Size-dependent nonlinear bending of microbeams based on a third-order shear deformation theory

Vietnam Journal of Mechanics - Tập 46 Số 2 - Trang 119-137 - 2024
Ngoc Duyen Dang1, Dinh Kien Nguyen2, Cong Ich Le3
1\(^1\) Faculty of Mechanical Engineering, Thuyloi University, 175 Tay Son, Dong Da, Hanoi, Vietnam<br> \(^2\) Graduate University of Science and Technology, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam
2\(^2\) Graduate University of Science and Technology, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam<br> \(^3\) Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam
3\(^4\) Faculty of Mechanical Engineering, Le Quy Don Technical University, 236 Hoang Quoc Viet, Hanoi, Vietnam

Tóm tắt

In this paper, the size-dependent nonlinear bending of microbeams subjected to mechanical loading is studied using a finite element formulation. Based on the von Kármán nonlinear relationship and the third-order shear deformation theory, a size-dependent nonlinear beam element is derived by using the modified couple stress theory (MCST) to capture the microstructural size effect. The element with explicit expressions for the element vector of internal forces and tangent stiffness matrix is derived by employing the transverse shear rotation as a variable. Nonlinear bending of microbeams under different mechanical loading is predicted with the aid of Newton–Raphson iterative method. Numerical investigation shows that the derived element is efficient, and it is capable of giving accurate results by several elements. The obtained results reveal the importance of the micro-size effect on the nonlinear behavior of the microbeams, and the deflections are overestimated when the microstructural effect is ignored. The effects of the material length scale parameter, boundary conditions and loading type on the bending response of the microbeams are studied and highlighted.

Từ khóa

#microbeam #micro-size effect #nonlinear bending #finite element formulation

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Vietnam Journal of Mechanics

Tập 46 Số 2

119-137

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