Static response and free vibration analysis of FGM plates using higher order shear deformation theory

Free vibration and static analysis of functionally graded material (FGM) plates are studied using higher order shear deformation theory with a special modification in the transverse displacement in conjunction with finite element models. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. The fundamental equations for FGM plates are derived using variational approach by considering traction free boundary conditions on the top and bottom faces of the plate. Results have been obtained by employing a continuous isoparametric Lagrangian finite element with 13 degrees of freedom per node. Convergence tests and comparison studies have been carried out to demonstrate the efficiency of the present model. Numerical results for different thickness ratios, aspect ratios and volume fraction index with different boundary conditions have been presented. It is observed that the natural frequency parameter increases for plate aspect ratio, lower volume fraction index n and smaller thickness ratios. It is also observed that the effect of thickness ratio on the frequency of a plate is independent of the volume fraction index. For a given thickness ratio non-dimensional deflection increases as the volume fraction index increases. It is concluded that the gradient in the material properties plays a vital role in determining the response of the FGM plates.     

Strongly nonlinear elliptic boundary value problems in Musielak–Orlicz spaces

Monatshefte für Mathematik - In this paper we prove an existence result of solutions for some strongly nonlinear elliptic problems with lower order term and $$L^1$$ -data in...     

Significance of Shape Factor in Heat Transfer Performance of Molybdenum-Disulfide Nanofluid in Multiple Flow Situations; A Comparative Fractional Study

In this modern era, nanofluids are considered one of the advanced kinds of heat transferring fluids due to their enhanced thermal features. The present study is conducted to investigate that how the suspension of molybdenum-disulfide (MoS2) nanoparticles boosts the thermal performance of a Casson-type fluid. Sodium alginate (NaAlg) based nanofluid is contained inside a vertical channel of width d and it exhibits a flow due to the movement of the left wall. The walls are nested in a permeable medium, and a uniform magnetic field and radiation flux are also involved in determining flow patterns and thermal behavior of the nanofluid. Depending on velocity boundary conditions, the flow phenomenon is examined for three different situations. To evaluate the influence of shape factor, MoS2 nanoparticles of blade, cylinder, platelet, and brick shapes are considered. The mathematical modeling is performed in the form of non-integer order operators, and a double fractional analysis is carried out by separately solving Caputo-Fabrizio and Atangana-Baleanu operators based fractional models. The system of coupled PDEs is converted to ODEs by operating the Laplace transformation, and Zakian’s algorithm is applied to approximate the Laplace inversion numerically. The solutions of flow and energy equations are presented in terms of graphical illustrations and tables to discuss important physical aspects of the observed problem. Moreover, a detailed inspection on shear stress and Nusselt number is carried out to get a deep insight into skin friction and heat transfer mechanisms. It is analyzed that the suspension of MoS2 nanoparticles leads to ameliorating the heat transfer rate up to 9.5%. To serve the purpose of achieving maximum heat transfer rate and reduced skin friction, the Atangana-Baleanu operator based fractional model is more effective. Furthermore, it is perceived that velocity and energy functions of the nanofluid exhibit significant variations because of the different shapes of nanoparticles.     

Synthesis,Antimicrobial, Anticancer,PASS, Molecular Docking,Molecular Dynamic Simulations & Pharmacokinetic Predictions of Some Methyl β-D-Galactopyranoside Analogs

A series of methyl β-D-galactopyranoside (MGP, 1) analogs were selectively acylated with cinnamoyl chloride in anhydrous N,N-dimethylformamide/triethylamine to yield 6-O-substitution products, which was subsequently converted into 2,3,4-tri-O-acyl analogs with different acyl halides. Analysis of the physicochemical, elemental, and spectroscopic data of these analogs revealed their chemical structures. In vitro antimicrobial testing against five bacteria and two fungi and the prediction of activity spectra for substances (PASS) showed promising antifungal functionality comparing to their antibacterial activities. Minimum inhibition concentration (MIC) and minimum bactericidal concentration (MBC) tests were conducted for four compounds (4, 5, 6, and 9) based on their activity. MTT assay showed low antiproliferative activity of compound 9 against Ehrlich’s ascites carcinoma (EAC) cells with an IC₅₀ value of 2961.06 µg/mL. Density functional theory (DFT) was used to calculate the thermodynamic and physicochemical properties whereas molecular docking identified potential inhibitors of the SARS-CoV-2 main protease (6Y84). A 150-ns molecular dynamics simulation study revealed the stable conformation and binding patterns in a stimulating environment. In-silico ADMET study suggested all the designed molecules to be non-carcinogenic, with low aquatic and non-aquatic toxicity. In summary, all these antimicrobial, anticancer and in silico studies revealed that newly synthesized MGP analogs possess promising antiviral activity, to serve as a therapeutic target for COVID-19.     

Can the SARS-CoV-2 Omicron Variant Confer Natural Immunity against COVID-19?

The coronavirus disease 2019 (COVID-19) pandemic is still ongoing, with no signs of abatement in sight. The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which is the causative agent of this pandemic and has claimed over 5 million lives, is still mutating, resulting in numerous variants. One of the newest variants is Omicron, which shows an increase in its transmissibility, but also reportedly reduces hospitalization rates and shows milder symptoms, such as in those who have been vaccinated. As a result, many believe that Omicron provides a natural vaccination, which is the first step toward ending the COVID-19 pandemic. Based on published research and scientific evidence, we review and discuss how the end of this pandemic is predicted to occur as a result of Omicron variants being surpassed in the community. In light of the findings of our research, we believe that it is most likely true that the Omicron variant is a natural way of vaccinating the masses and slowing the spread of this deadly pandemic. While the mutation that causes the Omicron variant is encouraging, subsequent mutations do not guarantee that the disease it causes will be less severe. As the virus continues to evolve, humans must constantly adapt by increasing their immunity through vaccination.     

Finite difference schemes for the two‐dimensional semilinear wave equation

In this article, two finite difference schemes for solving the semilinear wave equation are proposed. The unique solvability and the stability are discussed. The second‐order accuracy convergence in both time and space in the discrete H¹‐norm for the two proposed difference schemes is proved. Numerical experiments are performed to support our theoretical results.     

Plant-Based Indole Alkaloids: A Comprehensive Overview from a Pharmacological Perspective

Plant-based indole alkaloids are very rich in pharmacological activities, and the indole nucleus is considered to contribute greatly to these activities. This review’s fundamental objective is to summarize the pharmacological potential of indole alkaloids that have been derived from plants and provide a detailed evaluation of their established pharmacological activities, which may contribute to identifying new lead compounds. The study was performed by searching various scientific databases, including Springer, Elsevier, ACS Publications, Taylor and Francis, Thieme, Wiley Online Library, ProQuest, MDPI, and online scientific books. A total of 100 indole compounds were identified and reviewed. The most active compounds possessed a variety of pharmacological activities, including anticancer, antibacterial, antiviral, antimalarial, antifungal, anti-inflammatory, antidepressant, analgesic, hypotensive, anticholinesterase, antiplatelet, antidiarrheal, spasmolytic, antileishmanial, lipid-lowering, antimycobacterial, and antidiabetic activities. Although some compounds have potent activity, some only have mild-to-moderate activity. The pharmacokinetic profiles of some of the identified compounds, such as brucine, mitragynine, 7-hydroxymitragynine, vindoline, and harmane, were also reviewed. Most of these compounds showed promising pharmacological activity. An in-depth pharmacological evaluation of these compounds should be performed to determine whether any of these indoles may serve as new leads.     

Sustainable Development of Chitosan/Calotropis procera-Based Hydrogels to Stimulate Formation of Granulation Tissue and Angiogenesis in Wound Healing Applications

The formation of new scaffolds to enhance healing magnitude is necessarily required in biomedical applications. Granulation tissue formation is a crucial stage of wound healing in which granulation tissue grows on the surface of a wound by the formation of connective tissue and blood vessels. In the present study, porous hydrogels were synthesized using chitosan incorporating latex of the Calotropis procera plant by using a freeze–thaw cycle to stimulate the formation of granulation tissue and angiogenesis in wound healing applications. Structural analysis through Fourier transform infrared (FTIR) spectroscopy confirmed the interaction between chitosan and Calotropis procera. Latex extract containing hydrogel showed slightly higher absorption than the control during water absorption analysis. Thermogravimetric analysis showed high thermal stability of the 60:40 combination of chitosan (CS) and Calotropis procera as compared to all other treatments and controls. A fabricated scaffold application on a chick chorioallantoic membrane (CAM) showed that all hydrogels containing latex extract resulted in a significant formation of blood vessels and regeneration of cells. Overall, the formation of connective tissues and blood capillaries and healing magnitude decreased in ascending order of concentration of extract.     

A fully Galerkin method for the damped generalized regularized long‐wave (DGRLW) equation

In this article, a fully discrete Galerkin scheme based on a nonlinear Crank–Nicolson method to approximate the solution of the DGRLW equation is constructed. Some a priori bounds are proved as well as error estimates. Then, a linearized modification scheme by an extrapolation method is discussed. The two schemes are time second order convergence. The last part is devoted to some numerical results. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Influence of micro-structural defects on post-buckling and large-amplitude vibration of geometrically imperfect gradient plate

We propose a polynomial expansion method to investigate periodic motions around both collinear and triangular libration points in the planar circular restricted three-body problem. The polynomial expansion method focuses on the approximate nonlinear polynomial relations between the two directions in the motion plane, which provide an alternative way to inspect the periodic motions. Based on the nonlinear polynomial relations, the planar two-dimensional system is decoupled. As an example, the \(3\mathrm{rd}\) order analytical solutions for the periodic motion are determined by solving the decoupled system. The efficiency of the polynomial expansion method has been validated by numerical method.