Investigation of a Three-Dimensional Spectral Element Method for Helmholtz’s Equation

Mehdizadeh, Omid Z.; Paraschivoiu, Marius

doi:10.1007/3-540-44843-8_89

Cited by 5 publications

(13 citation statements)

References 14 publications

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“…In equation (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15), subscripts P in the retardation coefficients , and    indicate that these coefficients depend on the target material properties at P . In Equation (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14), G v is the velocity of the center of mass G. In Equation (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15), G M is the moment of the retardation forces about G, and G H is the angular momentum of the rigid body about G, and /  G P r GP (Equation 1-15 and Figure 10).…”

Section: Analysis Of New Penetration Datamentioning

confidence: 99%

“…In Equation (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14), G v is the velocity of the center of mass G. In Equation (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15), G M is the moment of the retardation forces about G, and G H is the angular momentum of the rigid body about G, and /  G P r GP (Equation 1-15 and Figure 10). …”

Section: Analysis Of New Penetration Datamentioning

confidence: 99%

“…Equation (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) about the center of mass G with axes along the Gxyz (Figure 10), and the angular velocity  of the rigid body -17) where the components are along the axes of the rotating frame …”

Section: Using the Inertia Matrixmentioning

confidence: 99%

“…The scalar equations arising from these equations can either be written by taking components along body-fixed Gxyz (F-frame) or Newtonian OXYZ (N-frame) axes. Equation (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)) is described in F-frame while (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) is described in the N-frame. Besides, for visualization of projectile penetration inside the target, all quantities should be translated to the N-frame.…”

Section: Materials Properties Data In a Newtonian Frame And Its Transfmentioning

confidence: 99%

“…Equations (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14), (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) and describe the differential equations of motion of the center of mass G (Figure 10), rotational motion of the body about the center of mass and the orientation of body fixed coordinates. These are (Figure 10 Since these are all vectors, we have a total of 18 independent time-dependent field quantities that are governed by coupled, nonlinear first order differential equations given in (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)…”

Section: Numerical Algorithms For Solving the Projectile Trajectorymentioning

confidence: 99%

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Analytic Simulation of Tissue Damage from Penetrating Wounds to the Heart

Eisler¹,

Chatterjee²,

Stone³

et al. 2006

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE 01-12-2006 REPORT TYPE PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER ATK Mission ResearchLaguna Hills, CA 92653-1327 SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S) U.S. Army Medical Research and Materiel Command Fort Detrick, Maryland 21702-5012 SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION / AVAILABILITY STATEMENTApproved for Public Release; Distribution Unlimited SUPPLEMENTARY NOTESOriginal contains colored plates: ALL DTIC reproductions will be in black and white. ABSTRACTATKMissionResearchwassponsoredbyDARPA'sVirtualSoldierprogramtoanalyticallysimulateresidualwoundtractsandtissuedyna micsassociatedwithasurvivablewoundfromanexplosivelydrivenfragmentpenetratingtheleftventricularwallofthehumanheart. LIST OF FIGURESFIGURE 1. Models for three fragment categories………………………………………… 9 FIGURE 2. 30 Caliber "Wedge Projectile" used in Task 3 Ballistic Experiments………. 10 FIGURE 3. Penetration Depth and Retardation forces vs. Velocity……………………… 11 FIGURE 4. Correlation between analytical predictions and ballistic test data for three different diameter spheres shot into 20% ordnance gelatin …………. 14 FIGURE 5. Schematic of Loading on a Flat Fragment …………………………………… 15 FIGURE 6. Schematic and Loading on a Cut Cylinder …………………………………… 15 The Mission Research effort consisted of three related tasks. In the first task entitled Analytical Simulation of Projectile Trajectory, Mission Research divided up fragments into three geometric categories -platelet, "chunky" fragment, and slender high aspect ratio projectile -with different governing parameters. For each fragment geometry, algorithms were developed that describe interaction of the fragment with human tissue and resulting projectile kinematics through different tissue layers of the human left ventricular wall. Prof. Andrew McCulloch, Ph.D. (University of California, San Diego -UCSD) and his team assisted Mission Research in executing the UCSD Continuity code to develop quasistatic constitutive models for the various layers of tissue through the left ventricular wall. From these qu...

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Section: Analysis Of New Penetration Datamentioning

confidence: 99%

Section: Analysis Of New Penetration Datamentioning

confidence: 99%

Section: Using the Inertia Matrixmentioning

confidence: 99%

Section: Materials Properties Data In a Newtonian Frame And Its Transfmentioning

confidence: 99%

Section: Numerical Algorithms For Solving the Projectile Trajectorymentioning

confidence: 99%

See 3 more Smart Citations

Analytic Simulation of Tissue Damage from Penetrating Wounds to the Heart

Eisler¹,

Chatterjee²,

Stone³

et al. 2006

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Transient waves in a compliant cylindrical cavity enclosing comminuted material

El‐Raheb¹

2006

Journal of Sound and Vibration

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An Acoustic Model for Wave Propagation in a Weak Layer

El‐Raheb¹

2005

Journal of Applied Mechanics

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An acoustic model is developed for transient wave propagation in a weak layer excited by prescribed pressure or prescribed acceleration at the boundary. The validity of the acoustic model is investigated for the two excitations. A comparison of transient response from the acoustic model and a 3D axisymmetric elastic model reveals that for prescribed acceleration the acoustic model fails to capture important features of the elastic model even as Poisson ratio ν approaches 1∕2. However for prescribed pressure, the two models agree since shear stress is reduced. For prescribed acceleration adopting the modal approach, the mixed boundary-value problem on the excited boundary is converted to a pure traction problem utilizing the influence method. To validate the elaborate modal approach a finite difference model is also developed.

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Investigation of a Three-Dimensional Spectral Element Method for Helmholtz’s Equation

Cited by 5 publications

References 14 publications

Analytic Simulation of Tissue Damage from Penetrating Wounds to the Heart

Analytic Simulation of Tissue Damage from Penetrating Wounds to the Heart

Transient waves in a compliant cylindrical cavity enclosing comminuted material

An Acoustic Model for Wave Propagation in a Weak Layer

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