Linear and geometrically nonlinear analysis of plane structures by using a new locking free triangular element

Abstract

This research is dedicated to propose a high-performance locking-free triangular plane element, which is based on the novel mixed finite element formulation. The new element has six nodes with two transitional degrees of freedom at each node. To improve the displacement and stress responses, a proper mixed interpolation of the strain fields is propounded. Moreover, Mixed Interpolation of Tensorial Components (MITC) has been employed to alleviate in-plane shear locking. The advantage of the employed method is that no additional degrees of freedom are introduced, and spurious instabilities have not been seen. The tensorial forms of the equations are employed in this paper to summarize the formulations. The element passes the numerical tests, which are required to show the accuracy, capability and convergence rate in the structural analysis. Both linear and geometrically nonlinear problems can be solved by the presented formulations. To incorporate the large deformations, Total-Lagrangian formulation will be utilized. Due to completely trace the equilibrium paths of plane problems, especially those with snap-through behavior, a Generalized Displacement Control Method (GDCM) is used as a nonlinear solver. Outcomes of several benchmark problems and some new plane structures, which are analyzed separately, illustrate the high accuracy and advantages of the proposed element, especially in curved structures and nonlinear problems.