Numerical Analysis of a Generalized Plane Plastica
Coulter, Brett Ainsley
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https://hdl.handle.net/2142/71698
Description
Title
Numerical Analysis of a Generalized Plane Plastica
Author(s)
Coulter, Brett Ainsley
Issue Date
1988
Doctoral Committee Chair(s)
Miller, Robert E.
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Civil
Engineering, Mechanical
Abstract
A numerical procedure is developed for finding the displacements, internal forces, and reaction forces on any planar, continuous, and flexible structural member such as a beam, column, ring, or simply-connected frame. Euler-Bernoulli theory, in which plane sections remain plane and strains are small, is assumed. Large displacements and rotations; linear elastic, nonlinear elastic and elastic-plastic material behavior; and general cross section shapes are admitted. For nonlinear elastic analysis a multi-linear stress-strain law is used, thereby allowing an accurate approximation to the constitutive laws of actual materials. For elastic-plastic analysis a more specific tri-linear stress-strain relation is assumed, and the material is assumed to harden in a kinematic fashion. Incremental loads are employed, and plastic loading, unloading, and reloading are all permitted.
There are three displacement and three force quantities at each end of the "plastica." For each loading increment at least three of these six quantities must be known in advance at both ends for the problem to be will-posed. With the known variables at one end and initial guesses of the unknown variables at the end, a shooting method combined with beam finite elements is used to predict the known (and unknown) variables at the other end. A Newton-type iteration scheme with finite-difference approximations to partial derivatives is then used to determine the variables at the initial end of the plastica, and to find the resulting configuration, internal forces, and reactions on the plastica for each loading increment.
Comparisons are made with numerical and analytical solutions to problems solved by others, and new examples are also included.
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