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Well-posedness of two-phase local/nonlocal integral polar models for consistent axisymmetric bending of circular microplates

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Applied Mathematics and Mechanics(English Edition) 2022年第5期43卷 637-652页

作者： Hai QING State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China

Previous studies have shown that Eringen’s differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular *** on the nonlocal integral models along the radial and circumferential directions,we propose nonlocal integral polar models in this *** proposed strainand stress-driven two-phase nonlocal integral polar models are applied to model the axisymmetric bending of circular *** governing differential equations and boundary conditions(BCs)as well as constitutive constraints are *** is found that the purely strain-driven nonlocal integral polar model turns to a traditional nonlocal differential polar model if the constitutive constraints are ***,the purely strain-and stress-driven nonlocal integral polar models are ill-posed,because the total number of the differential orders of the governing equations is less than that of the BCs plus constitutive *** nominal variables are introduced to simplify the mathematical expression,and the general differential quadrature method(GDQM)is applied to obtain the numerical *** results from the current models(CMs)are compared with the data in the *** is clearly established that the consistent softening and toughening effects can be obtained for the strain-and stress-driven local/nonlocal integral polar models,*** proposed two-phase local/nonlocal integral polar models(TPNIPMs)may provide an efficient method to design and optimize the plate-like structures for microelectro-mechanical systems.

关键词： softening effect toughening effect circular microplate nonlocal integral model general differential quadrature method(GDQM)

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