Alpha (α) assumed rotations and shear strains for spatially isotropic polygonal Reissner-Mindlin plate elements (αARS-Poly)

Abstract

This paper proposes simple and efficient alpha assumed rotations and shear strains for polygonal plate elements, named αARS-Poly. In the αARS approach, an alternative assumption of the tangent rotations along element boundaries is applied by using the approximation of the rotations in Timoshenko's beam theory. Then, the quadratic term of this assumed field is linearly scaled up by adding an artificial positive scaling factor $\alpha >0$. Through examination of the relative errors in the energy (s-) norm regarding α in numerical experiences, the value $\alpha =0.5$ can be chosen as a general-fixed value that possibly achieves the optimal relative errors of the s-norm. The value $\alpha =0.5$ seems to be not only mesh-independent but also problem-independent. The αARS-Poly element using $\alpha =0.5$ passes all critical tests (spatially isotropic, zero-energy mode, and bending path tests) for a finite plate element which ensures the element orientation-independent property, solution stability, and free shear-locking in the thin plate limit. The implementation of the αARS-Poly element is straightforward through a unified form of the stiffness matrix for all arbitrary convex-shaped polygonal meshes. Numerical results show that the proposed element achieves high reliable and optimal results with uniform and excellent convergent rates in the static and free vibration analyses.