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The Effect of Boundary Conditions on Finite Element Analysis Convergence Curves
Author(s) -
Melosh Robert,
Raju Rangnadha
Publication year - 1991
Publication title -
computer‐aided civil and infrastructure engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.773
H-Index - 82
eISSN - 1467-8667
pISSN - 1093-9687
DOI - 10.1111/j.1467-8667.1991.tb00408.x
Subject(s) - convergence (economics) , boundary (topology) , monotonic function , boundary value problem , finite element method , mathematics , mathematical analysis , minimax , superposition principle , displacement (psychology) , function (biology) , geometry , mathematical optimization , structural engineering , engineering , psychology , evolutionary biology , economics , psychotherapist , biology , economic growth
Abstract: This Paper explores the relation between the number of generalized displacement coordinates and finite element solution accuracy as a function of the class of boundary conditions. The study concludes that strain energy estimates for well‐behaved potential energy element models may be mulitvalued for successively finer grids. When the only non‐zero boundary values are nodal forces, the problem is minimax. When the only non‐zero boundary conditions are settlements, the problem is minimin. When boundary conditions involve a mix of nodal forces and settlements, multivalued convergence curves may arise. The authors suggest the use of superposition to circumvent non‐monotonic convergence.

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