The Application of a Finite Element Model of Nonlinear Continuous Medium in the Analysis of the Stress-Strain State of Structure Members
| Authors: Raenko M.I., Chainov N.D. | Published: 07.06.2018 |
| Published in issue: #5(698)/2018 | |
| Category: Mechanical Engineering and Machine Science | Chapter: Machines, Units and Processes (by Industry Branch) (Technical) | |
| Keywords: Green strain tensors, geometric and physical nonlinearities, Lagrangian approach, Piola–Kirchhoff stress tensors, associate theory of flow, Mises–Hencky criterion |
The application of a finite element model for solving the problem of continuous medium with geometrical and physical nonlinearities is considered in this work. The nonlinear medium is mathematically described using incremental methods. The model construction is based on the Lagrangian approach, where material coordinates of points, Piola-Kirchhoff second stress tensor and Green strain tensor are used. The solution of the plastic problem is based on the associate theory of flow. The flow function is derived from the Mises–Hencky criterion of plasticity that satisfactorily describes the plastic state of isotropic materials. As an example, problems are solved using the finite element method in the MSC.MARC software environment.
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