Identificação da matriz de rigidez à flexão da madeira de Pinus pinaster através do método dos campos virtuais
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2016-12-15
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Neste trabalho apresenta-se um estudo sobre a caraterização de propriedades elásticas de madeira de Pinus pinaster Ait. através de um ensaio heterogéneo de flexão de placa.
Nesse sentido, foram tratados dois planos de simetria material, o plano longitudinal-radial e o plano longitudinal-tangencial. O método proposto combina a técnica ótica de deflectometria com o método dos campos virtuais. Com este método inverso de caracterização material pretende-se identificar todas as componentes da matriz de rigidez à flexão, que
governam o comportamento constitutivo de placa fina de Kirchhoff-Love, através de um único ensaio. O procedimento proposto foi validado numericamente com base num modelo de elementos finitos do ensaio de flexão, assumindo cinco cenários de carregamento diferentes. Experimentalmente foi proposto um procedimento para o revestimento da
placa em madeira maciça, necessário para a hipótese de reflexão especular do princípio da técnica de deflectometria. O campo de rotação, determinado a partir do campo de fase, foi derivado numericamente usando uma aproximação polinomial no sentido de reconstruir o campo de curvaturas da deformada da placa. Esta grandeza cinemática, em conjunto
com a força pontual aplicada e as dimensões dos provetes foram posteriormente tratados pelo método dos campos virtuais. Os valores dos parâmetros elásticos obtidos por esta abordagem estão de acordo com os valores de referência apresentados na literatura para esta espécie de madeira e determinados usando ensaios clássicos independentes de tração
e de corte.
This work presents a study on the characterization of elastic properties of Pinus pinaster Ait. wood through a heterogeneous plate bending test. Both the longitudinal-radial and the longitudinal-tangential orthotropic planes were considered in the analysis. The proposed approach couples the deflectometry optical technique with the virtual fields method. Using this inverse identification method, all components of the bending stiffness matrix, governing the Love-Kirchhoff classical plate theory, can be determined from a single test. The approach was firstly validated using a finite element model of the bending test considering five different loading cases. Experimentally, a procedure was implemented in order to a coating the surface of the solid wood plate in order to guarantee the specular reflection required by the deflectometry technique. The slope fields were determined from the phase one. The former was then numerically differentiated by means of a polynomial approximation in order to reconstruct the curvature fields needed in the identification principle. The curvature fields, together with the applied punctual load and the plate dimensions were the input in the virtual fields method for material parameter identification. The values of the elastic parameters obtained from the proposed approach were found in good agreement with regard to reference ones reported in the literature for the same species and determined from independent classic tensile and shear mechanical tests.
This work presents a study on the characterization of elastic properties of Pinus pinaster Ait. wood through a heterogeneous plate bending test. Both the longitudinal-radial and the longitudinal-tangential orthotropic planes were considered in the analysis. The proposed approach couples the deflectometry optical technique with the virtual fields method. Using this inverse identification method, all components of the bending stiffness matrix, governing the Love-Kirchhoff classical plate theory, can be determined from a single test. The approach was firstly validated using a finite element model of the bending test considering five different loading cases. Experimentally, a procedure was implemented in order to a coating the surface of the solid wood plate in order to guarantee the specular reflection required by the deflectometry technique. The slope fields were determined from the phase one. The former was then numerically differentiated by means of a polynomial approximation in order to reconstruct the curvature fields needed in the identification principle. The curvature fields, together with the applied punctual load and the plate dimensions were the input in the virtual fields method for material parameter identification. The values of the elastic parameters obtained from the proposed approach were found in good agreement with regard to reference ones reported in the literature for the same species and determined from independent classic tensile and shear mechanical tests.
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Dissertação de Mestrado em Engenharia Mecânica
Palavras-chave
Madeira , Deflectometria , Método dos campos virtuais , Matriz de rigidez , Ensaio flexão