Effect of Extensibility on Large Deformation Three-Dimensional Static Behavior of Beams

ABSTRACT

The problem of static large deformation, three-dimensional, bending and torsion of extensible beams with equal principal stiffnesses is formulated within small strain theory and solved numerically. Torsion and bending are coupled and external load and boundary conditions may be deformation dependent. A Lagrangian description of the deformation is used and the extensibility condition is employed as the constitutive relation in the tangential direction. The model is compared to its counterpart for inextensible beams. The problem is solved by an incremental finite element algorithm, with a prediction-correction scheme. The matrix form of the extensible beam problem involves seven nonlinear deformation dependent stiffness matrices. A computer code has been developed to implement the solution technique and its numerical output is compared with available results for extensible beams. Finally seven beam problems are solved numerically to investigate effects of extensibility, torsion, movability of supports, and three-dimensional bending.

Notes

COMMUNICATED BY M. M. KAMAL