LAUSR

Abstract In this work we present a generalization of a finite element formulation, based on the new Unconstrained Vector Layerwise Theory (UVLWT), that allows a geometrically exact description of 2D laminated plane frames with accurate stress distribution. The formulation presents a natural and easy extension for 3D applications. The proposed generalization is based on a penalty strategy to couple frames at corners in a very accurate and elegant way. It consists on the introduction of rigid, semi-rigid and hinged connections among elements, for which all degrees of freedom of each lamina are considered and their energetically conjugate forces calculated. Flexible supports of the structure regarding the static reference have also been successfully developed and implemented. Although two-dimensional frames are the main object of this study, three-dimensional connection expressions are developed in order to promote future developments and insights. In order to have complete solutions, even when a snap-back or snap-trough occur, we present the arc-length approach adapted to the complete analysis of 2D frames by the UVLWT. From the analyzed examples, we can state that the UVLWT formulation and the developed connections presents the following capabilities:(i) geometric nonlinear modeling of laminated 2D frames assembled by slender or thick bars, without presenting problems of locking and system of equations bad conditioning; (ii) geometrically exact modeling of curved bars; (iii) consistent modeling of general flexible or rigid internal corner connections; (iv) consistent modeling of elastic external supports; (v) Zig-Zag effect consideration with accurate transverse stress distribution and (vi) straightforward extension for 3D applications as the finite rotation concept is not used.