The generalized plane strain problem and its application in three-dimensional stress measurement

1990 ◽  
Vol 27 (1) ◽  
pp. 43-49 ◽  
Author(s):  
Wu Zhenye ◽  
Li Shiping
Keyword(s):  
Plane Strain ◽  
Stress Measurement ◽  
Three Dimensional ◽  
Plane Strain Problem ◽  
Generalized Plane Strain

Thermal Stresses in Layered Electrical Assemblies Bonded With Solder

1991 ◽  
Vol 113 (4) ◽  
pp. 350-354 ◽  
Author(s):  
H. S. Morgan
Keyword(s):  
Residual Stresses ◽  
Plane Strain ◽  
3D Model ◽  
Thermal Stresses ◽  
Three Dimensional ◽  
Creep Models ◽  
Strain Model ◽  
Maximum Stresses ◽  
Generalized Plane Strain ◽  
Plane Strain Model

Thermal stresses in a layered electrical assembly joined with solder are computed with plane strain, generalized plane strain, and three-dimensional (3D) finite element models to assess the accuracy of the two-dimensional (2D) modeling assumptions. Cases in which the solder is treated as an elastic and as a creeping material are considered. Comparison of the various solutions shows that, away from the corners, the generalized plane strain model produces residual stresses that are identical to those computed with the 3D model. Although the generalized plane strain model cannot capture corner stresses, the maximum stresses computed with this 2D model are, for the mesh discretization used, within 12 percent of the corner stresses computed with the 3D model when the solder is modeled elastically and within 5 percent when the solder is modeled as a creeping material. Plane strain is not a valid assumption for predicting thermal stresses, especially when creep of the solder is modeled. The effect of cooling rate on the residual stresses computed with creep models is illustrated.

Simulation of Square-to-Oval Single Pass Rolling Using a Computationally Effective Finite and Slab Element Method

1992 ◽  
Vol 114 (3) ◽  
pp. 329-335 ◽  
Author(s):  
N. Kim ◽  
S. M. Lee ◽  
W. Shin ◽  
R. Shivpuri
Keyword(s):  
Finite Element ◽  
Plane Strain ◽  
Effective Strain ◽  
Rolling Direction ◽  
Three Dimensional ◽  
Computational Effort ◽  
Element Formulation ◽  
Single Pass ◽  
Dimensional Finite Element ◽  
Generalized Plane Strain

This paper presents details of a quasi three-dimensional finite element formulation for shape rolling, TASKS. This formulation uses a mix of two-dimensional finite element and slab element techniques to solve a generalized plane strain problem. Consequently, quasi steady state metal forming problems such as rolling of shapes can be analyzed with minimal computational effort. To verify the capability of the formulation square-to-round single pass rolling is simulated by TASKS and results compared with a fully three-dimensional simulation reported in literature. The results indicate reasonable agreement in roll forces, torques, and effective strain distributions during rolling. However, due to the generalized plane strain assumptions, nonhomogenieties in the rolling direction cannot be simulated. The large computational economy realized via TASKS gives this formulation the power to analyze roll pass designs with reasonable computational resources.

Three-dimensional thermo-mechanical analysis of continuous casting and comparison with two-dimensional models

2018 ◽  
Vol 53 (6) ◽  
pp. 421-434
Author(s):  
Reza Vaghefi ◽  
MR Hematiyan ◽  
Ali Nayebi
Keyword(s):  
Continuous Casting ◽  
Phase Change ◽  
Galerkin Method ◽  
Plane Strain ◽  
Plane Stress ◽  
Three Dimensional ◽  
Casting Process ◽  
Mechanical Analysis ◽  
Two Dimensional ◽  
Generalized Plane Strain

In this study, a three-dimensional thermo-elasto-plastic model is developed for simulating a continuous casting process. The obtained results are compared with those from different two-dimensional analyses, which are based on plane stress, plane strain, and generalized plane strain assumptions. All analyses are carried out using the meshless local Petrov–Galerkin method. The effective heat capacity method is employed to simulate the phase change process. The von Mises yield criterion and elastic–perfectly-plastic model are used to simulate the stress state during the casting process; while, material parameters are assumed to be temperature-dependent. Based on the three-dimensional and two-dimensional models, numerical results are provided to determine the stress, displacement, and temperature fields induced in the cast material. It is observed that the present meshless local Petrov–Galerkin method is accurate in three-dimensional thermo-mechanical analysis of highly nonlinear phase change problems. Reasonable agreements are observed between the results obtained from the three-dimensional analysis with those retrieved by the generalized plane strain assumption. However, it is observed that the results obtained under plane stress/strain conditions have some significant differences with the results obtained from three-dimensional modeling of continuous casting.

Generalized Plane Strain Study of Rotational Autofrettage of Thick-Walled Cylinders—Part II: Numerical Evaluation

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
S. M. Kamal ◽  
M. Perl
Keyword(s):  
Finite Element ◽  
Plane Strain ◽  
Numerical Evaluation ◽  
Hoop Stress ◽  
Three Dimensional ◽  
Fem Analysis ◽  
3D Fem ◽  
Theoretical Evaluation ◽  
Gun Barrel ◽  
Generalized Plane Strain

The theoretical modeling of the rotational autofrettage of a thick-walled cylinder based on the generalized plane strain assumption has been presented in part I of the paper. In order to access the potentiality of the proposed theoretical model, the numerical evaluation of the analytical solutions is important. This part of the paper presents numerical evaluation of the generalized plane strain model for typical thick-walled cylinders. The residual hoop stress generated in the rotational autofrettage of a typical gun barrel is compared with the residual hoop stresses in the conventional hydraulic and swage autofrettage processes. Comparison shows that the rotationally autofrettaged gun barrel is capable of producing the same level of compressive residual hoop stress at the inner surface as that of the hydraulic autofrettage. In order to corroborate the analytical solution, a three-dimensional finite element method (3D FEM) analysis of the rotational process is carried out in ANSYS finite element package and the results are compared with the theoretical results. The comparison shows a good matching of the results between the theoretical evaluation and the 3D FEM analysis. Finally, a short feasibility analysis of the rotational autofrettage process of typical cylinders is carried out for the practical realization of the process.

scholarly journals Displacements and Stress Functions of Straight Dislocations and Line Forces in Anisotropic Elasticity: A New Derivation and Its Relation to the Integral Formalism

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1721
Author(s):  
Markus Lazar
Keyword(s):  
Plane Strain ◽  
Stress Function ◽  
Function Fields ◽  
Three Dimensional ◽  
Anisotropic Elasticity ◽  
Green Tensor ◽  
Two Dimensional ◽  
Integral Formalism ◽  
Stress Functions ◽  
Generalized Plane Strain

The displacement and stress function fields of straight dislocations and lines forces are derived based on three-dimensional anisotropic incompatible elasticity. Using the two-dimensional anisotropic Green tensor of generalized plane strain, a Burgers-like formula for straight dislocations and body forces is derived and its relation to the solution of the displacement and stress function fields in the integral formalism is given. Moreover, the stress functions of a point force are calculated and the relation to the potential of a Dirac string is pointed out.

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