Three-node macro triangular shell element based on the assumed natural strains.

*(English)*Zbl 1146.74361Summary: Finite element models with simple triangular geometry facilitate pre-processing for the finite element analysis. In the present study, a robust shear deformable triangular shell element formulation is presented for general plate and shell analysis, using three-node mesh discretization. The present formulation is developed on the basis of the assumed natural strain (ANS) formulation to attenuate the shear locking effect. Furthermore, this study proposes macro triangular element scheme by dividing a three-node triangular mesh into three parts to produce three individual ANS triangular elements and then merges these by condensing out the virtual center node. The performance of the macro ANS element is highly enhanced by reducing the number of sampling locations of three sub triangular element, but still utilizes three-node mesh discretization same as does the mesh used for three-node triangular elements. The macro ANS element has invariant stiffness, possesses no commutable zero energy mechanism. Numerical tests are presented to illustrate the high performance nature of the macro ANS element in general shell analysis. In particular, the numerical study demonstrates that the macro ANS element completely removes the shear locking effect that has been detrimental in shear deformable linear triangular elements so far.