The Non-Stationary Dynamic Analytical Solution of a Spherical/Cylindrical Cavity Expansion

2020 ◽  
Vol 87 (11) ◽  
Author(s):  
V. R. Feldgun ◽  
D. Z. Yankelevsky
Keyword(s):  
Analytical Solution ◽  
General Solution ◽  
Cylindrical Cavity ◽  
Constant Velocity ◽  
Present Model ◽  
Elastic Region ◽  
Cavity Expansion ◽  
Special Cases ◽  
Significant Difference ◽  
Cavity Boundary

Abstract A review of the pertinent literature related to the dynamic expansion of a spherical/cylindrical cavity shows that all the solutions with kinematic boundary conditions deal with a constant velocity at the cavity boundary. This paper develops a new general solution of the nonstationary dynamic problem of cavity expansion, which allows the application of time-dependent motion conditions at the cavity boundary. This solution can be used, for example, in the development of approximate approaches for projectiles penetrating with a non-constant velocity into different targets. Due to the complexity of the nonlinear nonstationary problem, an analytical solution of the problem may be developed if simplified constitutive relationships are used. In the present model, a simplified material model with a locked equation of state and a linear shear failure relationship is implemented. This solution may be applied to different materials such as concrete, soil, and rock. Special cases of the newly developed nonstationary solution are compared with different spherical and cylindrical cavity expansions solutions reported in the literature, and a good agreement is obtained. The capability of the present model is demonstrated in a following investigation of representative cases of cavity expansion with zero, constant, and variable acceleration of the cavity boundary. A significant difference in the stress variation for the different cases is shown. Along with the general solution which deals with an elastic–plastic region, a simplified solution which disregards the contribution of the elastic region is presented and the evaluation of the elastic region effect may be assessed.

scholarly journals On a Generalization of One-Dimensional Kinetics

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1264
Author(s):  
Vladimir V. Uchaikin ◽  
Renat T. Sibatov ◽  
Dmitry N. Bezbatko
Keyword(s):  
Exact Solution ◽  
Asymptotic Behavior ◽  
Constant Velocity ◽  
Telegraph Equation ◽  
Material Derivative ◽  
Symmetric Random Walk ◽  
One Dimensional ◽  
Special Cases ◽  
Fractional Telegraph Equation ◽  
Asymmetric Case

One-dimensional random walks with a constant velocity between scattering are considered. The exact solution is expressed in terms of multiple convolutions of path-distributions assumed to be different for positive and negative directions of the walk axis. Several special cases are considered when the convolutions are expressed in explicit form. As a particular case, the solution of A. S. Monin for a symmetric random walk with exponential path distribution and its generalization to the asymmetric case are obtained. Solution of fractional telegraph equation with the fractional material derivative is presented. Asymptotic behavior of its solution for an asymmetric case is provided.

Dynamic finite cylindrical cavity-expansion models for cellular steel tube confined concrete targets normally impacted by rigid sharp-nosed projectiles

2021 ◽  
pp. 204141962110272
Author(s):  
Chaomei Meng ◽  
Dianyi Song ◽  
Qinghua Tan ◽  
Zhigang Jiang ◽  
Liangcai Cai ◽  
...  
Keyword(s):  
Cylindrical Cavity ◽  
Approximate Model ◽  
Steel Tube ◽  
Confinement Effect ◽  
Confined Concrete ◽  
Cavity Expansion ◽  
Depth Of Penetration ◽  
Cylindrical Cavity Expansion ◽  
Infinite Cylindrical Shell ◽  
Response Modes

Cellular steel-tube-confined concrete (CSTCC) targets show improved anti-penetration performance over single-cell STCC targets due to the confinement effect of surrounding cells on the impacted cell. Dynamic finite cylindrical cavity-expansion (FCCE) models including radial confinement effect were developed to predict the depth of penetration (DOP) for CSTCC targets normally penetrated by rigid sharp-nosed projectiles, and stiffness of radial confinement was achieved with the elastic solution of infinite cylindrical shell in Winkler medium. Steady responses of dynamic FCCE models were obtained on the assumption of incompressibility of concrete, failure of comminuted zone with Heok–Brown criterion and two possible response modes of the confined concrete in the impacted cell. Furthermore, a DOP model for CSTCC targets normally impacted by rigid projectiles was also proposed on the basis of the dynamic FCCE approximate model. Lastly, relevant penetration tests of CSTCC targets normally penetrated by 12.7 mm armor piecing projectile (APP) were taken as examples to validate the dynamic FCCE models and the corresponding DOP model. The results show that the DOP results based on dynamic FCCE model agree well with those of the CSTCC targets normally penetrated by rigid conical or other sharp-nosed projectiles.

Efficacy of gefitinib combined with bevacizumab versus gefitinib in advanced EGFR L858R NSCLC.

2021 ◽  
Vol 39 (15_suppl) ◽  
pp. e21185-e21185
Author(s):  
Xinmin Zhao ◽  
Xianghua Wu ◽  
Huijie Wang ◽  
Hui Yu ◽  
Si Sun ◽  
...  
Keyword(s):  
Liquid Biopsy ◽  
Therapeutic Option ◽  
Objective Response ◽  
Acquired Resistance ◽  
Response To Treatment ◽  
Control Group ◽  
Special Cases ◽  
Significant Difference ◽  
Experimental Group ◽  
Egfr Tkis

e21185 Background: 60-80% of EGFR+ NSCLC could benefit from the treatment of EGFR TKIs. However, as a result of acquired resistance, median progression-free survival (PFS) associated with EGFR-TKIs monotherapy was rarely longer than 11 months. Vascular endothelial growth factor (VEGF) and its receptor (VEGFR) play an important role in the angiogenesis and progression of NSCLC. The combination of EGFR-TKIs and anti-vascular drugs that inhibit the EGFR and VEGF/VEGFR pathways may be a potential therapeutic option for EGFR-mutant NSCLC. The purpose of our study was to evaluate whether gefitinib combined with bevacizumab is associated with an increased PFS benefit compared with gefitinib alone. Methods: This study is a randomized, open-controlled, single-center study. A total of 43 advanced non-squamous NSCLC patients with EGFR L858R mutations were enrolled, including 24 in the experimental group and 19 in the control group. The experimental group received gefitinib combined with bevacizumab (gefitinib 250 mg, QD+bevacizumab 7.5 mg/kg, Q3W), and the control group received gefitinib monotherapy (250 mg, QD). Response to treatment was evaluated after one month of the treatment, followed by once every two months, and adverse events were graded. The primary endpoint was PFS, and secondary endpoints included objective response rate (ORR), disease control rate (DCR), duration of response (DOR), overall survival (OS), and safety and tolerability evaluation. Samples at baseline (tissue or liquid biopsy), 43 days after treatment (liquid biopsy), and disease progression were subjected to genomic (139-gene NGS panel) profiling. Results: As of December 31, 2020, 22 patients were evaluable (12 for experimental group, 10 for control group). The ORR of the experimental group and the control group were 42% vs 60%, respectively, with no significant difference (experimental group: CR = 0, PR = 5, SD = 7, PD = 0; control group: CR = 0, PR = 6, SD = 4, PD = 0). Main adverse reactions included skin rash (n = 16), diarrhea (n = 24), hypertension (n = 2), proteinuria (n = 1). Other special cases developed fever, nausea and vomiting, elevated platelets, conjunctivitis, back pain, which were manageable. 36 patients with baseline liquid biopsy samples can be evaluated (33 plasma and 3 pleural fluid samples). Of these, EGFR L858R were detectable in 86% (n = 31) of patients. The most common co-mutated gene was TP53 (57%), followed by DNMT3A (49%) and TET2 (17%). Mutation profiles were comparable between the two groups. Conclusions: Compared to gefitinib monotherapy, gefitinib combined with bevacizumab in the treatment of non-squamous NSCLC with EGFR L858R showed similar efficacy and safety profiles.

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