Vol. 4, No. 4, 2009

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ISSN: 1559-3959
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

Vol. 4 (2009), No. 4, 659–674
Abstract

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 (l2 error metric in the order of 104), 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
Milestones
Received: 1 February 2008
Revised: 14 October 2008
Accepted: 16 October 2008
Published: 7 August 2009
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
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