On isotropic linear elastic material laws for directed planes

Abstract Pipelines carrying oil and gas are susceptible to fatigue failure (i.e., unstable fatigue crack propagation) due to fluctuating loading such as varying internal pressure and other external loadings. Fatigue crack growth (FCG) prediction through full-scale pipe tests can be expensive and time consuming, and experimental data is limited particularly in the face of large uncertainty involved. In contrast, numerical simulation techniques (e.g., XFEM) can be alternative to study the FCG, given that numerical models can be theoretically and/or experimentally validated with reasonable accuracy. In this study, capabilities and limitations of existing fatigue analysis code (e.g., direct cyclic approach with XFEM) in Abaqus for low cycle fatigue simulation are explored for compact-tension (CT) specimens and pipelines assuming linear elastic material behavior. The simulated FCG curve for a CT specimen is compared with that obtained from the analytical method using the stress intensity factor prescribed in ASTM E647. However, for real pipelines with elastic-plastic behavior, direct cyclic approach is not suitable, and an indirect cyclic approach is used based on the fracture energy parameters (e.g., J integral) calculated using XFEM in Abaqus. FCG law (e.g., power law relationship like Paris law) is used to generate the fatigue crack growth curve. For comparison, the FCG curve obtained through direct cyclic approach for pipelines assuming linear elastic material is also presented. The comparative studies here indicate that XFEM-based FCG simulation using appropriate techniques can be applied to pipelines for fatigue life prediction.

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Effect of Housing Support on Bearing Dynamics

Journal of Tribology ◽

10.1115/1.4031104 ◽

2015 ◽

Vol 138 (1) ◽

Cited By ~ 6

Author(s):

Lijun Cao ◽

Matthew D. Brouwer ◽

Farshid Sadeghi ◽

Lars-Erik Stacke

Keyword(s):

Finite Element ◽

Elastic Material ◽

Contact Forces ◽

Support Structure ◽

Linear Elastic Material ◽

Outer Race ◽

Linear Elastic ◽

Elastomeric Material ◽

Bearing Dynamics ◽

Element Method

The objective of this investigation was to determine the effect of housing support on bearing performance and dynamics. In order to achieve the objective, an existing dynamic bearing model (DBM) was coupled with flexible housing model to include the effect of support structure on bearing dynamics and performance. The DBM is based on the discrete element method, in which the bearing components are assumed to be rigid. To achieve the coupling, a novel algorithm was developed to detect contact conditions between the housing support and bearing outer race and then calculate contact forces based on the penalty method. It should be noted that although commercial finite element (FE) software such as abaqus is available to model flexible housings, combining these codes with a bearing model is quite difficult since the data transfer between the two model packages is time-consuming. So, a three-dimensional (3D) explicit finite element method (EFEM) was developed to model the bearing support structure for both linear elastic and nonlinear inelastic elastomeric materials. The constitutive relationship for elastomeric material is based on an eight chain model, which captures hyperelastic behavior of rubber for large strains. The viscoelastic property is modeled by using the generalized Maxwell-element rheological model to exhibit rate-dependent behaviors, such as creep and hysteresis on cyclic loading. The results of this investigation illustrate that elastomeric material as expected has large damping to reduce vibration and absorb energy, which leads to a reduction in ball–race contact forces and friction. A parametric study confirmed that the viscoelastic stress (VS) contributes significantly to the performance of the material, and without proper amount of viscoelasticity it loses its advantage in vibration reduction and exhibits linear elastic material characteristics. As expected, it is also demonstrated that housing supports made of linear elastic material provide minimal damping and rely on the bearing friction to dissipate energy. A study of housing support geometry demonstrates that bearing support plays a large role on the dynamic performance of the bearing. Motion of bearing outer race is closely related to the geometry and symmetry of the housing.

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Comparison of Ortho-planar Spring design optimization based on Linear Elastic and Hyper Elastic Materials

MATEC Web of Conferences ◽

10.1051/matecconf/201816601004 ◽

2018 ◽

Vol 166 ◽

pp. 01004

Author(s):

Ruetai Graipaspong ◽

Teeranoot Chanthasopeephan

Keyword(s):

Topology Optimization ◽

Elastic Material ◽

Maximum Stress ◽

Nonlinear Material ◽

Small Displacement ◽

Linear Elastic Material ◽

Output Displacement ◽

Linear Elastic ◽

Hyper Elastic ◽

Matlab Programming

In this paper, compliant Ortho-planar spring was designed based on a three-dimensional topology optimization method. The computation was developed using MATLAB programming. The objective of this work was to apply dual method to design an Ortho-planar spring while the design should have minimum mass and at the same time satisfy a set of constrained displacement. Throughout this paper, we analyzed a method for designing an Ortho-planar spring using linear elastic material and hyperelastic material. The results showed that under small displacement conditions, the output displacement, maximum stress magnitude, and the maximum stress of linear elastic assumption and hyper-elastic material were relatively close to each other. However, the mass fraction and the layout as the result of the optimization process was different. As for larger displacement, the maximum stress of linear elastic material appeared 2.59 times higher than the maximum stress of the hyper-elastic material model. The topology optimization output based on linear material was invalid because the topology of the computed Ortho-planar spring was not appeared as a one-piece layout while the design based on nonlinear material looked promising.

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