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Sensitivity of inelastic response to numerical integration of strain energy
Author(s) -
Kamat M. P.
Publication year - 1976
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620100615
Subject(s) - cantilever , dissipative system , beam (structure) , strain energy , numerical integration , bending moment , strain hardening exponent , numerical analysis , mechanics , finite element method , structural engineering , materials science , physics , mathematics , mathematical analysis , engineering , composite material , quantum mechanics
The exact solution to the quasi‐static, inelastic response of a cantilever beam of rectangular cross‐section subjected to a bending moment at the tip is obtained. The material of the beam is assumed to be linearly elastic‐linearly strain‐hardening. This solution is then compared with three different numerical solutions of the same problem obtained by minimizing the total potential energy using Gaussian quadratures of two different orders and a Newton‐Cotes scheme for integrating the strain energy of deformation. Significant differences between the exact dissipative strain energy and its numerical counterpart are emphasized. The consequence of this on the non‐linear transient responses of a beam with solid cross‐section and that of a thin‐walled beam on elastic supports under impulsive loads are examined.