Um modelo geometricamente exato de barras com grandes deformações, que considera a distorção e o empenamento geral da seção transversal, e sua discretização pelo método dos elementos finitos. / A fully nonlinear geometrically exact multi-parameter rod model that incorporates general in-plane and out-of-plane cross-sectional changes, and its discretization by Finite Element Method.

AUTOR(ES)
DATA DE PUBLICAÇÃO

2008

RESUMO

The main purpose of this work is to present a fully nonlinear geometrically-exact multi-parameter rod model that incorporates general in-plane cross-sectional changes as well as general out-of-plane cross-sectional warping. The formulation constitutes an extension of the earlier works presented in [1] to [6], [8] and [9], in the sense that the restrictions to a rigid cross-section and to a Saint-Venant-like elastic warping are now removed from the theory. Our approach defines energetically conjugated cross-sectional resultants in terms of generalized stresses and strains, based on the concept of a cross-section director. Besides their practical importance, the use of cross-sectional resultants simplifies the derivation of equilibrium equations and the enforcement of boundary conditions, in either weak or strong senses. In addition, the corresponding tangent bilinear weak form is obtained in a more expedient way, rendering always symmetric for hyperelastic materials and conservative loadings (even far from equilibrium states). Definition of a cross-section director plays a central role in the present model. Accordingly, it allows the introduction of independent degrees-of-freedom to describe both the in-plane cross-sectional changes and the out-of-plane warping. Fully three-dimensional finite strain constitutive equations can therefore be employed with no spurious stiffening. The ideas are general and extension to inelastic rods, in particular to those of elastoplastic materials, is straightforward once a stress integration scheme within a time step is at hand. Finite rotations are treated here by the Euler-Rodrigues formula in a pure Lagrangean framework. We assume a straight reference configuration for the rod axis, but initially curved rods can also be considered if regarded as a stress-free deformed state from the straight position (see [11]). The use of convective non-Cartesian coordinate systems is this way avoided and only components on orthogonal frames are employed. Moreover, initial curvatures that are completely independent of the isoparametric concept are possible to be attained, which can be used even in (for example) straight finite elements. Altogether, the present assumptions allow a consistent basis for the proper representation of profile (distortional) deformations, which are typical of coldformed thin-walled rod structures. We believe this is one of the main features of our formulation, as the use of more complex shell models in order to capture such phenomena becomes unnecessary.

ASSUNTO(S)

deformação estrutural finite element method in-plane changes out-of-plane changes barras finite strain mecânica das estruturas método dos elementos finitos rod theory

ACESSO AO ARTIGO

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