Large increment method for elastic and elastoplastic analysis of plates

• We introduce a novel force-based iterative finite element method called Large Increment Method (LIM).
• A force-based plate element is used for the elastoplastic analysis of plate using LIM for the first time.
• The convergence and accuracy of the PQ2 element using LIM is verified by solving the linear elastic plate bending problems.
• The good performance of LIM in elastoplastic problem is verified.

The displacement-based finite element method (FEM) has become a method of choice for material nonlinear analysis of plates. For material nonlinear problems, the displacement-based FEM relies upon a step-by-step incremental approach and the repetitive computation of the systematic stiffness matrix. These shortcomings lead to the error accumulation and huge computational consumption, which encourage the reconsideration of force-based methods for elastoplastic problems. In this paper, a force-based Large Increment Method (LIM) is employed for the elastoplastic analysis of plates using a force-based 4-node quadrilateral plate element which is based on Mindlin–Reissner plate theory. The consistent elastoplastic flexibility matrix of plate element is derived and implemented to solve elastoplastic plate problems. Two numerical examples are presented to illustrate the mesh convergence of the plate element by solving the linear elastic thin and moderately thick plate problems by comparing with the analytical solutions and displacement-based plate elements. Two simple elastoplastic plate problems are presented to illustrate the accuracy and the computational efficiency of LIM by comparing with the results from the FEM software ABAQUS.