Variational principles and convergence of finite element approximations of a holonomic elastic-plastic problem

1987 ◽  
Vol 52 (1) ◽  
pp. 101-117 ◽  
Author(s):  
B. D. Reddy ◽  
T. B. Griffin
Keyword(s):  
Finite Element ◽  
Variational Principles ◽  
Elastic Plastic ◽  
Finite Element Approximations

A Finite Element Analysis of the General Rolling Contact Problem for a Viscoelastic Rubber Cylinder

1988 ◽  
Vol 16 (1) ◽  
pp. 18-43 ◽  
Author(s):  
J. T. Oden ◽  
T. L. Lin ◽  
J. M. Bass
Keyword(s):  
Finite Element ◽  
Variational Principles ◽  
Standing Waves ◽  
Rolling Contact ◽  
Finite Element Models ◽  
Viscoelastic Cylinder ◽  
Element Analysis ◽  
Elastic Rubber ◽  
Frictional Effects ◽  
Rough Foundation

Abstract Mathematical models of finite deformation of a rolling viscoelastic cylinder in contact with a rough foundation are developed in preparation for a general model for rolling tires. Variational principles and finite element models are derived. Numerical results are obtained for a variety of cases, including that of a pure elastic rubber cylinder, a viscoelastic cylinder, the development of standing waves, and frictional effects.

scholarly journals Symmetric Nature of Stress Distribution in the Elastic-Plastic Range of Pinus L. Pine Wood Samples Determined Experimentally and Using the Finite Element Method (FEM)

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 39
Author(s):  
Łukasz Warguła ◽  
Dominik Wojtkowiak ◽  
Mateusz Kukla ◽  
Krzysztof Talaśka
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Stress Distribution ◽  
Moisture Content ◽  
Tool Geometry ◽  
Wood Fibers ◽  
Data Set ◽  
Plastic Deformations ◽  
Pine Wood ◽  
Elastic Plastic

This article presents the results of experimental research on the mechanical properties of pine wood (Pinus L. Sp. Pl. 1000. 1753). In the course of the research process, stress-strain curves were determined for cases of tensile, compression and shear of standardized shapes samples. The collected data set was used to determine several material constants such as: modulus of elasticity, shear modulus or yield point. The aim of the research was to determine the material properties necessary to develop the model used in the finite element analysis (FEM), which demonstrates the symmetrical nature of the stress distribution in the sample. This model will be used to analyze the process of grinding wood base materials in terms of the peak cutting force estimation and the tool geometry influence determination. The main purpose of the developed model will be to determine the maximum stress value necessary to estimate the destructive force for the tested wood sample. The tests were carried out for timber of around 8.74% and 19.9% moisture content (MC). Significant differences were found between the mechanical properties of wood depending on moisture content and the direction of the applied force depending on the arrangement of wood fibers. Unlike other studies in the literature, this one relates to all three stress states (tensile, compression and shear) in all significant directions (anatomical). To verify the usability of the determined mechanical parameters of wood, all three strength tests (tensile, compression and shear) were mapped in the FEM analysis. The accuracy of the model in determining the maximum destructive force of the material is equal to the average 8% (for tensile testing 14%, compression 2.5%, shear 6.5%), while the average coverage of the FEM characteristic with the results of the strength test in the field of elastic-plastic deformations with the adopted ±15% error overlap on average by about 77%. The analyses were performed in the ABAQUS/Standard 2020 program in the field of elastic-plastic deformations. Research with the use of numerical models after extension with a damage model will enable the design of energy-saving and durable grinding machines.

scholarly journals 3D Unsteady Diffusion and Reaction-Diffusion with Singularities by GFEM with 27-Node Hexahedrons

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Estaner Claro Romão
Keyword(s):  
Finite Element ◽  
Variable Temperature ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Third Order ◽  
Order Of Accuracy ◽  
Finite Element Approximations ◽  
Temperature Solution ◽  
The One ◽  
Primary Variable

The Galerkin Finite Element Method (GFEM) with 8- and 27-node hexahedrons elements is used for solving diffusion and transient three-dimensional reaction-diffusion with singularities. Besides analyzing the results from the primary variable (temperature), the finite element approximations were used to find the derivative of the temperature in all three directions. This technique does not provide an order of accuracy compatible with the one found in the temperature solution; thereto, a calculation from the third order finite differences is proposed here, which provide the best results, as demonstrated by the first two applications proposed in this paper. Lastly, the presentation and the discussion of a real application with two cases of boundary conditions with singularities are proposed.

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