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Transverse and
torsional shear stresses in prismatic bodies having
inhomogeneous material properties using a new 2D stress
function
Lampros C. Kourtis, Haneesh Kesari, Dennis R. Carter and Gary S. Beaupré |
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Vol. 4 (2009), No. 4, 659–674
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Abstract |
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We introduce a new formulation to concurrently calculate torsional and transverse shear stresses in prismatic beams with homogeneous or inhomogeneous material properties. This new formulation is generated using kinematic assumptions for the torsion problem and using a new stress function for the transverse shear problem that accounts for Poisson effects. The effect of gradients in material properties is captured explicitly as body forces. The results using this new formulation are compared to full three-dimensional solutions and show good agreement ( error metric in the order of ), while both modeling and computational costs are significantly lower. The numerical implementation of this new formulation can be used to analyze stresses in arbitrary cross sections ranging from structural members (civil) to long bones (biomechanics) with either homogeneous or inhomogeneous material properties. |
Keywords
stress function, inhomogeneous material properties, shear
stress, torsion, transverse shear
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Milestones
Received: 1 February 2008
Revised: 14 October 2008
Accepted: 16 October 2008
Published: 7 August 2009
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Authors |
| Lampros C. Kourtis | |
| Bone and Joint Center of
Excellence VA Palo Alto Health Care System Palo Alto, CA 94304 United States |
Biomechanical Engineering
Division 496 Lomita Mall, Room 226 Stanford University Stanford, CA 94305 United States |
| Haneesh Kesari | |
| Mechanics and Computation
Division Department of Mechanical Engineering 496 Lomita Mall Stanford University Stanford, CA 94305 United States |
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| Dennis R. Carter | |
| Bone and Joint Center of
Excellence VA Palo Alto Health Care System Palo Alto, CA 94304 United States |
Biomechanical Engineering
Division 496 Lomita Mall, Room 226 Stanford University Stanford, CA 94305 United States |
| Gary S. Beaupré | |
| Bone and Joint Center of
Excellence VA Palo Alto Health Care System Palo Alto, CA 94304 United States |
Biomechanical Engineering
Division 496 Lomita Mall, Room 226 Stanford University Stanford, CA 94305 United States |
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