An adaptive triangular element of absolute nodal coordinate formulation for thin plates and membranes

An adaptive triangular element based on the absolute nodal coordinate formulation is developed for thin plates and membranes in this work. An elegant theory for thin plate and membrane is first generated under the Kirchhoff-Love assumptions, where the Green strain tensor is decomposed into membrane strain and bending strain tensors. The Hsieh-Clough-Tocher triangular element is extended into the frame of the absolute nodal coordinate formulation for the first time and corresponding shape functions are then derived. The elastic force and Jacobian matrix of the membrane element are explicitly derived by the multiplication of constant tensors and generalized coordinates, resulting in higher efficiency than the plate element. The same group of generalized coordinates is used in membrane and plate elements. Based on this characteristic, a novel adaptive algorithm is proposed based on the stress states to determine at which Gauss points only the membrane strain needs to be considered. The accuracy and adaptability are validated using several benchmark problems. The present adaptive element can improve efficiency without loss of accuracy in cases where most of the membrane is fully tensioned and a part of the local region is slack or wrinkled.