Forming Limit Diagrams of Perforated St12 Steel Sheets

One of the unique characteristics of sheet metals is their formability, which is determined by the forming limit diagrams. These diagrams specify the maximum deformation limit before part’s failure. For several applications of metal sheets, they have to be in the perforated format. Existence of holes in the perforated sheets may adversely deteriorate the forming limit of metal sheets. In this study, the effect of perforated sheets’ hole size and hole layout on their formability are investigated. Several specimens of St12 steel with 0.6 mm thickness, different widths, two various hole sizes of 2 and 4 mm, and two layouts of triangular and square were prepared. The specimens were tested using Nakajima test (stretch with a hemispherical punch) to generate the forming limit diagrams. It was observed that both the diameter and layout of the punched holes have a significant effect on the formability of the perforated sheets. The perforated sheets with triangular hole layout showed higher forming limits due to their larger ligament ratios.

Forming Limit Diagrams of Perforated St12 Steel Sheets

One of the unique characteristics of sheet metals is their formability, which is determined by the forming limit diagrams. These diagrams specify the maximum deformation limit before part’s failure. For several applications of metal sheets, they have to be in the perforated format. Existence of holes in the perforated sheets may adversely deteriorate the forming limit of metal sheets. In this study, the effect of perforated sheets’ hole size and hole layout on their formability are investigated. Several specimens of St12 steel with 0.6 mm thickness, different widths, two various hole sizes of 2 and 4 mm, and two layouts of triangular and square were prepared. The specimens were tested using Nakajima test (stretch with a hemispherical punch) to generate the forming limit diagrams. It was observed that both the diameter and layout of the punched holes have a significant effect on the formability of the perforated sheets. The perforated sheets with triangular hole layout showed higher forming limits due to their larger ligament ratios.

On quantum deformations of AdS3 × S3 × T4 and mirror duality

We consider various integrable two-parameter deformations of the AdS3 × S3 × T4 superstring with quantum group symmetry. Working on the string worldsheet in light-cone gauge and to quadratic order in fermions, we obtain their common massive tree-level two-body S matrix, which matches the expansion of the conjectured exact q-deformed S matrix. We then analyze the behavior of the exact S matrix under mirror transformation — a double Wick rotation on the worldsheet — and find that it satisfies a mirror duality relation analogous to the distinguished q-deformed AdS5 × S5 S matrix in the one parameter deformation limit. Finally, we show that the fermionic q-deformed AdS5 × S5 S matrix also satisfies such a relation.

$$ T\overline{T} $$-deformed fermionic theories revisited

We revisit $$ T\overline{T} $$ T T ¯ deformations of d = 2 theories with fermions with a view toward the quantization. As a simple illustration, we compute the deformed Dirac bracket for a Majorana doublet and confirm the known eigenvalue flows perturbatively. We mostly consider those $$ T\overline{T} $$ T T ¯ theories that can be reconstructed from string-like theories upon integrating out the worldsheet metric. After a quick overview of how this works when we add NSR-like or GS-like fermions, we obtain a known non-supersymmetric $$ T\overline{T} $$ T T ¯ deformation of a $$ \mathcal{N} $$ N = (1, 1) theory from the latter, based on the Noether energy-momentum. This world- sheet reconstruction implies that the latter is actually a supersymmetric subsector of a d = 3 GS-like model, implying hidden supercharges, which we do construct explicitly. This brings us to ask about different $$ T\overline{T} $$ T T ¯ deformations, such as manifestly supersymmetric $$ T\overline{T} $$ T T ¯ and also more generally via the symmetric energy-momentum. We show that, for theories with fermions, such choices often lead us to doubling of degrees of freedom, with potential unitarity issues. We show that the extra sector develops a divergent gap in the “small deformation” limit and decouples in the infrared, although it remains uncertain in what sense these can be considered a deformation.

Studying novel 1D potential via the AIM

In this work, we would like to apply the asymptotic iteration method (AIM) to a newly proposed Morse-like deformed potential introduced recently by Assi, Alhaidari and Bahlouli.[Formula: see text] This interesting potential can support bound states and/or resonances. However, in this work, we are only interested in bound states. We considered several choices of the potential parameters and obtained the associated spectrum. Finally, we study the small deformation limit at which this finite spectrum system will transition to infinite spectrum size.

Application of Modified Hoek–Brown Strength Criterion in Water-Rich Soft Rock Tunnel

When a tunnel is excavated in the water-rich soft rock stratum, the strength of the soft rock is greatly reduced due to the seepage of groundwater. The condition may result in engineering accidents, such as large deformation, limit invasion, and even local collapse of the tunnel. Therefore, it is very important to research the stability of the surrounding rock in the water-rich soft rock tunnel. The water-rich disturbance factor considering the seepage influence of groundwater and blasting disturbance is proposed, and the generalized Hoek–Brown strength criterion is modified on the basis of the immersion softening test of soft rock. In accordance with the classical elastic–plastic mechanics theory, the stress, strain, and displacement calculation formulas of the tunnel surrounding rock are derived. The displacement of tunnel surrounding rock is analyzed using the derived formula and the modified Hoek–Brown strength criterion and then compared with the measured value. Results show that the displacement of surrounding rock, which is calculated by modified Hoek–Brown strength criterion considering water-rich disturbance factor and the displacement calculation formula, is close to the measured deformation of surrounding rock in water-rich soft rock tunnel, and the error is small. Therefore, the modified Hoek–Brown strength criterion can be applied to the water-rich soft rock tunnel, and the derived displacement calculation formula can accurately calculate the deformation of tunnel surrounding rock. It is of great significance to the study of surrounding rock stability of water-rich soft rock tunnel.

SIMULATION OF T-JOINTS BETWEEN RHS STEEL MEMBERS WITH OFFSET IN ABAQUS CAE

The current paper focuses on numerical simulation peculiarities of offset welded rectangular hollow section joints. Understanding the modelling techniques can result in easier and faster and above all correct outcomes from FEA for future use. The steel joints under discussion are composed from cold-formed regular rectangular hollow sections where RHS brace members are laterally shifted from chord axis. Joints work under monotonically increasing compression load applied to a brace top. Numerical models were developed in FE programme Abaqus. FE-models is composed of C3D8R 8-noded solid linear brick elements with an emphasis on mesh size effect and modelling of a weld seam. FE advanced model were compiled considering both material and geometric nonlinearities. For validation purposes, the full-scale laboratory tests were conducted. Proposed FE models reliably predict the structural behaviour of welded offset T-joints thanks to good agreement achieved on deformation limit 3 % b0 with the maximum deviation 10.3 %.

Approach of Pavement Surface Layer Degradation Caused by Tire Contact Using Semi-Analytical Model

New methods of degradations on the pavement’s surface, such as top-down cracking and delamination, caused by the repeated passage of heavy vehicles led to questions about the impact of the contact between the tire and the pavement. In fact, to increase the service life of the structures, future road design methods must have a precise knowledge of the consequences of the contact parameters on the state of stress and deformation in the pavement. In this paper, tractive rolling contact under the effect of friction is modeled by Kalker’s theory using a semi-analytical method (SAM). A tire profile is performed thanks to a digitization by fringes or a photogrammetry technique. The effect of rolling on the main surface extension deformations is then highlighted to study top cracking. At the end of the SAM calculation, contact areas are closed to 200 μdef, exceeding the allowable micro-deformation limit for the initiation of cracking. In addition, results on the main strain directions also give information on the direction of cracking (initiation of longitudinal or transverse cracks). The cracking then becomes evident, leading to a reduced service life.

Deformation limit and bimeromorphic embedding of Moishezon manifolds

Let [Formula: see text] be a holomorphic family of compact complex manifolds over an open disk in [Formula: see text]. If the fiber [Formula: see text] for each nonzero [Formula: see text] in an uncountable subset [Formula: see text] of [Formula: see text] is Moishezon and the reference fiber [Formula: see text] satisfies the local deformation invariance for Hodge number of type [Formula: see text] or admits a strongly Gauduchon metric introduced by D. Popovici, then [Formula: see text] is still Moishezon. We also obtain a bimeromorphic embedding [Formula: see text]. Our proof can be regarded as a new, algebraic proof of several results in this direction proposed and proved by Popovici in 2009, 2010 and 2013. However, our assumption with [Formula: see text] not necessarily being a limit point of [Formula: see text] and the bimeromorphic embedding are new. Our strategy of proof lies in constructing a global holomorphic line bundle over the total space of the holomorphic family and studying the bimeromorphic geometry of [Formula: see text]. S.-T. Yau’s solutions to certain degenerate Monge–Ampère equations are used.