Hierarchical models for failure analysis of plates bent by distributed and localized transverse loadings

The failure analysis of simply supported, isotropic, square plates is addressed. Attention focuses on minimum failure load amplitudes and failure locations, von Mises＇ equivalent stress along the plate thickness is also addressed. Several distributed and localized loading conditions are considered. Loads act on the top of the plate. Bi-sinusoidal and uniform loads are taken into account for distributed loadings, while stepwise constant centric and off-centric loadings are addressed in the case of localized loadings. Analysis is performed considering plates whose length-to-thickness ratio a/h can be as high as 100 （thin plates） and as low as 2 （very thick plates）. Results are obtained via several 2D plate models. Classical theories （CTs） and higher order models are applied. Those theories are based on polynomial approximation of the displacement field. Among the higher order theories （HOTs） HOTsa models account for the transverse shear deformations, while HOTs models account for both transverse shear and transverse normal deformations. LHOTs represent a local application of the higher order theories. A layerwise approach is thus assumed： by means of mathematical interfaces, the plate is considered to be made of several fictitious layers. The exact 3D solution is presented in order to determine the accuracy of the results obtained via the 2D models. In this way a hierarchy among the 2D theories is established. CTs provide highly accurate results for a/h greater than 10 in the case of distributed loadings and greater than 20 for localized loadings. Results obtained via HOTs are highly accurate in the case of very thick plates for bi-sinusoidal and centric loadings. In the case of uniform and off-centric loadings a high gradient is present in the neighborhood of the plate top. In those cases, LHOTs yield results that match the exact solution.

Finite Element Method Analysis of the Stress for Line Pipe with Corrode Groove During Outdoor Storage

The basic principle of corrode groove on outside of steel pipe during storage was analyzed in this paper, namely the water film on the contacted surface of steel pipe, which gathered from humidity in the air, rain or gel, and the suspended particles in air, and the corrosive composition, such as SO2, CO2, O2 and NaCI, in addition to the inhomogeneity of the organization and composition, which lead to the corrosion cell reaction, so that cause the corrosion initial from the contact surface of the between steel pipes, so as to form the corrosion groove. At the same time, the corrosion groove with depth of 0.125t （t pipe wall thickness） on the pipe of φ 1016 mm×21 mm ×70 API SPEC 5L was simulated using the FEM （finite element method）, and the stress and strain distribution of the defect area near corrosion groove were solved at the inner pressure of 12 MPa, 10 MPa, 8 MPa, 6 MPa, 4 MPa and 2 MPa, respectively, which showed that no matter the pressure values were, the maximum stress and strain were lied at the bottom of corrosion defects groove and were in good linear relationship with the internal pressure increasing from 2 MPa to 6 MPa. When the internal pres- sures were greater than 6 MPa, they felled into the nonlinear model and to be yielded or even to be destroyed. In addition, the residual strength and the limit operation pressure of the corrode pipe with the defects groove of 0.125t were calculated or simulated according to the theoretical calculation, the finite element method based on the stress, the finite element method based on strain, DNV-RP-F101, ASME B31G and experimental methods respectively. The results showed that the residual strength and the limit operation pressure of the defective parts solved by the finite element method based on stress were 424 MPa, and 15.34 MPa, respectively, which was very close to that of experimental method, the residual strength was 410 MPa and the limit operation pressure 14.78 MPa. Besides, the results also showed that it was feasible and effective to simulate the residual strength of the structure with corrosion defects using the finite element method.