Linear stability of the steady flow past rectangular cylinders

The primary instability of the flow past rectangular cylinders is studied to comprehensively describe the influence of the aspect ratio $AR$ and of rounding the leading- and/or trailing-edge corners. Aspect ratios ranging between $0.25$ and $30$ are considered. We show that the critical Reynolds number ( $\textit {Re}_c$ ) corresponding to the primary instability increases with the aspect ratio, starting from $\textit {Re}_c \approx 34.8$ for $AR=0.25$ to a value of $\textit {Re}_c \approx 140$ for $AR = 30$ . The unstable mode and its dependence on the aspect ratio are described. We find that positioning a small circular cylinder in the flow modifies the instability in a way strongly depending on the aspect ratio. The rounded corners affect the primary instability in a way that depends on both the aspect ratio and the curvature radius. For small $AR$ , rounding the leading-edge corners has always a stabilising effect, whereas rounding the trailing-edge corners is destabilising, although for large curvature radii only. For intermediate $AR$ , instead, rounding the leading-edge corners has a stabilising effect limited to small curvature radii only, while for $AR \geqslant 5$ it has always a destabilising effect. In contrast, for $AR \geqslant 2$ rounding the trailing-edge corners consistently increases $\textit {Re}_c$ . Interestingly, when all the corners are rounded, the flow becomes more stable, at all aspect ratios. An explanation for the stabilising and destabilising effect of the rounded corners is provided.

Flight Stability Analysis of a Flexible Rocket Using Finite Elements and Reduced-Order Modeling

The coupling of advanced structural and aerodynamic methods is a complex and computationally demanding task. In many cases, simplifications must be made. For the flight simulation of flexible aerospace vehicles, it is common to reduce the overall structure down to a series of linked degenerate structures such as Euler-Bernoulli beams in order to expedite the structural portion of the solution process. The current study employs the sophistication and generality of finite-element based modeling with the concepts of reduced-order modeling to create a general flexible-body flight simulation program. The program was created for use with the MATLAB-Simulink programming package. A parametric analysis on the stability of flexible rockets is performed and results are presented for a variety of rocket configurations based on the SPHADS-1 vehicle under development at Ryerson University. The primary instability mode under study is that associated with the flapping and twisting motions of the tailfins under aerodynamic loading. By varying the average fin thickness, both stable and unstable behaviour is recorded for a variety of flight conditions.

Flight Stability Analysis of a Flexible Rocket Using Finite Elements and Reduced-Order Modeling

The coupling of advanced structural and aerodynamic methods is a complex and computationally demanding task. In many cases, simplifications must be made. For the flight simulation of flexible aerospace vehicles, it is common to reduce the overall structure down to a series of linked degenerate structures such as Euler-Bernoulli beams in order to expedite the structural portion of the solution process. The current study employs the sophistication and generality of finite-element based modeling with the concepts of reduced-order modeling to create a general flexible-body flight simulation program. The program was created for use with the MATLAB-Simulink programming package. A parametric analysis on the stability of flexible rockets is performed and results are presented for a variety of rocket configurations based on the SPHADS-1 vehicle under development at Ryerson University. The primary instability mode under study is that associated with the flapping and twisting motions of the tailfins under aerodynamic loading. By varying the average fin thickness, both stable and unstable behaviour is recorded for a variety of flight conditions.

Bipolar Bone Defects in Shoulders With Primary Instability: Dislocation Versus Subluxation

Background: In shoulders with traumatic anterior instability, a bipolar bone defect has been recognized as an important indicator of the prognosis. Purpose: To investigate bipolar bone defects at primary instability and compare the difference between dislocation and subluxation. Study Design: Cohort study; Level of evidence, 3. Methods: There were 156 shoulders (156 patients) including 91 shoulders with dislocation and 65 shoulders with subluxation. Glenoid defects and Hill-Sachs lesions were classified into 5 size categories on 3-dimensional computed tomography (CT) scans and were allocated scores ranging from 0 (no defect) to 4 points (very large defect). To assess the combined size of the glenoid defect and Hill-Sachs lesion, the scores for both lesions were summed (range, 0-8 points). Patients in the dislocation and subluxation groups were compared regarding the prevalence of a glenoid defect, a bone fragment of bony Bankart lesion, a Hill-Sachs lesion, a bipolar bone defect, and an off-track Hill-Sachs lesion. Then, the combined size of the bipolar bone defects was compared between the dislocation and subluxation groups and among patients stratified by age at the time of CT scanning (<20, 20-29, and ≥30 years). Results: Hill-Sachs lesions were observed more frequently in the dislocation group (75.8%) compared with the subluxation group (27.7%; P < .001), whereas the prevalence of glenoid defects was not significantly different between groups (36.3% vs 29.2%, respectively; P = .393). The combined defect size was significantly larger in the dislocation versus subluxation group (mean ± SD combined defect score, 2.1 ± 1.6 vs 0.8 ± 0.9 points, respectively; P < .001) due to a larger Hill-Sachs lesion at dislocation than subluxation (glenoid defect score, 0.5 ± 0.9 vs 0.3 ± 0.6 points [ P = .112]; Hill-Sachs lesion score, 1.6 ± 1.2 vs 0.4 ± 0.7 points [ P < .001]). Combined defect size was larger in older patients than younger patients in the setting of dislocation (combined defect score, <20 years, 1.6 ± 1.2 points; 20-29 years, 1.9 ± 1.5 points; ≥30 years, 3.4 ± 1.6 points; P < .001) but was not different in the setting of subluxation (0.8 ± 1.0, 0.7 ± 0.9, and 0.8 ± 0.8 points, respectively; P = .885). An off-track Hill-Sachs lesion was observed in 2 older patients with dislocation but was not observed in shoulders with subluxation. Conclusion: The bipolar bone defect was significantly more frequent, and the combined size was greater in shoulders with primary dislocation and in older patients (≥30 years).

BUCKLING DELAMINATION IN COMPRESSED NO-TENSION HOMOGENEOUS BRITTLE BEAM-COLUMNS REINFORCED WITH FRP

The main issue of this paper is the instability of no-tension structural members reinforced with FRP. This study concerns the instability of FRP reinforcement. The primary instability problem of a compressed element involves the partialization of the inflex section. In particular, in the case of a compressed slender element reinforced on both tense and compressed side FRP delamination phaenomenon could occur on the latter. This entails the loss of the reinforcement effectiveness in the compressed area for nominal load values much lower than material effective strength. Therefore, structural elements or portions thereof which absorb axial components in the direction of the reinforcement may exhibit relatively modest performance with respect to the unreinforced configuration. By employing a no-tension material linear in compression, an analytical solution for FRP buckling delamination length is provided. The main objective of this paper is to provide a simplified tool that allows to evaluate the critical load of the reinforced beam-column and to predict the tension at which delamination and the loss of effectiveness of reinforcement in the compressed area could occur.

Biomechanical Substantiation of the Strength and Stiffness of a Hip Joint Capsule Defect Fixation with Polypropylene Mesh

Formulation of the problem Dislocation of the femoral component of the endoprosthesis is one of the most frequent complications of total hip replacement. The best option for the “treatment” of dislocation of the hip endoprosthesis is to prevent the development of primary instability. There are cases in which even with the correct installation of the endoprosthesis components, dislocations arise due to the weakness or defect of the capsular–ligament apparatus. Currently, many methods have been developed to strengthen and restore the posterior structures of the capsule of the hip joint with the help of auto- and allomaterials, which differ in both the fixation technique and the characteristics of the materials themselves. In this paper, we propose a method for restoring and strengthening the posterior structures of the capsule of the hip joint using polypropylene-based graft implants. The purpose of this study is to, with the help of specialized software, build a model of the capsule of the hip joint after capsulotomy and to determine the stiffness capabilities of the defect covered with polypropylene mesh. Results The study was performed using a software package based on the finite-element method. As a result of the performed calculations, pictures of the distribution of the stress–strain state in the “head-capsule” system were obtained. To assess the effectiveness of the method of closing the capsule, from the viewpoint of rigidity, as the main characteristics, the values of the opening of the cut are selected. Conclusions Under the kinematic loading of the model, the smallest values of the opening of the section are obtained when it is closed by a grid. In the case of thread fixation, the values were higher by 8.5%. However, the values of equivalent stresses, both in the capsule and in the head, in the model with the grid turned out to be the largest. These stresses were higher by 23.8% in the capsule and by 60.4% in the head than the same values for the thread fixation model. The obtained results indicate that the model with a grid is more rigid in the considered fixation variants.

Postoperative Recurrence of Instability After Arthroscopic Bankart Repair for Shoulders With Primary Instability Compared With Recurrent Instability: Influence of Bipolar Bone Defect Size

Background: In shoulders with traumatic anterior instability, a bipolar bone defect has recently been recognized as an important indicator of the prognosis. Purpose: To investigate the influence of bipolar bone defects on postoperative recurrence after arthroscopic Bankart repair performed at primary instability. Study Design: Cohort study; Level of evidence, 3. Methods: The study group consisted of 45 patients (45 shoulders) who underwent arthroscopic Bankart repair at primary instability before recurrence and were followed for at least 2 years. The control group consisted of 95 patients (95 shoulders) with recurrent instability who underwent Bankart repair and were followed for at least 2 years. Glenoid defects and Hill-Sachs lesions were classified into 5 size categories on 3-dimensional computed tomography and were allocated scores ranging from 0 for no defect to 4 for the largest defect. The shoulders were classified according to the total score for both lesions (0-8 points). The postoperative recurrence rate was investigated for each score of bipolar bone defects and was compared between patients with primary instability and patients with recurrent instability. The same analysis was performed for the age at operation (<20 years, 20-29 years, or ≥30 years) and for the presence of an off-track Hill-Sachs lesion. Results: Bipolar bone defects were smaller in shoulders with primary instability (mean ± SD defect score, 1.4 ± 1.5 points) than in those with recurrent instability (3.6 ± 1.9 points) and were larger in older patients than in younger patients at the time of primary instability. The postoperative recurrence rate was low (6.7%) in shoulders with primary instability regardless of the size of the bipolar bone defect and the patient’s age, whereas the postoperative recurrence rate was high (23.2%) in shoulders with recurrent instability, especially among patients younger than 20 years with bipolar bone defects of 2 points or greater. An off-track Hill-Sachs lesion was found in only 1 patient in the oldest age group (2.2%) at primary instability, but it was found in 19 patients (20%) at recurrent instability, including 14 patients younger than 30 years. Among patients with an off-track lesion, the postoperative recurrence rate was significantly higher in patients younger than 20 years with recurrent instability (recurrence rates: <20 years, 71.4%; 20-29 years, 14.3%; ≥30 years, 0%). Conclusion: The recurrence rate was consistently low in patients with primary instability and was significantly influenced by bipolar bone defect size and patient age in patients with recurrent instability.

From primary instabilities to secondary instabilities in Görtler vortex flows

We have studied the transformation process from primary instabilities to secondary instabilities with direct numerical simulations and stability theories (Spatial Biglobal and plane-marching parabolized stability equations) in detail. First Mack mode and second Mack mode are shown to be able to evolve into the sinuous mode and the varicose mode of secondary instability, respectively. Although the characteristics of second Mack mode eventually lose in the downstream due to the synchronization with the continuous spectrum, second Mack mode is found to be able to trigger a sequence of mode resonations which in turn give birth to highly unstable secondary instabilities. In contrast, first Mack mode does not involve in any mode synchronization. Nevertheless, it can still “jump" to a sinuous mode of secondary instability with a much larger growth rate than that of the first Mack mode. Therefore, secondary instabilities of Görtler vortices are highly receptive to the primary instabilities in the upstream, so that one should consider the primary instability in the upstream and the secondary instability in the downstream as a whole in order to get an accurate prediction of the boundary layer transition.