Nonlinear in-plane thermomechanical stability of shallow sandwich micro-arches including strain gradient tensors. (English) Zbl 1543.74046
Summary: The microstructural-dependent nonlinear in-plane stability characteristics of functionally graded (FG) sandwich shallow micro-arches subjected to a uniformly distributed lateral load in conjunction with a temperature rise are investigated in the current study. In this regard, the third-order shear flexible arch formulations are established within the framework of the modified strain gradient continuum mechanics. The considered sandwich micro-arches are made of nanocomposites reinforced with graphene nanofillers based upon various FG lamination patterns. The Chebyshev-Gauss-Lobatto type of gridding scheme together with the pseudo arc-length continuation technique are employed to employ a numerical solution strategy for tracing the size-dependent lateral load-deflection and lateral load-axial load nonlinear stability plots. It is observed that by adding a rise in the temperature to the applied uniform lateral load, the first bifurcation lateral load enhances, while the second one reduces. Also, it is dedicated that there is a unique value of the applied uniform lateral load corresponding to which the axial resultant load as well as the induced lateral deflection in the micro-arch are the same for all values of the temperature rise. Moreover, it is revealed that by increasing the value of the rise in the temperature, the size dependency in the value of the upper limit lateral load becomes less prominent, while it enhances in the value of the lower limit lateral load.
MSC:
| 74G60 | Bifurcation and buckling |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74F05 | Thermal effects in solid mechanics |
| 74E30 | Composite and mixture properties |
| 74M25 | Micromechanics of solids |
| 74S99 | Numerical and other methods in solid mechanics |
Keywords:
nanocomposite; curved beam; strain gradient elasticity; Chebyshev-Gauss-Lobatto gridding scheme; pseudo arc-length continuation methodReferences:
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