Geometrically exact static isogeometric analysis of arbitrarily curved plane Bernoulli–Euler beam. (January 2022)

• Record Type: Journal Article
• Authors: Borković, A.; Marussig, B.; Radenković, G.
• Is Part Of: Thin-walled structures. Volume 170(2022)
• Publication Date: 2022-01
• Subjects: Bernoulli–Euler beam -- Strongly curved beams -- Geometrically exact analysis -- Analytical constitutive relation; Thin-walled structures -- Periodicals; 690.1
• DOI: 10.1016/j.tws.2021.108539
• Languages: English
• ISSNs: 0263-8231

Abstract

Abstract: We present a geometrically exact nonlinear analysis of elastic in-plane beams in the context of finite but small strain theory. The formulation utilizes the full beam metric and obtains the complete analytic elastic constitutive model by employing the exact relation between the reference and equidistant strains. Thus, we account for the nonlinear strain distribution over the thickness of a beam. In addition to the full analytical constitutive model, four simplified ones are presented. Their comparison provides a thorough examination of the influence of a beam's metric on the structural response. As a benchmark result, an analytical solution for a pure bending of a strongly curved cantilever beam is derived. We show that the appropriate formulation depends on the curviness of a beam at all configurations. Furthermore, the nonlinear distribution of strain along the thickness of strongly curved beams must be considered to obtain a complete and accurate response. Highlights: A rigorous nonlinear static IGA of in-plane beams is developed and implemented. The nonlinear distribution of strain over the height of a beam is taken into account. The complete analytic constitutive relation between energetically conjugated pairs is used. The curviness of a beam at each configuration determines the appropriate formulation.