Postcritical Behavior of Nonlocal Strain Gradient Arches: Formulation and Differential Quadrature Solution
Publication: Journal of Engineering Mechanics
Volume 149, Issue 2
Abstract
Arches are important components in nanostructures and systems. Because of the remarkable strength of nanomaterials, nanoarches are slender, thus enhancing their vulnerability to geometric instability, such as buckling. Although molecular simulations are often employed to analyze nanostructures, their use in routine analysis/design is formidable due to prohibitively exhaustive computation. Equivalent continuum models were developed as alternatives. The buckling and postcritical phenomena of the classical arch also form an important benchmark problem in nonlinear mechanics. This study investigates the buckling and the postcritical behavior of nanoarch subjected to inward pressure using nonlocal (NL), strain gradient (SG) continuum theory. The governing equations are derived in the form of a sixth-order nonlinear integrodifferential equation, unlike the fourth-order for a classical arch. The equation is then solved numerically using a differential quadrature (DQ) with appropriate boundary conditions. An incremental-iterative arc-length continuation is employed for the solution of the resulting algebraic system of equations. The equilibrium paths are traced for the possible instability modes, such as symmetric/antisymmetric bifurcations, snap-through and limit point instability, ascertained with the internal-external force diagrams. A particular instability mode is triggered at a certain threshold/range of the slenderness ratio of the arch, which is significantly influenced by the NL and SG interactions. These interactions not only cause quantitative changes in the instability behavior but also lead to qualitative changes, such as cessation, shift, and conversion of modes, more prominently for SG arches. Similar to classical arches, the prebuckling nonlinearity is shown to be significant.
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Published In
Journal of Engineering Mechanics
Volume 149 • Issue 2 • February 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Apr 24, 2022
Accepted: Sep 14, 2022
Published online: Nov 25, 2022
Published in print: Feb 1, 2023
Discussion open until: Apr 25, 2023
ASCE Technical Topics:
- Arches
- Bifurcations
- Buckling
- Continuum mechanics
- Design (by type)
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Geometrics
- Highway and road design
- Material mechanics
- Materials engineering
- Nanomechanics
- Solid mechanics
- Strain
- Structural behavior
- Structural dynamics
- Structural engineering
- Structural members
- Structural strength
- Structural systems
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