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Research Papers

Generalized Finite-Volume Theory for Elastic Stress Analysis in Solid Mechanics—Part I: Framework

[+] Author and Article Information
Marcio A. A. Cavalcante

ASME Member Civil and Environmental Engineering Department,  University of Virginia, Charlottesville, VA 22904-4742

Marek-Jerzy Pindera1

ASME Member Civil and Environmental Engineering Department,  University of Virginia, Charlottesville, VA 22904-4742

1

Corresponding author.

J. Appl. Mech 79(5), 051006 (Jun 22, 2012) (11 pages) doi:10.1115/1.4006805 History: Received August 31, 2011; Revised April 22, 2012; Posted May 09, 2012; Published June 22, 2012; Online June 22, 2012

A generalized finite-volume theory is proposed for two-dimensional elasticity problems on rectangular domains. The generalization is based on a higher-order displacement field representation within individual subvolumes of a discretized analysis domain, in contrast with the second-order expansion employed in our standard theory. The higher-order displacement field is expressed in terms of elasticity-based surface-averaged kinematic variables, which are subsequently related to corresponding static variables through a local stiffness matrix derived in closed form. The novel manner of defining the surface-averaged kinematic and static variables is a key feature of the generalized finite-volume theory, which provides opportunities for further exploration. Satisfaction of subvolume equilibrium equations in an integral sense, a defining feature of finite-volume theories, provides the required additional equations for the local stiffness matrix construction. The theory is constructed in a manner which enables systematic specialization through reductions to lower-order versions. Part I presents the theoretical framework. Comparison of predictions by the generalized theory with its predecessor, analytical and finite-element results in Part II illustrates substantial improvement in the satisfaction of interfacial continuity conditions at adjacent subvolume faces, producing smoother stress distributions and good interfacial conformability.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Discretization of the analysis domain into rectangular (β,γ) subvolumes (left), after Bansal and Pindera [23]. Note the local coordinate system x¯2(β)-x¯3(γ) attached at the center of the (β,γ) subvolume (right).

Grahic Jump Location
Figure 2

Surface-averaged kinematic variables on the four faces of (β,γ) subvolume

Grahic Jump Location
Figure 3

Surface-averaged static variables on the four faces of (β,γ) subvolume

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