TY - JOUR

T1 - Qualitative convergence in the discrete approximation of the euler problem

AU - Domokos, Gabor

PY - 1993/1/1

Y1 - 1993/1/1

N2 - There are two mathematically rigorous ways to derive Euler's differential equation of the elastica. The first is to start from integral rules and use variational principles, whereas the second is to regard the continuous rod as a limit of a discrete sequence of elastically connected rigid elements when the length of the elements decreases to zero. Discrete models of the Euler buckling problem are investigated. The global number s of solutions of the boundary-value problem is expressed as a function of the number of elements in the discrete model, s = s(n), at constant loading P. The functions s(n) are described by the characteristic parameters nxand n2, and graphs of nx(P) and n2(P) are plotted. Observations related to these diagrams reveal interesting features in the behavior of the discrete model, from the point of view of both theory and application.

AB - There are two mathematically rigorous ways to derive Euler's differential equation of the elastica. The first is to start from integral rules and use variational principles, whereas the second is to regard the continuous rod as a limit of a discrete sequence of elastically connected rigid elements when the length of the elements decreases to zero. Discrete models of the Euler buckling problem are investigated. The global number s of solutions of the boundary-value problem is expressed as a function of the number of elements in the discrete model, s = s(n), at constant loading P. The functions s(n) are described by the characteristic parameters nxand n2, and graphs of nx(P) and n2(P) are plotted. Observations related to these diagrams reveal interesting features in the behavior of the discrete model, from the point of view of both theory and application.

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U2 - 10.1080/08905459308905200

DO - 10.1080/08905459308905200

M3 - Article

AN - SCOPUS:0347583405

VL - 21

SP - 529

EP - 543

JO - Mechanics Based Design of Structures and Machines

JF - Mechanics Based Design of Structures and Machines

SN - 1539-7734

IS - 4

ER -