A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations

The limiting process that leads to the formulation of hypersingular boundary integral equations is first discussed in detail. It is shown that boundary integral equations with hypersingular kernels are perfectly meaningful even at non-smooth boundary points, and that special interpretations of the integrals involved are not necessary. Careful analysis of the limiting process has also strong relevance for the development of an appropriate numerical algorithm. In the second part, a new general method for the evaluation of hypersingular surface integrals in the boundary element method (BEM) is presented. The proposed method can be systematically applied in any BEM analysis, either with open or closed surfaces, and with curved boundary elements of any kind and order (of course, provided the density function meets necessary regularity requirements at each collocation point). The algorithm operates in the parameter plane of intrinsic coordinates and allows any hypersingular integral in the BEM to be directly transformed into a sum of a double and a one-dimensional regular integrals. Since all singular integrations are performed analytically, standard quadrature formulae can be used. For the first time, numerical results are presented for hypersingular integrals on curved (distorted) elements for three-dimensional problems

Hypersingular Integral Equations for Crack Problems

The investigation of scattering of waves by cracks in an elastic medium and by thin scatterers in an acoustic medium, via analytical and experimental methods, seems to be of continuing importance to nondestructive evaluation. On the analytical side, formulation and numerical solution of crack scattering problems using boundary integral equations is popular and effective because of the very nature of a crack, but this approach still suffers some shortcomings of an analytical nature. That is, the governing equations in their primitive form involve a hypersingular kernel function, and the usual process of regularization to lower the kernel singularity usually introduces undesirable features in the analysis accompanied by computational difficulty

Elastic Wave Scattering by Arbitrarily Shaped Voids

This work is motivated by the need for realistic ultrasonic probability of detection (POD) models in nondestructive evaluation (NDE). Past POD models have utilized flaw farfield scattering amplitudes along with other system parameters to predict the expected signal in postulated measurement geometries [1]. However, numerical evaluations of scattering amplitudes have generally been restricted to idealized flaw shapes and, to our knowledge, no scheme to calculate scattering amplitudes of arbitrary shape has ever been implemented in 3D. Volumetric shapes with an axis of symmetry have been examined with T-matrix and MOOT [2,3] but the axisyrametric limitation precludes a large portion of all expected flaw shapes. Furthermore, a quasi-plane wave assumption is often made. This assumption can become inappropriate for critical flaw sizes on the order of the beam size. A truly general POD model needs to have these assumptions removed

Elastic Wave Scattering by Irregular Shaped Flaws

This work is part of a continuing effort to develop a capability for quantifying the scattering of ultrasonic waves by arbitrarily shaped flaws. The general problem of elastodynamic behavior of a homogeneous, isotropic defect in an otherwise homogeneous, isotropic fullspace is cast as a Boundary Integral Equation (BIE). A general scattering model is needed to provide information for probability of detection (POD) models and inversion schemes for cases when low or high frequency approximations are not appropriate. Previously the Boundary Element Method (BEM), a method for solving the BIE, was adapted to NDE and the void problem was investigated [1]. Here we focus on the inclusion problem, experimental verification, and to overall extensions of the capability

Beam-Flattener Design for High Energy Radiographic Inspection

This report documents the work done to develop a beam flattener for use in the inspection of rocket motors at ATK Space Systems Utah facilities. The following pages provide a brief introduction to the necessity of this project, comprehensive description of the design methodology, and experimentally-based conclusions regarding project success

Effects of Stride Length and Running Mileage on a Probabilistic Stress Fracture Model

The fatigue life of bone is inversely related to strain magnitude. Decreasing stride length is a potential mechanism of strain reduction during running. If stride length is decreased, the number of loading cycles will increase for a given mileage. It is unclear if increased loading cycles are detrimental to skeletal health despite reductions in strain. Purpose: To determine the effects of stride length and running mileage on the probability of tibial stress fracture. Methods: Ten male subjects ran overground at their preferred running velocity during two conditions: preferred stride length and 10% reduction in preferred stride length. Force platform and kinematic data were collected concurrently. A combination of experimental and musculoskeletal modeling techniques was used to determine joint contact forces acting on the distal tibia. Peak instantaneous joint contact forces served as inputs to a finite element model to estimate tibial strains during stance. Stress fracture probability for stride length conditions and three running mileages (3, 5, and 7 miles·d−1) were determined using a probabilistic model of bone damage, repair, and adaptation. Differences in stress fracture probability were compared between conditions using a 2 × 3 repeated-measures ANOVA. Results: The main effects of stride length (P = 0.017) and running mileage (P = 0.001) were significant. Reducing stride length decreased the probability of stress fracture by 3% to 6%. Increasing running mileage increased the probability of stress fracture by 4% to 10%. Conclusions: Results suggest that strain magnitude plays a more important role in stress fracture development than the total number of loading cycles. Runners wishing to decrease their probability for tibial stress fracture may benefit from a 10% reduction in stride length

http://www.medscape.com/viewarticle/714780_print

Abstract and Introduction Abstract The fatigue life of bone is inversely related to strain magnitude. Decreasing stride length is a potential mechanism of strain reduction during running. If stride length is decreased, the number of loading cycles will increase for a given mileage. It is unclear if increased loading cycles are detrimental to skeletal health despite reductions in strain. Purpose: To determine the effects of stride length and running mileage on the probability of tibial stress fracture. Methods: Ten male subjects ran overground at their preferred running velocity during two conditions: preferred stride length and 10% reduction in preferred stride length. Force platform and kinematic data were collected concurrently. A combination of experimental and musculoskeletal modeling techniques was used to determine joint contact forces acting on the distal tibia. Peak instantaneous joint contact forces served as inputs to a finite element model to estimate tibial strains during stance. Stress fracture probability for stride length conditions and three running mileages (3, 5, and 7 miles·d −1 ) were determined using a probabilistic model of bone damage, repair, and adaptation. Differences in stress fracture probability were compared between conditions using a 2 × 3 repeated-measures ANOVA. Results: The main effects of stride length (P = 0.017) and running mileage (P = 0.001) were significant. Reducing stride length decreased the probability of stress fracture by 3% to 6%. Increasing running mileage increased the probability of stress fracture by 4% to 10%. Conclusions: Results suggest that strain magnitude plays a more important role in stress fracture development than the total number of loading cycles. Runners wishing to decrease their probability for tibial stress fracture may benefit from a 10% reduction in stride length