Axial Buckling and Dynamic Stability of Functionally Graded Microshells Based on the Modified Couple Stress Theory

Abstract

A nonclassical¯rst-order shear deformation shell model is developed to analyze the axial buckling and dynamic stability of microshells made of functionally graded materials (FGMs). For this purpose, the modi¯ed couple stress elasticity theory is implemented into the¯rst-order shear deformation shell theory. Unlike the classical shell theory, the newly developed shell model contains an internal material length scale parameter to capture e±ciently the size e®ect. By using the Hamilton's principle, the higher-order governing equations and boundary conditions are derived. Afterward, the Navier solution is utilized to predict the critical axial buckling loads of simply-supported functionally graded (FG) microshells. Moreover, the governing equations are written in the form of Mathieu-Hill equations and then Bolotin's method is employed to determine the instability regions. A parametric study is conducted to investigate the in°uences of static load factor, axial wave number, dimensionless length scale parameter, material property gradient index, length-to-radius and length-to-thickness aspect ratios on the axial buckling and dynamic stability responses of FGM microshells. It is revealed that size e®ect plays an important role in the value of critical axial buckling load and instability region of FGM microshells especially corresponding to those with lower aspect ratios.

Eigenanalyses of Functionally Graded Micro-Scale Beams Entrapped in an Axially-Directed Magnetic Field with Elastic Restraints

“…[68][69][70] In brief, for an elastic Hookean material (with a volume V ) in a domain , the MCST proposes the strain energy to be the additive decomposition of the classical and nonclassical strain energy components in the form:…”

Buckling analysis of cylindrical thin-shells using strain gradient elasticity theory

“…Substituting Eq. (16) in Eqs. (18)(19)(20), the components of strain and strain gradient in orthogonal curvilinear coordinates can be written as [56] e ðiÞ ðjÞ ¼…”

“…Recently, the shell formulation using strain gradient theory was derived to solve the vibration problem [52]. Also, axial buckling and stability problem of functionally graded micro-shells were addressed using modified couple-stress theory [16]. Some other attempts at modeling shell buckling using gradient theories include [25,32].…”

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

“…Micro/nanoshells are an important and widely used form of micro/nanostructures in various engineering fields. Gholami et al [ 35 ] analyzed the dynamic stability and axial buckling of functionally graded cylindrical microshells. Based on the strain gradient elasticity theory, Zhang et al [ 36 ] developed a shear deformable functionally graded microshell model.…”