Analysis of micropolar elastic beams

Ramezani, Shojaa; Naghdabadi, R.; Sohrabpour, Saeed

doi:10.1016/j.euromechsol.2008.06.006

Cited by 59 publications

(48 citation statements)

References 12 publications

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“…Also, a more general case of loading on the beam is considered including shear tractions on the top and bottom surfaces of the beam, couple tractions in these surfaces, and axial body forces whose axes of action possibly do not coincide with the centroid of sections. It is noted that though the couple stress theory is conceptually a special case of the micropolar theory, the results of this paper cannot be obtained from the micropolar-based Timoshenko beam formulation presented in Ramezani et al [15] by dropping or simplifying some terms. This is because of the fact that if the rotation vector of the microstructure is set equal to the rotation of macrostructure, the anti-symmetric part of the Cauchy stress tensor vanishes, while the anti-symmetric part generally is appeared in the couple stress theory.…”

mentioning

confidence: 75%

“…The components of σ skew can be determined from the rotational equation of motion of the material elements [15], i.e., ∂m xy /∂ x + (σ zx − σ xz ) + ρ l y − Jφ = 0, where ρ, l y , and J represent beam density, body couple per unit mass about the y-axis, and microinertia, respectively. It is noted that in the couple stress theory, the microinertia J is commonly neglected.…”

Section: Theory and Formulationmentioning

confidence: 99%

“…The deflection of Bernoulli-Euler beams has been investigated by Park and Gao [14] using the modified couple stress theory. Timoshenko beam formulations based on the micropolar theory and the modified couple stress theory were introduced by Ramezani et al [15] and Ma et al [16], respectively. In this paper, considering both the bending and axial deformations, a Timoshenko beam formulation is proposed on the basis of the couple stress theory using the principles of linear and angular momentum.…”

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confidence: 99%

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Investigation of the size effects in Timoshenko beams based on the couple stress theory

et al. 2010

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In this paper, a size-dependent Timoshenko beam is developed on the basis of the couple stress theory. The couple stress theory is a non-classic continuum theory capable of capturing the small-scale size effects on the mechanical behavior of structures, while the classical continuum theory is unable to predict the mechanical behavior accurately when the characteristic size of structures is close to the material length scale parameter. The governing differential equations of motion are derived for the couple-stress Timoshenko beam using the principles of linear and angular momentum. Then, the general form of boundary conditions and generally valid closed-form analytical solutions are obtained for the axial deformation, bending deflection, and the rotation angle of cross sections in the static cases. As an example, the closed-form analytical results are obtained for the response of a cantilever beam subjected to a static loading with a concentrated force at its free end. The results indicate that modeling on the basis of the couple stress theory causes more stiffness than modeling by the classical beam theory. In addition, the results indicate that the differences between the results of the proposed model and those based on the classical Euler-Bernoulli and classical Timoshenko beam theories are significant when the beam thickness is comparable to its material length scale parameter.Keywords Size-dependent behavior · Timoshenko beam · Couple stress theory · Material length scale parameter

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confidence: 75%

Section: Theory and Formulationmentioning

confidence: 99%

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confidence: 99%

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Investigation of the size effects in Timoshenko beams based on the couple stress theory

et al. 2010

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“…First equation and system of rest three equations can be solved independently. We have to mention that system (61) coincide with the one presented in [30] up to notation. Therefore analysis and verification presented in [30] take place in considered here case.…”

Section: Timoshenko's Theory Of the Micropolar Curved Rodsmentioning

confidence: 99%

“…The model of micropolar beams based on the classical Euler-Bernoulli hypothesis has been considered in [27,28] and on Timoshenko's hypothesis in [29][30][31][32]. Various models of micropolar cured rods have been considered in [3,11,25,[33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Zozulya

2017

Curved and Layered Structures

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New models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress and strain tensors, vectors of displacements and rotation and body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then in the same way as in the theory of elasticity, system of differential equations in term of displacements and boundary conditions for Fourier coefficients have been obtained. The Timoshenko's and EulerBernoulli theories are based on the classical hypothesis and 2-D equations of linear micropolar elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scale when taking into account micropolar couple stress and rotation effects.

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A micropolar shell model for hard‐magnetic soft materials

Dadgar‐Rad

Hossain

2022

Numerical Meth Engineering

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Hard-magnetic soft materials (HMSMs) are particulate composites that particles with high coercivity are dispersed in a soft matrix. Since applying the magnetic loading induces a body couple in HMSMs, the resulting Cauchy stress is predicted to be asymmetric. Therefore, the micropolar continuum theory can be employed to capture the deformation of these materials. On the other hand, the geometries and structures made of HMSMs often possess small thickness compared to the overall dimensions of the body. Accordingly, in the present contribution, a 10-parameter micropolar shell formulation to model the finite elastic deformation of thin hard-magnetic soft structures under magnetic stimuli is developed. The proposed shell formulation allows for using three-dimensional constitutive laws without any need for modification to apply the plane stress assumption in thin structures. A nonlinear finite element formulation is also presented for the numerical solution of the governing equations. To alleviate the locking phenomenon, the enhanced assumed strain method is employed. Several examples are presented that demonstrate the performance and effectiveness of the proposed formulation.

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Analysis of micropolar elastic beams

Cited by 59 publications

References 12 publications

Investigation of the size effects in Timoshenko beams based on the couple stress theory

Investigation of the size effects in Timoshenko beams based on the couple stress theory

Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

A micropolar shell model for hard‐magnetic soft materials

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