The corotational (CR) method is effective for extending linear elements to geometrically nonlinear analysis, but faces challenges with penalty elements based on modified couple stress theory due to C 1 continuity requirements. This paper presents an alternative CR formulation for geometrically nonlinear analysis of couple stress elasticity, approximating rigid body rotation incrementally. Then, a 4-node, 12-DOF plane element US-Q4[Formula: see text]-CS for size-dependent materials is extended for geometrically nonlinear analysis. Numerical examples demonstrate the new nonlinear element’s excellent performance in simulating size effects for the case of geometric nonlinearity.
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Liu et al. (2024) studied this question.
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