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.

On the Use of a Plane-Strain Model to Solve Generalized Plane-Strain Problems

1997 ◽  
Vol 64 (1) ◽  
pp. 236-238 ◽  
Author(s):  
Shoufeng Hu ◽  
N. J. Pagano
Keyword(s):  
Finite Element ◽  
Plane Strain ◽  
Three Dimensional ◽  
Element Analysis ◽  
Out Of Plane ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Strain Model ◽  
Generalized Plane Strain ◽  
Plane Strain Model

Many composite problems are generalized plane strain in nature. They are often solved using three-dimensional finite element analyses. We propose a technique to solve these problems with a plane-strain model, which is achieved by introducing some artificial out-of-plane thermal strains in a two-dimensional finite element analysis. These artificial thermal strains are chosen such that an identical stress field is obtained, while the actual strains and displacements can also be determined.

A New Embedded-Zone Method on Computation of the Transverse Elastic Properties of Fiber-Reinforced Composites

2005 ◽  
Author(s):  
Xiaochun Wang
Keyword(s):  
Plane Strain ◽  
Elastic Properties ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Zone Method ◽  
Two Dimension ◽  
The Matrix ◽  
Strain Model ◽  
Plane Strain Model

There are many methods on computation of transverse elastic properties of unidirectional fiber-reinforced composites when using the finite element method, such as three-dimension model, two-dimension plane strain model, unit cell model, etc[1]. But unit cell models could be used only when the fibers are arrayed regularly. The computations of three- and two-dimension plane strain models are tremendous when many fine fibers are spread randomly in the matrix so that the properties of block of composite must be computed. The paper proposes a new embedded-zone method to compute the transverse elastic properties for a block of fiber-reinforced composites containing a great amount of fibers embedded in the matrix stochastically while using very little computational work compared with three- and two-dimension plane strain model. The transverse elastic modulus and shear modulus of unidirectional fiber-reinforced composites are computed.

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.

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