Differential quadrature-based solution for non-classical Euler-Bernoulli beam theory

Ishaquddin,; Gopalakrishnan, S.

doi:10.1016/j.euromechsol.2020.104135

Cited by 7 publications

(4 citation statements)

References 47 publications

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“…The cantilever beam has the advantages of simple structure and easy theoretical calculation so that the SPA can be simplified as a cantilever beam. The nonlinear Euler-Bernoulli beam(NEBB) is a simplified linear elastic theory used to calculate the stress and deformation characteristics of beams [20] , and the SPA is made of elastic material;…”

Section: The Design Of a Soft Pneumatic Actuatormentioning

confidence: 99%

Deformation estimation of Soft Pneumatic Actuators under external force baesd on experimental nonlinear Euler-Bernoulli beam

Li¹,

Lai²,

Tang³

2022

Preprint

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Soft pneumatic actuators(SPAs) can be adapted to grasp objects of different shapes, and it is helpful to estimate the SPA's deformation under external force, but their low stiffness bring signifcant challenges to the experimental characterization and modeling of their statics. Aiming at achieving the target of estimating SPA's deformation through establishing relation models between external force, air pressure, and SPA's deformation, a practical and straightforward estimation method is proposed in this paper. The nonlinear Euler-Bernoulli beam(NEBB) is applied, the SPA is simplified as a nonlinear cantilever beam, and the complex internal air pressure effect is equivalent to the external moment to analyze the SPA's deformation. The proposed nonlinear beam SPA method and finite element method(FEA) are compared with the experimental data, respectively, and the estimated deformation curves of proposed nonlinear beam SPA method agree well with the experimental results than FEA. It is shown that SPA's deformation can be estimated accurately through the proposed method. The study establishes a nonlinear beam SPA method baesd on nonlinear Euler-Bernoulli beam to estimate the SPA's deformation under external force and can potentially be used to analyze various SPAs’s mechanical property.

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Section: The Design Of a Soft Pneumatic Actuatormentioning

confidence: 99%

Deformation estimation of Soft Pneumatic Actuators under external force baesd on experimental nonlinear Euler-Bernoulli beam

Li¹,

Lai²,

Tang³

2022

Preprint

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“…The mechanical behavior of classical beams has been described using numerical [4,5] and theoretical methods [6,7], where their static and dynamic responses are studied with ordinary calculus. Accordingly, structural studies on beams with a variable cross-section [8], and in beams that have discontinuities [9,10] or that are cracked [2,11], have been reported.…”

Section: Introductionmentioning

confidence: 99%

Effects of Hausdorff Dimension on the Static and Free Vibration Response of Beams with Koch Snowflake-like Cross Section

2023

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In this manuscript, static and free vibration responses on Euler–Bernoulli beams with a Koch snowflake cross-section are studied. By applying the finite element method, the transversal displacement in static load condition, natural frequencies, and vibration modes are solved and validated using Matlab. For each case presented, the transversal displacement and natural frequency are analyzed as a Hausdorff dimension function. It is found that the maximum displacement increases as the Hausdorff dimension increases, with the relationship ymax=k0.79lndH+0.37, being k the iteration number of pre-fractal. The natural frequencies increase as ω∼M2.51, whereas the bending stiffness is expressed as EI=1165.4ln(dH+k). Numerical examples are given in order to discuss the mechanical implications.

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“…The Euler-Bernoulli beam theory, a classical approach to bending, is widely recognized as a fundamental method. This theory, however, overlooks the impact of transverse shear deformation on bending solutions [25]. Timoshenko pioneered the study of thick beams by considering transverse shear deformation and assuming a constant transverse shear strain along the beam thickness [26].…”

Section: Introductionmentioning

confidence: 99%

Theoretical Analysis on Thermo-Mechanical Bending Behavior of Timber–Concrete Composite Beams

Guan,

Dai,

Zhang

et al. 2023

Buildings

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In this study, an analytical approach is introduced for predicting the bending behavior of a timber–concrete composite (TCC) beam subjected to a mechanical load and a non-uniform temperature field, in which the orthotropy of timber as well as interfacial slip are taken into consideration. The analytical model addresses the non-uniform temperature field using Fourier series expansion based on the heat transport theory. The stresses and displacements of the TCC beam under the thermo-mechanical condition are governed by the thermo-elasticity theory, and the corresponding solution is derived analytically by solving a group of non-homogeneous partial differential equations. The proposed solution is in good agreement with the finite element solution and exhibits higher accuracy compared to the Euler–Bernoulli beam solution that relies on the assumption of transverse shear deformation and isotropy. An extensive investigation is carried out to analyze how the bending behavior of TCC beams is influenced by variations in interfacial shear stiffness and temperature field.

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Differential quadrature-based solution for non-classical Euler-Bernoulli beam theory

Cited by 7 publications

References 47 publications

Deformation estimation of Soft Pneumatic Actuators under external force baesd on experimental nonlinear Euler-Bernoulli beam

Deformation estimation of Soft Pneumatic Actuators under external force baesd on experimental nonlinear Euler-Bernoulli beam

Effects of Hausdorff Dimension on the Static and Free Vibration Response of Beams with Koch Snowflake-like Cross Section

Theoretical Analysis on Thermo-Mechanical Bending Behavior of Timber–Concrete Composite Beams

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