Isogeometric analysis for non-classical Bernoulli-Euler beam model incorporating microstructure and surface energy effects

Yin, Shuohui; Deng, Yang; Yu, Tiantang; Gu, Shuitao; Zhang, Gongye

doi:10.1016/j.apm.2020.07.015

Cited by 27 publications

(4 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Altenbach and Eremeyev [17] derived the governing equations for thin shells by including surface energy effects and determined effective stiffness constants of a linear elastic Cosserat shell accounting for surface stress contributions. Non-classical models for Bernoulli-Euler beams, Timoshenko beams, shear deformation beams, Kirchhoff plates, Mindlin plates, Love-Kirchhoff shells, and shear deformation shells have recently been developed in [8,10,[18][19][20][21][22][23] by incorporating microstructure and surface energy effects. Non-classical models for thin rods including microstructure effects have also been provided using couple stress, micropolar and non-local elasticity theories [24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

A new model for spatial rods incorporating surface energy effects

Zhang,

Gao,

Guo

2024

Mathematics and Mechanics of Solids

Self Cite

View full text Add to dashboard Cite

A new non-classical model for spatial rods incorporating surface energy effects is developed using a surface elasticity theory. A variational formulation based on the principle of minimum total potential energy is employed, which leads to the simultaneous determination of the equilibrium equations and complete boundary conditions. The newly developed spatial rod model contains three surface elasticity constants to account for surface energy effects. The new model recovers the classical elasticity-based Kirchhoff rod model as a special case when the surface energy effects are not considered. To illustrate the new spatial rod model, two sample problems are analytically solved by directly applying the general formulas derived. The first one is the buckling of an elastic rod of circular cross-section with fixed-pinned supports, and the other is the equilibrium analysis of a helical rod deformed from a straight rod. An analytical formula is derived for the critical buckling load required to perturb the axially compressed straight rod, and two closed-form expressions are obtained for the force and couple needed in deforming the helical rod. These formulas reduce to those based on classical elasticity when the surface energy effects are suppressed. For the buckling problem, it is found that the critical buckling load predicted by the current new model is always higher than that given by the classical elasticity-based model, and the difference between the two sets of predicted values is significantly large when the radius of the rod is sufficiently small but diminishes as the rod radius increases. For the helical rod problem, the numerical results reveal that the force and couple predicted by the current model are, respectively, significantly larger and smaller than those predicted by the classical model when the rod radius is very small, but the difference is diminishing with the increase of the rod radius.

show abstract

Section: Introductionmentioning

confidence: 99%

A new model for spatial rods incorporating surface energy effects

Zhang,

Gao,

Guo

2024

Mathematics and Mechanics of Solids

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the recent years, Zhao et.al [25] presented a new Bernoulli-Euler beam model based on modified gradient elasticity, Yin et. al [26] did isogeometric analysis for non-classical Bernoulli-Euler beam model incorporating microstructure and surface energy effects, Esen [27] investigated size-dependent Timoshenko microbeams subjected to a moving load, and Chen [28] et.al reformulated microbeams by incorporating the general strain gradient elasticity theory. Also some studies modeled microbeams including functionally graded material [29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Design of two layer clamped-clamped microsensor based on classical and non-classical theories

Yekta,

Rahi

2023

Preprint

View full text Add to dashboard Cite

In this paper, the two-layer micro sensor is modeled as a two-layer clamped-clamped microbeam and it is optimized using the genetic algorithm. Using the results of this research, clamped- clamped microbeams can be designed in such a way that the performance of microsensors whose structure includes these microbeams will be improved. The quality factor, the sensitivity, and the maximum stress are selected as objective functions. The thickness of each layer, the width of the microbeam, and the length of the microbeam are selected as design variables. The optimization is done based on classical and non-classical theory by the genetic algorithm. The results based on both theories are approximately equal. The length of the microbeam is the most important variable and very changes (approximately 190%). The thickness of the silicon layer has the least effect on the results and changes just lower than 2μm (approximately 20%). The results show that when the maximum stress decreases and the sensitivity increases, the quality factor decreases which is undesirable. Maximum sensitivity obtains when the microbeam is very small.

show abstract

“…Zhang et al [88] studied the response of Timoshenko nanobeams accounting for the effects of couple stress and surface energy. Yin et al [89] studied the microstructure and surface energy effects on the deflection and free vibration of homogeneous Euler-Bernoulli nanobeams using isogeometric analysis. Regarding TFG small scale beams, the coupled effects of microstructure, residual surface stress, and surface elasticity on the size-depedent mechanics of elastic and viscoelastic TFG nanobeams was investigated [90][91][92][93][94][95].…”

Section: Introductionmentioning

confidence: 99%

A Comprehensive Study of Bending and Stability Responses of 2D-FG Nanobeams Using a Microstructure-Surface Energy-Based Model under Various Boundary Conditions

Attia

Shanab

2022

JNanoR

View full text Add to dashboard Cite

The size-dependent bending and static stability characteristics of nanobeams made of bi-directional functionally graded materials (2D-FGMs) under different boundary conditions are comprehensively investigated. Based on the modified couple stress theory and surface elasticity theory, the size-dependent model is formulated for 2D-FG Euler-Bernoulli beam. The material properties of the beam smoothly change along both the axial and thickness directions according to power-law distribution. The continuous spatial variations of the single material length scale parameter and the three surface constants are incorporated to describe the effects of microstructure and surface energy, respectively. This model accounts for the axial and transverse displacements, the exact position of the physical neutral plane, and Poisson’s effect. To obtain the static response of the present model, Ritz method is employed by approximating the axial and transverse displacements in terms of polynomial forms. Different boundary conditions, i.e., Simply-simply (S-S), Clamped-clamped (C-C), Clamped-simply (C-S), and Clamped-free (C-F), are considered and satisfied by adding auxiliary functions to the displacement functions. Numerical results with various cases of boundary conditions are performed with an insight to explore the effects of gradient indices in thickness and length directions, surface energy, material length scale parameter, slenderness ratio, and thickness on the static deflection and buckling responses of 2D-FG nanobeams. Results disclose that, the material properties, the surface energy, and microstructure effects have a significant effect on the bending, and buckling responses of 2D-FG nanobeams. Hence, this study can be helpful in the design and optimization of 2D-FG nanobeams in bending and buckling responses.

show abstract

Isogeometric analysis for non-classical Bernoulli-Euler beam model incorporating microstructure and surface energy effects

Cited by 27 publications

References 55 publications

A new model for spatial rods incorporating surface energy effects

A new model for spatial rods incorporating surface energy effects

Design of two layer clamped-clamped microsensor based on classical and non-classical theories

A Comprehensive Study of Bending and Stability Responses of 2D-FG Nanobeams Using a Microstructure-Surface Energy-Based Model under Various Boundary Conditions

Contact Info

Product

Resources

About