Abstract
In this paper, a finite element simulation of nonlinear elasto-plastic deformations of Reissner-Mindlin bending plates is described. The previously proposed four-node Q4g element with transverse energy of shearing for thick bending plates is extended to account for isotropic material nonlinearities. An incremental finite element procedure has been used for the elasto-plastic analysis of the thick bending plate. Modified Newton-Raphson method has been used to solve the nonlinear equations. Von-Mises yield criteria have been applied for yielding of the materials along with the associated flow rule. To verify the present element, simple tests are demonstrated and various elasto-plastic problems in which the development of the plastic zone are solved.
Highlights
I n recent years, considerable work has been devoted to the study of nonlinear elasto-plastic responses of ReissnerMindlin bending plates, since plates are very important parts of engineering structures
The first order shear deformation theories (FSDTs), which include transverse shear deformation, for bending plates have been initially proposed by Reissner [11] and further developed by Mindlin [12]
Having a finite element method for linear elastic analysis of Reissner-Mindlin bending plates, we further develop the model to investigate the elasto-plastic behavior and plastic zone of the structures under consideration
Summary
I n recent years, considerable work has been devoted to the study of nonlinear elasto-plastic responses of ReissnerMindlin bending plates, since plates are very important parts of engineering structures. The first order shear deformation theories (FSDTs), which include transverse shear deformation, for bending plates have been initially proposed by Reissner [11] and further developed by Mindlin [12]. These theories are widely employed in the nonlinear elasto-plastic behavior. A finite element method for analyzing the elasto-plastic plate bending problems is presented. Having a finite element method for linear elastic analysis of Reissner-Mindlin bending plates, we further develop the model to investigate the elasto-plastic behavior and plastic zone of the structures under consideration. The generalized forces per unit of length of the plate side can be obtained using the stress field; these forces are the bending moments (M) and the shear forces (V): M h 2
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