Study the effect of the incompatible elements on the elastic-plastic behavior of isotropic plates and beams under axial and bending loading

One of the most remarkable achievements of finite element method is introducing isoparametric elements. Although these elements are able to use in numerous applications, the lower order isoparametric elements make some difficulties such as shear locking, volumetric locking and hourglass. These issues may improve with an increase in the number of the elements or by increasing the order of the elements, which increases the computational time. Therefore for solving these problems, using the lower order elements with incompatible modes, which enhances accuracy and reduces the computational time, could be considered as an alternative solution option. The aim of this paper is to study the effect of using the incompatible elements on the elastoplastic behavior of isotropic plates and beams under uniform axial and bending loadings. For this purpose, 3D standard elements with eight and twenty nodes and incompatible eight-node elements are used in modeling the 3-D case studies. Besides, the 2D standard elements with four and eight nodes and incompatible ones with four nodes are employed to analyze the 2-D plane stress problems. The obtained results show that using 3D incompatible elements achieves the faster rate of convergence in the solution procedure for obtaining the displacement components and also makes significant run-time reduction. However, there are not any remarkable differences between the obtained plastic Von-Mises stresses using 2D standard and incompatible elements.