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New insights into the strong formulation finite element method for solving elastostatic and elastodynamic problems

100%
Fantuzzi N.
Curved and Layered Structures
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2014
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tom 1
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nr 1
EN
This present paper has a complete and homogeneous presentation of plane stress and plane strain problems using the Strong Formulation Finite Element Method (SFEM). In particular, a greater emphasis is given to the numerical implementation of the governing and boundary conditions of the partial differential system of equations. The paper’s focus is on numerical stability and accuracy related to elastostatic and elastodynamic problems. In the engineering literature, results are mainly reported for isotropic and homogeneous structures. In this paper, a composite structure is investigated. The SFEM solution is compared to the ones obtained using commercial finite element codes. Generally, the SFEM observes fast accuracy and all the results are in very good agreement with the ones presented in literature.
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Vibration analysis of multi-stepped and multi-damaged parabolic arches using GDQ

51%
Viola E., Miniaci M., Fantuzzi N., Marzani A.
Curved and Layered Structures
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2015
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tom 2
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nr 1
EN
This paper investigates the in-plane free vibrations of multi-stepped and multi-damaged parabolic arches, for various boundary conditions. The axial extension, transverse shear deformation and rotatory inertia effects are taken into account. The constitutive equations relating the stress resultants to the corresponding deformation components refer to an isotropic and linear elastic material. Starting from the kinematic hypothesis for the in-plane displacement of the shear-deformable arch, the equations of motion are deduced by using Hamilton’s principle. Natural frequencies and mode shapes are computed using the Generalized Differential Quadrature (GDQ) method. The variable radius of curvature along the axis of the parabolic arch requires, compared to the circular arch, a more complex formulation and numerical implementation of the motion equations as well as the external and internal boundary conditions. Each damage is modelled as a combination of one rotational and two translational elastic springs. A parametric study is performed to illustrate the influence of the damage parameters on the natural frequencies of parabolic arches for different boundary conditions and cross-sections with localizeddamage.Results for the circular arch, derived from the proposed parabolic model with the derivatives of some parameters set to zero, agree well with those published over the past years.
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