Three dimensional elements with Lagrange multipliers for the modified couple stress theory

2017 ◽  
Vol 62 (1) ◽  
pp. 97-110 ◽  
Author(s):  
Young-Rok Kwon ◽  
Byung-Chai Lee
Keyword(s):  
Lagrange Multipliers ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Three Dimensional ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Modified Couple Stress

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

Materials ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 729 ◽  
Author(s):  
Yunfei Liu ◽  
Yanqing Wang
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Three Dimensional ◽  
Modified Couple Stress Theory ◽  
Graphene Foam ◽  
Stress Theory ◽  
Size Dependent ◽  
Type Size ◽  
Modified Couple Stress ◽  
Distribution Type

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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