Size-dependent nonlinear bending of tapered cantilever microbeam based on modified couple stress theory

A size-dependent beam formulation based on the classical beam theory and modified couple stress theory (MCST) is derived for nonlinear bending analysis of a microcantilever under an end force/moment. The microbeam is linearly tapered in the directions of width and height. The formulation is derived using the concept of the co-rotational formulation in which the vector of internal forces and tangent stiffness matrix are firstly constructed in the element-attached coordinates and then transferred to the global ones. The nonlinear response is predicted by the iterative method and the arc-length technique. The numerical investigation confirms the efficiency of the derived formulation, and it can predict accurate nonlinear responses of the microcantilever by using just several elements. The result reveals the importance of the microstructural size effects on the nonlinear responses and ignoring the size effects leads to an overestimation of the deflections. The impacts of various factors such as the scale parameter and the tapered ratio on the nonlinear behavior of the microcantilever are investigated in detail. © 2024, Publishing House of Natural Science and Technology, VAST. All rights reserved.