Geometrically Nonlinear Static Analysis Of
3D Trusses Using The Arc-length Method
Author(s)
G. A. Hrinda
Abstract
Rigorous analysis of geometrically nonlinear structures demands the creation of
mathematical models that accurately include loading and support conditions and,
more importantly, model the stiffness and response of the structure. Nonlinear
geometric structures often contain critical points with snap-through behavior
during the response to large loads. Studying the post buckling behavior during a
portion of a structure's unstable load history may be necessary. Primary
structures made from ductile materials will stretch enough prior to failure for
loads to redistribute producing sudden and often catastrophic collapses that are
difficult to predict. The responses and redistribution of the internal loads during
collapses and possible sharp snap-back of structures have frequently caused
numerical difficulties in analysis procedures. The presence of critical stability
points and unstable equilibrium paths are major difficulties that numerical
solutions must pass to fully capture the nonlinear response. Some hurdles still
exist in finding nonlinear responses of structures under large geometric changes.
Predicting snap-through and snap-back of certain structures has been difficult
and time consuming. Also difficult is finding how much load a structure may
still carry safely. Highly geometrically nonlinear responses of structures
exhibiting complex snap-back behavior are presented and analyzed with a finite
element approach. The arc-length method will be reviewed and shown to predict
the proper response and follow the nonlinear equilibrium path through limit
points.
Keywords: nonlinear, truss, arc-length, finite element, snap-back, Crisfield,
tangent stiffness, equilibrium path, Nastran, bifurcation.
Keywords
nonlinear, truss, arc-length, finite element, snap-back, Crisfield,
tangent stiffness, equilibrium path, Nastran, bifurcation.
Related Book
Other papers in this volume
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