Catastrophe Analysis of Structures by Discretization and Modal Transforms

This paper is concerned with the catastrophe of static instability of multi-degree-of-freedom systems representing typical civil engineering structures like beams, columns, arches, plates and stiffened plates. The proposed method makes use of discretization methods, such as a finite element method and a simplified element method, and also some diffeomorphic transformations similar to modal analysis. The main interest of the study is the classification of the catastrophe of the structures through the evaluation of certain derivatives of potential in the light of the Thorn and Thompsons' theories. Numerical illustrations were performed on the structures, including elastically supported columns, plates, stiffened plates, lateral buckling of beams and shallow arches. Among new findings, the unstable symmetric buckling for lateral buckling, and hyperbolic umbilics for the simultaneous buckling of stiffened plates and of elastically supported columns are particularly noted

Catastrophes of Elastic Column Structures

The elasto-static instability phenomena of structures can be typically classified by the catastrophe theory in the local form near a certain singular point of their total potential energy. Then, the imperfection sensitivity of the structures can be evaluated in terms of the bifurcation set, mapping the singular points of the equilibrium space to the control space. In ordinary structural problems, this consists of a simple loading parameter and some imperfection parameters. In this paper, several simplified column models are studied by the catastrophe theory. They include both continuous and discrete models exhibiting stable symmetric, unstable symmetric, asymmetric and their compound buckling. From a comparison of the results of the two-degree-of-freedom systems, namely the continuous systems and the finite element discrete systems, the following conclusions are drawn : (i) The discrete analysis can be shown to realize the instability phenomena, predicted by the continuous analysis. The results of the discrete analysis are shown to converge to those of the continuous analysis generally, as the number of discrete finite elements increases. (ii) The imperfection sensitivity of the structures can be evaluated qualitatively and quantitatively by means of the bifurcation set in the control space through the catastrophe theory. (iii) For a legitimate evaluation of the “cusp and dual cusp catastrophe”, the 4th order non-linear terms must be earnestly considered in expressions for both the strain energy and the external work. Then, the stable symmetric buckling model is shown to indicate a typical cusp catastrophe. (iv) The unstable symmetric buckling model can be shown to indicate a typical dual cusp catastrophe for a relatively small stiffness of the elastic foundation, the cusp catastrophe for a relatively large stiffness and the compound double cusp catastrophe at a certain critical stiffness value. (v) The asymmetric buckling model can be shown to indicate the typical fold catastrophe for a relatively small stiffness of the inclined elasic foundation, the dual cusp catastrophe for a relatively large stiffness and the compound hyperbolic umbilic catastrophe at a certain critical stiffness value

<臨床>胃切除術後の単位体積当たりの骨密度の変化 : Dual energy X-ray absorptiometry (DXA) 法による検討

We used dual energy X-ray absorptiometry (DXA) to study changes in estimated volumetric bone mineral density (EstVBMD) of the lumbar spine after gastrectomy. The study group comprised 41 men and 32 women. When EstVBMD was compared according to sex among patients younger than 60 years of age, patients 60 to 69 years of age, and patients these three groups in men (0.185 g/cm_3, 0.187 g/cm_3, 0.187 g/cm_3, respectively). In contrast , EstVBMD was significantly lower in women 60 to 69 years of age (0.157 g/cm_3) and those 70 years of age or older (0.159 g/cm_3) than in women younger than 60 years (0.200 g/cm_3) (P<0.01). When the relation between EstVBMD and the number of months after gastrectomy was studied according to sex in patients younger than 70 years, EstVBMD negatively correlated with the interval after operation in men (r= -0.365, P<0.05), whereas ther e was no correlation between these variables in women. These results suggest that after gastrectomy bone mineral density decreases gradually in men younger than 70 years, but not in women. The lack of a consistent change in bone mineral density after gastrectomy in women is apparently caused by the marked effect on bone metabolism of decreased female hormone levels after menopause.胃切除後の腰椎の骨密度の変化を dual energy X-ray absorptiornetory （DXA） 法で測定し, 単位体積当たりの計測値（Estimated volumetric bone mineral density: EstVBMD）を求めることにより検討した. 男女別に60歳未満, 60歳代, 70歳以上の群で比較すると, 男性では 0.185 g/cm_3, 0.187 g/cm_3, 0.187 g/cm_3と大差がなかった. 一方, 女性では 0.200 g/cm_3, 0.157 g/cm_3, 0.159 g/cm_3 と60歳未満の症例と比較し60歳代, 70歳以上の症例では減少し有意差を認めた. 70歳未満の症例で男女別に術後月数と骨密度との関係をみると, 男性では経過期間とともに骨密度は減少し, 負の相関関係 （r= -0.365, P<0.05）が認められたが, 女性では両者は独立した関係であった. 70歳未満の男性では胃切術後に徐々に骨塩量が低下するが, 女性では閉経後の女性ホルモン減少が強く骨代謝に現れるため胃切術後の影響が個々で異なることが示唆された

ASK1-p38-NR4A2 Axis in H2O2-induced Necrosis

Background: The molecular mechanisms of p38 MAPK-mediated necrosis currently have not been well elucidated. Results: During oxidative stress, NR4A2 is phosphorylated and translocated into the cytosol in an ASK1-p38-dependent manner, which ultimately leads to the promotion of necrosis. Conclusion: ASK1-p38 MAPK pathway-dependent phosphorylation and subsequent cytoplasmic translocation of NR4A2 promote oxidative stress-induced necrosis. Significance: We found a novel intracellular signaling pathway that regulates oxidative stress-induced and p38-mediated necrosis.p38 mitogen-activated protein kinases (MAPKs) play important roles in various cellular stress responses, including cell death, which is roughly categorized into apoptosis and necrosis. Although p38 signaling has been extensively studied, the molecular mechanisms of p38-mediated cell death are unclear. ASK1 is a stress-responsive MAP3K that acts as an upstream kinase of p38 and is activated by various stresses, such as oxidative stress. Here, we show that NR4A2, a member of the NR4A nuclear receptor family, acts as a necrosis promoter downstream of ASK1-p38 pathway during oxidative stress. Although NR4A2 is well known as a nucleus-localized transcription factor, we found that it is translocated into the cytosol after phosphorylation by p38. Because the phosphorylation site mutants of NR4A2 cannot rescue the cell death-promoting activity, ASK1-p38 pathway-dependent phosphorylation and subsequent cytoplasmic translocation of NR4A2 may be required for oxidative stress-induced cell death. In addition, NR4A2-mediated cell death does not depend on caspases and receptor-interacting protein 1 (RIP1)-RIP3 complex, suggesting that NR4A2 promotes an RIP kinase-independent necrotic type of cell death. Our findings may enable a more precise understanding of molecular mechanisms that regulate oxidative stress-induced and p38-mediated necrosis

Exfiltration and infiltration effect on sewage flow and quality: a case study of Hue, Vietnam

Sewage generated in Southeast Asia is typically characterized by small per-capita flow and low concentration. This study investigated the impacts of exfiltration (leaking-out) and infiltration (leaking-in) on sewage flow and quality in Hue, Vietnam. Sewage flow and quality were continuously monitored at the sewer outlet of a residential drainage area for 68 and 82 days during dry and rainy seasons, respectively. Infiltration was estimated based on the least sewage flow before morning. Lithium tracer tests were conducted to estimate the exfiltration ratio. The results indicated that sewage of the target sewer was weaker than the typical weak-strength sewage even on no-rain days of the dry season. Monitoring of electrical conductivity indicated that rainfall persistently decreased the sewage concentration for a maximum duration of 228 h. The estimated infiltration accounted for 11% and 62% of the total sewage inflow to the sewer during dry and rainy seasons, respectively. The tracer test indicated that exfiltration ratios during the dry and rainy seasons were 65.6% and 24.0%, respectively. As a result of developing the water balance, only 23% of the water supplied to the area reached the sewer outlet in the dry season, while 123% flowed in the rainy season. These results demonstrate that exfiltration decreased the sewage flow in the dry season, while infiltration significantly increased the sewage flow and decreased the sewage concentration in the rainy season. To the best of our knowledge, this is the first study to quantify the impacts of infiltration and exfiltration on sewage in Southeast Asia

Salvage surgery with a tumor prosthesis for femoral condylar nonunion at the very advanced age of 90 years

We report an unusual case of multifragmentary condylar femoral nonunion with severe synovitis and bone loss in a 90-year-old woman. Initially, conservative treatment of the condylar femoral fracture was indicated because the fracture was severely comminuted and the patient was very advanced in age. The fracture failed to heal. Salvage surgery with a total knee tumor endoprosthetic replacement was performed. Four years postoperatively, the patient was walking without knee pain using a walker. We believe that the present results justify the use of a megaprosthesis in the treatment of benign conditions even in very elderly patients. © 2012