Analysis of Soft Fibers with Kinematic Constraints and Cross-Links by Finite Deformation Beam Theory
Publication: Journal of Engineering Mechanics
Volume 137, Issue 8
Abstract
This paper presents a hybrid analytical–computational mechanics formulation for an arbitrarily curved Timoshenko beam undergoing planar finite deformation and subjected to kinematic constraints in the form of fixed displacement and cross-linking. On the basis of an analytical reduction of the governing equations, the system reduced to a single nonlinear differential equation coupled with integral equations associated with translational constraints. An effective numerical formulation of the problem with general distributed and pointwise constraints is shown to be possible by using a simple finite-element procedure. To illustrate the efficiency and accuracy of the method, several examples are introduced to study both stable and bifurcation problems and a system of interacting fibers with different types of cross-link constraints. Because of the reduction of discretization error and the dimension of the matrix system, the proposed formulation is likely to be an attractive computational platform for modeling large-scale multifiber problems, as in fibrous microstructure simulations and other applications.
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Published In
Journal of Engineering Mechanics
Volume 137 • Issue 8 • August 2011
Pages: 527 - 536
Copyright
© 2011 American Society of Civil Engineers.
History
Received: May 27, 2010
Accepted: Feb 22, 2011
Published online: Feb 24, 2011
Published in print: Aug 1, 2011
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