American Society of Civil Engineers


Analysis of Soft Fibers with Kinematic Constraints and Cross-Links by Finite Deformation Beam Theory


by Franck Vernerey, (corresponding author), (Assistant Professor, Dept. of Civil, Environmental, Architectural Engineering, Univ. of Colorado at Boulder, 1111 Engineering Dr. 428, UCB, ECOT 422, Boulder, CO 80309-0428 E-mail: franck.vernerey@colorado.edu) and Ronald Y. S. Pak, (Professor, Dept. of Civil, Environmental, Architectural Engineering, Univ. of Colorado at Boulder, 1111 Engineering Dr. 428, UCB, Boulder, CO 80309-0428.)

Journal of Engineering Mechanics, Vol. 137, No. 8, August 2011, pp. 527-536, (doi:  http://dx.doi.org/10.1061/(ASCE)EM.1943-7889.0000256)

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Document type: Journal Paper
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.


ASCE Subject Headings:
Fibers
Beams
Structures
Kinematics
Deformation

Author Keywords:
Flexible fibers
Fibrous networks
Beams
Structures
Cross-links
Large deformation