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

Qing, Hai

doi:10.1007/s10483-022-2843-9

Cited by 13 publications

(2 citation statements)

References 44 publications

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“…This symmetry endows objects with a sense of aesthetic balance. Many engineering structures, such as bridges, buildings, and mechanical components, adopt axisymmetric design [17][18]. Axisymmetric structures have strong stability, can withstand huge loads and wind forces, and resist the impact of natural disasters such as earthquakes [19][20].…”

Section: Axisymmetric Mechanical Problemsmentioning

confidence: 99%

Complete Edge Smooth Finite Interpolation Method for Limit Upper Limit Analysis of Axisymmetric Structures

2024

jemm

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Axisymmetric structures have applications in various fields such as engineering and architecture. This type of structure exhibits complex stress distribution and failure modes when subjected to ultimate loads, and the importance of the analysis method for its upper limit in the engineering field is self-evident. Its upper limit analysis is mainly used to evaluate the stability and load-bearing capacity of axisymmetric structures under load. The intention of the fully edge smooth finite interpolation method is to improve the accuracy and efficiency of analysis. It improves the interpolation function to maintain smoothness at the boundary, and uses adaptive mesh partitioning and local refinement to make the analysis more accurate and efficient. Therefore, the purpose of this article's in-depth study on the perfect edge smooth finite interpolation method is to introduce smooth functions and finite interpolation techniques, accurately simulate structures, avoid risks, and reduce losses. This article mainly applies numerical simulation and experimental comparison to compare the axisymmetric structures of thick walled cylinders, frustums, and spheres. The ultimate load of each structure is obtained by changing the distortion coefficient and radius ratio. The experimental results show that in cylindrical testing, the performance difference between the two methods is greatest when the radius ratio is 3.5. The error between the perfectly smooth finite interpolation method and the analytical value is smaller, while the direct iteration method has a larger error.

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Section: Axisymmetric Mechanical Problemsmentioning

confidence: 99%

Complete Edge Smooth Finite Interpolation Method for Limit Upper Limit Analysis of Axisymmetric Structures

2024

jemm

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“…Through Eringen’s nonlocal differential model (ENDM) is extendedly applied to address the size effect of microstructures, inconsistent size-dependent responses are obtained for tensile bar (Benvenuti and Simone, 2013; Pisano and Fuschi, 2003) and flexural beams (Li et al, 2015a; Reddy and Pang, 2008; Zhang et al, 2019a; Zhang and Qing, 2020; Tang and Qing, 2021). In addition, it is also reported that ENDM would lead to ill-posed mathematical formulation for high-order shear deformation beams(Zhang and Qing, 2021b, 2021c; Zhang et al, 2021) and plates(Peddieson et al, 2003; Qing, 2022), since the order of differential governing equations is higher than the number of boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Free damping vibration of functionally graded porous viscoelastic nonlocal microbeam with thermal effect

Song

Qing

2022

Journal of Vibration and Control

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Combining classic Kelvin–Voigt viscoelastic model and two-phase local/nonlocal integral models (TPNIM), two-phase local/nonlocal integral viscoelastic models (TPNIVM) are proposed to study the free thermo-damping vibration of functionally graded porous microbeam with four different porous distribution patterns. The differential governing equations, boundary conditions, and constitutive constraints are formulated. The axial stress due to environmental temperature variation is derived explicitly. Several nominal variables are introduced to simplify the mathematical formulae. Laplace transformation is applied to obtain the explicit expression for bending deflection and moment. On considering the boundary conditions and constitutive constraints, a complex coefficients nonlinear equation is obtained to determine the complex characteristic frequency. A two-step numerical method is proposed to solve the elastic vibration frequency and damping ratio. The influence of nonlocal parameters, porous distribution parameters, and environmental temperature variation on the elastic vibration frequency and damping ratio is investigated numerically for different boundary conditions. The numerical results show that, under different boundary conditions, the compressive thermal stresses lead to the decrease of nominal vibration frequencies, and the increase of critical viscos coefficient and the damping ratio. With the increase of [Formula: see text] and the decrease of [Formula: see text], the damping ratio increases and decrease for strain-driven (εD) and stress-driven (σD) nonlocal models, respectively.

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A size-dependent axisymmetric plate element: application to MEMS

Rahaeifard,

Karimzadeh

2024

Arch Appl Mech

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

Cited by 13 publications

References 44 publications

Complete Edge Smooth Finite Interpolation Method for Limit Upper Limit Analysis of Axisymmetric Structures

Complete Edge Smooth Finite Interpolation Method for Limit Upper Limit Analysis of Axisymmetric Structures

Free damping vibration of functionally graded porous viscoelastic nonlocal microbeam with thermal effect

A size-dependent axisymmetric plate element: application to MEMS

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