Modelagem de vigas de compósitos laminados usando elementos finitos formulados na notação strain gradient

AUTOR(ES)

Florentino Augusto Fagundes

DATA DE PUBLICAÇÃO

2002

RESUMO

This work analyzes laminated .composite beams using finite elements formulated in strain gradient notation, which is a physically interpretable notation. Strain Gradient notation allows for the evaluation of modeling capabilities of finite elements, as well as for the identification and elimination of modeling errors a-priori. Initially a literature review is performed on laminated composites, on the finite element method an on finite elements modeling errors. Subsequently, fundamental aspects of the finite element method, of the mechanics of laminated composites and of strain gradient notation are presented. A two-node (six degree-of-freedom) element for the analysis of laminated composite beams which has the capacity of modeling transverse shear deformation is presented. Through strain gradient notation, the presence of a spurious term in the transverse shear strain γxz is identified. This spurious term is a parasitic shear term. Its removal corrects the element, this allowing for obtaining physically correct answers. The finite element is implemented into a FORTRAN code in its both versions, that is, with and without parasitic shear. Numerical analyses are performed with the intent to compare solutions contaminated by the effects of parasitic shear with correct solutions. In general, it is observed that both solutions converge to the same result. However, the solution correct for parasitic shear presents a significantly higher rate of convergence. This demonstrates the artificial stiffening effect caused by parasitic shear. It is also observed that solutions for transverse shear strain and stress generated by the model containing parasitic shear are qualitatively erroneous, and do not converge to the correct solutions even with greater level of mesh refinement. Therefore, it is demonstrated the need for removing the spurious term a-priori for obtaining correct solutions for laminated composite beam problems.

ASSUNTO(S)

método dos elementos finitos engenharia mecanica materiais laminados vigas

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