A Probabilistic Analysis of a Nonlinear Structure Using Random Fields to Quantify Geometric Shape Uncertainties

Pepin, Jason E.; Thacker, Ben H.; Rodriguez, Edward A.; Riha, David S.

doi:10.2514/6.2002-1641

Cited by 11 publications

(3 citation statements)

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“…In reality, the material properties vary spatially from one material location to another potentially leading to local failure in a location where the stress is not at its peak value but where the local material strength may be lower than the value assumed in the analysis. This type of spatial variation can be treated with the use of random fields and is the subject of ongoing research in our laboratory (Pepin et al, 2002). In addition, in the present analysis, failure is defined as a local failure occurring at the element with the greatest value of the response function (e.g.…”

Section: Discussionmentioning

confidence: 99%

The effect of three-dimensional shape optimization on the probabilistic response of a cemented femoral hip prosthesis

Nicolella

Thacker

Katoozian

et al. 2006

Journal of Biomechanics

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Section: Discussionmentioning

confidence: 99%

The effect of three-dimensional shape optimization on the probabilistic response of a cemented femoral hip prosthesis

Nicolella

Thacker

Katoozian

et al. 2006

Journal of Biomechanics

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“…When sufficient data is available, the correlation matrix can be directly calculated 13 . However, when faced with limited observations or computational capacity, different strategies may be used to estimate ߩ క ሺ݅, ݆ሻ.…”

Section: Field Uncertaintymentioning

confidence: 99%

“…When a spatial correlation function is assumed, the accuracy of the subsequent uncertainty 3 analysis depends on the precision of the correlation function. One way to reduce the number of random variables is by considering the contribution of each eigenvalue-eigenvector pair of the covariance matrix averaged over the entire domain 13 . This data reduction approach may also be used, for instance, to establish a coarse random field model of the material in the context of high fidelity finite element simulations of structures.…”

Section: Field Uncertaintymentioning

confidence: 99%

Evidence-Based Design Optimization of Energy Absorbing Components under Material Field Uncertainty

Salehghaffari¹,

Rais‐Rohani²

2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

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An evidence-based framework for optimization of structural components under material field uncertainty is developed. The approach is applied to the evidence-based design optimization (EBDO) of a stiffened tube under axial impact load using an isotropic-elastic-plastic constitutive model to simulate dynamic material behavior. Uncertainty modeling considers the changes in material parameters that are caused by variability in material properties as well as incertitude in the experimental data and the procedure for determination of these parameters. Spatial variability is modeled using a joint field belief structure that includes the effects of both incertitude and randomness on the estimated material properties across the structural component. With propagation of field uncertainties, the evidence-based objective and design constraint functions are modeled. Surrogate models are used in different steps to facilitate both the field uncertainty propagation and subsequent solution of the EBDO problem. The results of the application of the developed methodology to EBDO of an energy-absorbing component are presented and discussed.

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Computational Analysis of Bone Fracture
Nicolella
¹
,
Bredbenner
²

2014
Accidental Injury
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Age-related non-traumatic fractures are a major public health problem with fracture of the proximal femur resulting in significant patient mortality. Currently, the clinical gold standard for assessing an individual's fracture risk is dual-energy x-ray absorptiometry (DEXA). Although DXA-based bone mineral density (BMD) measurements have been shown to correlate with fracture risk, BMD distributions describing normal individuals and those who have suffered a hip fracture contain significant overlap, thereby reducing the specificity of BMD based fracture risk categorization. Since bone strength results from a combination of bone mass, bone micro-architecture and material properties, and overall bone geometry, two-dimensional imaging based diagnostic approaches such as DEXA are limited in their ability to specifically predict bone strength. Engineering models of skeletal structures that combine descriptions of three dimensional bone geometry, bone mass distribution, and bone material behavior into a high fidelity simulation have been shown to predict bone strength with an improved accuracy compared to DEXA alone, albeit with some limitations. Specifically, voxel based finite element models derived from QCT image data are based on correlations between predicted structural stiffness and structural failure and therefore are generally only valid for simple uniaxial loading; it is unlikely this approach would be valid for more complex applied loads. Furthermore, these models generally use simplified bone material descriptions that do not capture the demonstrated non-linear damaging behavior of bone and do not model bone material

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A Probabilistic Analysis of a Nonlinear Structure Using Random Fields to Quantify Geometric Shape Uncertainties

Cited by 11 publications

References 1 publication

The effect of three-dimensional shape optimization on the probabilistic response of a cemented femoral hip prosthesis

The effect of three-dimensional shape optimization on the probabilistic response of a cemented femoral hip prosthesis

Evidence-Based Design Optimization of Energy Absorbing Components under Material Field Uncertainty

Computational Analysis of Bone Fracture

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