Nonlinear thermoelastic fractional-order model of nonlocal plates: Application to postbuckling and bending response
Nonlinear thermoelastic fractional-order model of nonlocal plates: Application to postbuckling and bending response
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DOI：
10.1016/j.tws.2021.107809
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发表时间：
2021-07
影响因子：
6.4
通讯作者：
Sansit Patnaik;Sai Sidhardh;F. Semperlotti
中科院分区：
文献类型：
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作者：
Sansit Patnaik;Sai Sidhardh;F. Semperlotti
本研究提出了一种综合框架不变分数阶框架，用于热、机械联合载荷作用下非局部板的几何非线性弯曲和后屈曲分析。分数阶运动框架不同于基于整数阶力学的经典非局部公式，它是正定的和热力学一致的。正定性质使变分原理的应用能够推导出定态良好的热力学控制方程。这些理论进步的直接优势体现在分数阶方法的能力上，该方法可以通过扩展经典（局部）Koiter方法获得基于能量的渐近方法。该方法允许分析评估非局部相互作用对细长结构在受压载荷作用下分叉和临界后响应性质的影响。此外，分数阶方法的正定性质允许开发精确的分数阶有限元方法，使其能够模拟受任何热机械载荷和边界条件组合影响的非局部结构。上述优点对于后屈曲状态下非局部结构的全面一致分析尤为重要。理论框架是用来提供分析和数值见解的综合热和机械载荷对非局部板的非线性响应的影响。数值结果还表明，将该框架应用于不同载荷和边界条件下的非局部板的非线性热弹性分析时，具有较高的一致性。
This study presents a comprehensive frame-invariant fractional-order framework for the geometrically nonlinear bending and postbuckling analysis of nonlocal plates subject to combined thermal and mechanical loads. The fractional-order kinematic framework, unlike classical nonlocal formulations based on integer-order mechanics, is positive-definite and thermodynamically consistent. The positive-definite nature enables the application of variational principles to derive well-posed thermomechanical governing equations. A direct advantage of these theoretical advancements is reflected in the ability of the fractional-order approach to enable an energy-based asymptotic method obtained by extending the classical (local) Koiter’s approach. This method allows the analytical assessment of the impact of nonlocal interactions on the nature of the bifurcation and post-critical response of slender structures when subject to compressive loads. Further, the positive-definite nature of the fractional-order approach allows the development of an accurate fractional-order finite element method enabling the simulation of nonlocal structures subject to any combination of thermomechanical loads and boundary conditions. The above stated advantages are particularly important for a comprehensive and consistent analysis of nonlocal structures in the postbuckling regime. The theoretical framework is used to provide analytical and numerical insights on the effect of combined thermal and mechanical loads on the nonlinear response of nonlocal plates. Numerical results also demonstrate the high-level consistency of the framework when applied to the nonlinear thermoelastic analysis of nonlocal plates under different loading and boundary conditions.