Accurate solutions of a thin rectangular plate deflection under large uniform loading

Liu, Ling; Zhong, Xiaoxu; Liao, Shijun

doi:10.1016/j.apm.2023.06.037

Cited by 2 publications

(2 citation statements)

References 44 publications

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“…The nonlinear bending analysis of the plate is one of the important topics in the engineering field, which attracts many researchers [24][25][26]. For instance, Liu et al [27] studied the large deflection of a thin rectangular plate exposed to uniform loads. Gao et al [28] studied the large deflection of a cantilever beam exposed to tip and distributed loads.…”

Section: Introductionmentioning

confidence: 99%

The Nonlinear Bending of Sector Nanoplate via Higher-Order Shear Deformation Theory and Nonlocal Strain Gradient Theory

Sadeghian,

Jamil,

Palevicius

et al. 2024

Mathematics

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In this context, the nonlinear bending investigation of a sector nanoplate on the elastic foundation is carried out with the aid of the nonlocal strain gradient theory. The governing relations of the graphene plate are derived based on the higher-order shear deformation theory (HSDT) and considering von Karman nonlinear strains. Contrary to the first shear deformation theory (FSDT), HSDT offers an acceptable distribution for shear stress along the thickness and removes the defects of FSDT by presenting acceptable precision without a shear correction parameter. Since the governing equations are two-dimensional and partial differential, the extended Kantorovich method (EKM) and differential quadrature (DQM) have been used to solve the equations. Furthermore, the numeric outcomes were compared with a reference, which shows good harmony between them. Eventually, the effects of small-scale parameters, load, boundary conditions, geometric dimensions, and elastic foundations are studied on maximum nondimensional deflection. It can be concluded that small-scale parameters influence the deflection of the sector nanoplate significantly.

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Section: Introductionmentioning

confidence: 99%

The Nonlinear Bending of Sector Nanoplate via Higher-Order Shear Deformation Theory and Nonlocal Strain Gradient Theory

Sadeghian,

Jamil,

Palevicius

et al. 2024

Mathematics

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“…In the design of Flexible Printed Circuits (FPCs), it is critical to address several considerations to ensure their durability and functionality. Firstly, FPCs are inherently more delicate than their rigid counterparts and are prone to mechanical damage, such as cracks or fractures 22 , particularly when subjected to external stress or forces 23 . This vulnerability is heightened in environments where the FPCs may contact other components, especially in settings prone to movement or vibration.…”

mentioning

confidence: 99%

Mathematical modeling of flexible printed circuit configuration: a study in deformation and optimization

Meng,

Ding,

Khan

et al. 2024

Sci Rep

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This manuscript offers an exhaustive analysis of Flexible Printed Circuits (FPCs), concentrating on enhancing their design to surmount two primary challenges. Firstly, it seeks to obviate contact with proximate components. Secondly, it aspires to adhere to pre-established curvature constraints. Predicated on the curvature properties of FPCs, we have developed a model adept at accurately forecasting FPC deformation under diverse conditions. Our inquiry entails a thorough examination of various FPC configurations, including bell, 'U', and 'S' shapes. Central to our methodology is the strategic optimization of FPC spatial arrangements, aiming to avert mechanical interference and control curvature, thus mitigating mechanical strain. This dual-faceted strategy is pivotal in enhancing the durability and operational reliability of FPCs, particularly in contexts demanding elevated flexibility and precision. Our research offers essential insights into the refinement of FPC design, skillfully addressing the complexities associated with curvature and physical interaction. Collectively, this study advocates a comprehensive framework for the design and implementation of FPCs, significantly advancing the field of contemporary electronics by ensuring these components meet the evolving demands of the industry.

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Accurate solutions of a thin rectangular plate deflection under large uniform loading

Cited by 2 publications

References 44 publications

The Nonlinear Bending of Sector Nanoplate via Higher-Order Shear Deformation Theory and Nonlocal Strain Gradient Theory

The Nonlinear Bending of Sector Nanoplate via Higher-Order Shear Deformation Theory and Nonlocal Strain Gradient Theory

Mathematical modeling of flexible printed circuit configuration: a study in deformation and optimization

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