modified couple stress elasticity

Shang

Cen

et al. 2021

Numerical Meth Engineering

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This work proposes a simple but robust 4-node 24-DOF facet shell element for static analysis of small-scale thin shell structures. To accommodate the size effects, the modified couple stress theory is employed as the theoretical basis.The element is constructed via two main innovations. First, the trial functions that can a priori satisfy related governing differential equations are adopted as the basic functions for formulating the element interpolations. Second, the generalized conforming theory and the penalty function method are employed to meet the C 1 continuity requirement in weak sense for ensuring the computation convergence property. Several benchmarks of shells with different geometries are tested to assess the new facet shell element's capability. The numerical results reveal that the element can effectively simulate the size-dependent mechanical behaviors of small-scale thin shells, exhibiting satisfactory numerical accuracy and low susceptibility to mesh distortion. Moreover, as the shell element uses only six degrees of freedom per node, it can be incorporated into the commonly available finite element programs very readily.

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Section: Introductionmentioning

confidence: 99%

An efficient 4‐node facet shell element for the modified couple stress elasticity

Shang

Cen

et al. 2021

Numerical Meth Engineering

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“…Howbeit, the atomistic modeling and molecular simulations are powerful tools for describing the size-dependent characteristics of small size structures; their application is not more economical because of the extra computational attempts. To prevail over such problems, a variety of size-dependent elasticity models including the nonlocal elasticity theory, 17 strain gradient elasticity theory, and modified couple stress theory 18 are established for incorporating small size effects via standardizing some scale parameters and have been broadly exerted for the designing and study of the mechanical character of micro-or nanostructures. [19][20][21][22][23] The smart material discussed in the previous paragraph has been extensively applied in micro-/nanostructures and devices.…”

Section: Introductionmentioning

confidence: 99%

Modified strain gradient theory for nonlinear vibration analysis of functionally graded piezoelectric doubly curved microshells

Movahedfar

Kheirikhah

Mohammadi

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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Based on modified strain gradient theory, nonlinear vibration analysis of a functionally graded piezoelectric doubly curved microshell in thermal environment has been performed in this research. Three scale parameters have been included in the modeling of thin doubly curved microshell in order to capture micro-size effects. Graded material properties between the top and bottom surfaces of functionally graded piezoelectric doubly curved microshell have been considered via incorporating power-law model. It is also assumed that the microshell is exposed to a temperature field of uniform type and the material properties are temperature-dependent. By analytically solving the governing equations based on the harmonic balance method, the closed form of nonlinear vibration frequency has been achieved. Obtained results indicate the relevance of calculated frequencies to three scale parameters, material gradation, electrical voltage, curvature radius, and temperature changes.

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“…Based on the strain gradient elasticity theory, Zhang et al [ 36 ] developed a shear deformable functionally graded microshell model. Ghayesh and Farokhi [ 37 ] studied the nonlinear dynamical characteristics of doubly curved shallow microshells. SafarPour et al [ 38 ] investigated the influences of various temperature distributions on the vibration of functionally graded rotating cylindrical microshells.…”

Section: Introductionmentioning

confidence: 99%

Size-Dependent Free Vibration and Buckling of Three-Dimensional Graphene Foam Microshells Based on Modified Couple Stress Theory

Liu

Wang

2019

Materials

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In this research, the vibration and buckling of three-dimensional graphene foam (3D-GrF) microshells are investigated for the first time. In the microshells, three-dimensional graphene foams can distribute uniformly or non-uniformly through the thickness direction. Based on Love’s thin shell theory and the modified couple stress theory (MCST), size-dependent governing equations and corresponding boundary conditions are established through Hamilton’s principle. Then, vibration and axial buckling of 3D-GrF microshells are analyzed by employing the Navier method and Galerkin method. Results show that the graphene foam distribution type, size effect, the foam coefficient, the radius-to-thickness ratio, and the length-to-radius ratio play important roles in the mechanical characteristics of 3D-GrF microshells.

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Nonlinear dynamics of doubly curved shallow microshells

Cited by 28 publications

References 53 publications

An efficient 4‐node facet shell element for the modified couple stress elasticity

An efficient 4‐node facet shell element for the modified couple stress elasticity

Modified strain gradient theory for nonlinear vibration analysis of functionally graded piezoelectric doubly curved microshells

Size-Dependent Free Vibration and Buckling of Three-Dimensional Graphene Foam Microshells Based on Modified Couple Stress Theory

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