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An asymptotic approach to analysis of 3D beam stress‐strain elastic states
Author(s) -
Saurin Vasily,
Kostin Georgy
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810335
Subject(s) - mathematics , mathematical analysis , cartesian coordinate system , boundary value problem , torsion (gastropod) , ordinary differential equation , beam (structure) , elasticity (physics) , differential equation , geometry , physics , medicine , surgery , optics , thermodynamics
A regular asymptotic approach to analysis of 3D beam stress–strain states is proposed based on the linear theory of elasticity and the method of integrodifferential relations. Using the integral formulation of Hooke's law and polynomial expansions of unknown stress and displacement functions with respect to transversal Cartesian coordinates the initial system of partial differential equations is reduced to a countable system of ordinary differential equations with constant coefficients. For rectilinear beams with rectangular cross–sections the consistent boundary value problems describing independently the compression and stretch, bends, and torsion states are derived. To find equilibrium stress and admissible displacement fields satisfying boundary conditions an effective numerical algorithm is worked out. Integral and local criteria for explicit bilateral estimates of resulted solution quality are proposed. The numerical results are presented and discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)