Original scientific paper
https://doi.org/10.17559/TV-20160624100741
Formulation and Solution of Curved Beams with Elastic Supports
Fernando Sarria
; Public University of Navarre, Tejos building, Campus Arrosadia, 31006 Pamplona, Spain
Faustino N. Gimena
orcid.org/0000-0001-7912-9082
; Public University of Navarre, Tejos building, Campus Arrosadia, 31006 Pamplona, Spain
Pedro Gonzaga
orcid.org/0000-0001-9384-6432
; Public University of Navarre, Tejos building, Campus Arrosadia, 31006 Pamplona, Spain
Mikel Goñi
; Public University of Navarre, Tejos building, Campus Arrosadia, 31006 Pamplona, Spain
Lázaro Gimena
; Public University of Navarre, Tejos building, Campus Arrosadia, 31006 Pamplona, Spain
Abstract
This article presents the general system of differential equations that governs the behaviour of a curved beam, which can be solved by either numerical or analytical methods. The obtained solution represents the matricial expression of transference. The stiffness matrix is derived directly rearranging the transfer matrix. Through twelve equations are shown the elastic conditions of the support in both ends of the curved piece. By joining the twelve equations of the stiffness matrix expression with the twelve equations of support conditions, we determined a unique system of equations associated to the curved beam with elastic supports. Establishing the elastic conditions has always been a problem, since previous traditional models do not look at the whole system, of twenty four equations, with all the unknowns and all the functions. Two examples of pieces with elastic supports are developed to show the applicability of the proposed method.
Keywords
analytical and numerical solutions; curved beam; stiffness matrix; support equations; transfer matrix
Hrčak ID:
200598
URI
Publication date:
26.5.2018.
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