An Inverse Finite Element Method for the Determination of Unsteady Temperatures and Heat Fluxes on Surfaces of 3-D Objects

2013 ◽  
Author(s):  
Brian H. Dennis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Material Properties ◽  
Measurement Errors ◽  
Heat Conduction Problem ◽  
Three Dimensional ◽  
Inverse Heat Conduction Problem ◽  
Heat Fluxes ◽  
Inverse Finite Element Method ◽  
Element Method

The direct measurement of temperatures and heat fluxes may be difficult or impossible on boundaries that are obstructed, such as internal cavities, or exposed to harsh environmental conditions that would destroy the thermal sensors. In such circumstances, one may inversely determine the temperature and heat fluxes on these unknown boundaries by using over-specified conditions on boundaries where such information can be readily collected. This assumes the geometry and material properties of the domain are known. Algorithms for solving these problems, such those based on finite difference, finite element, and boundary element, are well known for the case where measured boundary conditions are not a function of time. In this work, I demonstrate an inverse finite element method that effectively solves this inverse heat conduction problem using over-specified temperatures and heat fluxes that are time varying. The material properties may highly heterogeneous and non-linear. A boundary regularization method in space and time is used to stabilize the method for cases involving errors in temperature and heat flux measurements. Several three dimensional examples are given using simulated measurements with and without measurement errors, to demonstrate the accuracy of the method.

Nonhomogeneous Ventricular Wall Strain: Analysis of Errors and Accuracy

1993 ◽  
Vol 115 (4B) ◽  
pp. 497-502 ◽  
Author(s):  
Lewis K. Waldman ◽  
Andrew D. McCulloch
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Measurement Errors ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Noninvasive Methods ◽  
Single Plane ◽  
Cardiac Deformation ◽  
Cardiac Strain ◽  
Element Method

Nonhomogeneous distributions of strains are simulated and utilized to determine two potential errors in the measurement of cardiac strains. First, the error associated with the use of single-plane imaging of myocardial markers is examined. We found that this error ranges from small to large values depending on the assumed variation in stretch. If variations in stretch are not accompanied by substantial regional changes in ventricular radius, the associated error tends to be quite small. However, if the nonuniform stretch field is a result of substantial variations in local curvature from their reference values, large errors in stretch and strain occur. For canine hearts with circumferential radii of 2 to 4 cm, these errors in stretch may be as great as 30 percent or more. Moreover, gradients in stretch may be over- or underestimated by as much as 100 percent. In the second part of this analysis, the influence of random measurement errors in the coordinate positions of markers on strains computed from them is studied. Arrays of markers covering about 16 cm2 of ventricular epicardium are assumed and nonuniform stretches imposed. The reference and deformed positions of the markers are perturbed with Gaussian noise with a standard deviation of 0.1 mm, and then strains are computed using either homogeneous strain theory or a nonhomogeneous finite element method. For the strain distributions prescribed, it is found that the finite element method reduces the error resulting from noise by about 50 percent over most of the region. Accurate measurements of cardiac strain distributions are needed for correlation with and validation of realistic three-dimensional stress analyses of the heart. Moreover, with the advent of increasingly effective noninvasive methods to measure cardiac deformation such as magnetic resonance imaging, the use of nonhomogeneous strain analysis to determine more accurate strain distributions has increasing clinical significance.

Temperature Analysis of Piercing Process Based on Material Properties in Diescher's Mill with Finite Element Method

2013 ◽  
Vol 830 ◽  
pp. 93-96 ◽  
Author(s):  
Lu Lu ◽  
Hong Xia Cui
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Material Properties ◽  
External Surface ◽  
Three Dimensional ◽  
Internal Surface ◽  
Work Piece ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Element Method

In this paper, the simulation of the piercing process is performed by the three-dimensional finite-element method in Dieschers mill. The material properties of steel 33Mn2V are introduced. The simulated results visualize dynamic evolution of temperature, especially inside the workpiece. Its show the distribution of temperature on the internal and external surface of the work-piece is non-uniform. The temperature of the internal surface is far higher than that of the external surface of workpiece.

Towards Predicting Relative Belt Edge Endurance With the Finite Element Method

1990 ◽  
Vol 18 (4) ◽  
pp. 216-235 ◽  
Author(s):  
J. De Eskinazi ◽  
K. Ishihara ◽  
H. Volk ◽  
T. C. Warholic
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Shear Deformations ◽  
Element Analysis ◽  
Vertical Loading ◽  
Predicted Values ◽  
Element Method

Abstract The paper describes the intention of the authors to determine whether it is possible to predict relative belt edge endurance for radial passenger car tires using the finite element method. Three groups of tires with different belt edge configurations were tested on a fleet test in an attempt to validate predictions from the finite element results. A two-dimensional, axisymmetric finite element analysis was first used to determine if the results from such an analysis, with emphasis on the shear deformations between the belts, could be used to predict a relative ranking for belt edge endurance. It is shown that such an analysis can lead to erroneous conclusions. A three-dimensional analysis in which tires are modeled under free rotation and static vertical loading was performed next. This approach resulted in an improvement in the quality of the correlations. The differences in the predicted values of various stress analysis parameters for the three belt edge configurations are studied and their implication on predicting belt edge endurance is discussed.

scholarly journals Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1388
Author(s):  
Daniele Oboe ◽  
Luca Colombo ◽  
Claudio Sbarufatti ◽  
Marco Giglio
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Strain Field ◽  
Element Analysis ◽  
Inverse Finite Element Method ◽  
Shape Sensing ◽  
Definition Of ◽  
High Level ◽  
Element Method

The inverse Finite Element Method (iFEM) is receiving more attention for shape sensing due to its independence from the material properties and the external load. However, a proper definition of the model geometry with its boundary conditions is required, together with the acquisition of the structure’s strain field with optimized sensor networks. The iFEM model definition is not trivial in the case of complex structures, in particular, if sensors are not applied on the whole structure allowing just a partial definition of the input strain field. To overcome this issue, this research proposes a simplified iFEM model in which the geometrical complexity is reduced and boundary conditions are tuned with the superimposition of the effects to behave as the real structure. The procedure is assessed for a complex aeronautical structure, where the reference displacement field is first computed in a numerical framework with input strains coming from a direct finite element analysis, confirming the effectiveness of the iFEM based on a simplified geometry. Finally, the model is fed with experimentally acquired strain measurements and the performance of the method is assessed in presence of a high level of uncertainty.

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