Shape Functions Research Articles

Computation of shear buckling stress of thin-walled sections using constrained spline finite strip method

The direct strength method (DSM) design for shear incorporates the elastic shear buckling stress of the cross-section to evaluate the ultimate shear capacity of thin-walled members. To calculate the shear buckling stress using the finite strip method (FSM), the shape functions for longitudinal interpolation are an issue, while capturing the phase change of displacements along the plate strip. This paper presents a novel constrained spline finite strip method (cSFSM) that eliminates the phase change of displacements. Although constrained buckling analysis for shear stresses is reported in the literature based on FSM, the present study is unique in determining pure buckling stresses for simply supported members subjected to shear edge stress. The formulation also provides an accurate representation of the variation of shear stress along the longitudinal and transverse directions of the plate. Hence, coarse discretization of cross-section is sufficient to obtain the accurate shear buckling stress. The formulation is demonstrated on channel sections with lips subjected to shear edge stresses, and elastic buckling stresses are compared with results available in the literature and also with the finite element method (FEM). Illustrative examples are presented on lipped channel members with different end conditions and longitudinal stiffeners on flanges and webs, to calculate the pure elastic buckling stresses under shear edge stresses. The calculation of buckling stresses for members subjected to longitudinal variation of shear and flexural stresses is also presented to calculate coupled and uncoupled buckling stresses.

Large intestinal nutritional and physicochemical parameters from different dog sizes reshape canine microbiota structure and functions in vitro

ABSTRACT Different dog sizes are associated with variations in large intestinal physiology including gut microbiota, which plays a key role in animal health. This study aims to evaluate, using the CANIM-ARCOL (Canine Mucosal Artificial Colon), the relative importance of gut microbes versus physicochemical and nutritional parameters of the canine colonic environment in shaping microbiota structure and functions. CANIM-ARCOL was set up to reproduce nutrient availability, bile acid profiles, colonic pH, and transit time from small, medium, or large dogs according to in vivo data, while bioreactors were all inoculated with a fecal sample collected from medium size dogs (n = 2). Applying different dog size parameters resulted in a positive association between size and gas or SCFA production, as well as distinct microbiota profiles as revealed by 16S Metabarcoding. Comparisons with in vivo data from canine stools and previous in vitro results obtained when CANIM-ARCOL was inoculated with fecal samples from three dog sizes revealed that environmental colonic parameters were sufficient to drive microbiota functions. However, size-related fecal microbes were necessary to accurately reproduce in vitro the colonic ecosystem of small, medium, and large dogs. For the first time, this study provides mechanistic insights on which parameters from colonic ecosystem mainly drive canine microbiota in relation to dog size. The CANIM-ARCOL can be used as a relevant in vitro platform to unravel interactions between food or pharma compounds and canine colonic microbiota, under different dog size conditions. The potential of the model will be extended soon to diseased situations (e.g. chronic enteropathies or obesity).

Therapeutic potential to target sialylation and SIGLECs in neurodegenerative and psychiatric diseases.

Sialic acids, commonly found as the terminal carbohydrate on the glycocalyx of mammalian cells, are pivotal checkpoint inhibitors of the innate immune system, particularly within the central nervous system (CNS). Sialic acid-binding immunoglobulin-like lectins (SIGLECs) expressed on microglia are key players in maintaining microglial homeostasis by recognizing intact sialylation. The finely balanced sialic acid-SIGLEC system ensures the prevention of excessive and detrimental immune responses in the CNS. However, loss of sialylation and SIGLEC receptor dysfunctions contribute to several chronic CNS diseases. Genetic variants of SIGLEC3/CD33, SIGLEC11, and SIGLEC14 have been associated with neurodegenerative diseases such as Alzheimer's disease, while sialyltransferase ST8SIA2 and SIGLEC4/MAG have been linked to psychiatric diseases such as schizophrenia, bipolar disorders, and autism spectrum disorders. Consequently, immune-modulatory functions of polysialic acids and SIGLEC binding antibodies have been exploited experimentally in animal models of Alzheimer's disease and inflammation-induced CNS tissue damage, including retinal damage. While the potential of these therapeutic approaches is evident, only a few therapies to target either sialylation or SIGLEC receptors have been tested in patient clinical trials. Here, we provide an overview of the critical role played by the sialic acid-SIGLEC axis in shaping microglial activation and function within the context of neurodegeneration and synaptopathies and discuss the current landscape of therapies that target sialylation or SIGLECs.

Synthesis Methodology for Discrete MIMO PID Controller with Loop Shaping on LTV Plant Model via Iterated LMI Restrictions

This paper presents a methodology for synthesizing discrete MIMO PID controllers through iterative solutions of LMIs. It justifies the necessity of direct synthesis of discrete controllers in digital control systems. The proposed methodology allows for synthesizing an LTI controller for an LTV plant model, ensuring the robust stability of the synthesized system. Robustness is further ensured by the small-gain theorem and a novel approach to loop shaping, enabling the use of arbitrary shape functions. As a result, this methodology provides a broad statement of the problem with performance criteria necessary for practical application in control systems. Numerical examples are used to illustrate the methodology, which is implemented using the MATLAB toolbox, freely available for use.

A new Hermite finite element for nonlinear Kirchhoff rods: The plane case

AbstractThis article presents the formulation of a finite element method for nonlinear Kirchhoff rods, based on a interpolation of the rod's geometry in terms of Hermite shape functions. The critical use of the same interpolation scheme for both the geometry and the kinematics of the rod is shown to lead to the correct invariant properties of the final numerical formulation, thus leading to the correct resolution of the fundamental equilibrium relations along it (balance of forces and moments). The so‐called “self‐straining” is completely avoided. Several numerical examples are presented illustrating the adequacy of the proposed formulation for the analysis of thin rods undergoing large finite deformations.

Finslerian wormhole solution in the framework of modified gravity

Abstract This article investigates the properties of a wormhole model in a specific gravity theory, namely f(Ric, T) = Ric + 2λ T. The wormhole solution is analyzed using an exponential shape function. The study examines various parameters, such as density, radial pressure, transverse pressure, equation-of-state parameters, and energy conditions, within the framework of deformed gravity. The research emphasizes the influence of the parameter λ on energy condition violations and the equilibrium state of the Finslerian wormhole solution. These effects are attributed to anisotropic and hydrostatic forces present in modified gravity. The study demonstrates that the gravity model effectively captures the characteristics of wormholes within the Finslerian space-time. Additionally, the identified features of the wormhole are utilized to visualize its structure by creating a three-dimensional representation of the embedded surface. In summary, this research contributes to understanding wormholes in modified gravity theories, highlighting the importance of the parameter λ in determining their behavior and properties.

Belugas (Delphinapterus leucas) create facial displays during social interactions by changing the shape of their melons

Beluga whales are considered unique among odontocetes in their ability to visibly alter the appearance of their head by changing the shape of the melon, but only anecdotal observations are available to evaluate the use or potential function of these melon shapes. This study of belugas in professionally managed care aimed to establish an ethogram for the repertoire of categorizable melon shapes and then evaluate their potential function as intentional communication signals by determining if they were produced and elaborated during social interactions of varying behavioral contexts while in the line of sight of a recipient. Five different melon shapes were reliably identified in video observations of the primary study population (n = 4) and externally validated in a second aquarium population (n = 51). Among the 2570 melon shapes observed from the primary study subjects, melon shapes occurred 34 × more frequently during social interactions (1.72 per minute) than outside of social interactions (0.05 per minute). Melon shapes occurring during social interactions were performed within the line of sight of a recipient 93.6% of the time. The frequency of occurrence of the different melon shapes varied across behavioral contexts. Elaboration of melon shapes through extended duration and the occurrence of concurrent open mouth displays varied by shape type and across behavioral contexts. Melon shapes seem to function as visual displays, with some characteristics of intentional communication. This ability could yield adaptive benefits to belugas, given their complex social structure and hypothesized mating system that emphasizes pre-copulatory female mate choice.

An analog PWM pixel circuit with shaping function for low grayscale display of Micro-LEDs

This paper presents a new analog pulse width modulation (PWM) micro light-emitting diode (LED) pixel circuit with a shaping function. The rising/falling time of PWM signal generated by the proposed pixel circuit can be greatly reduced to improve the low grayscale display quality of micro-LED. Metal oxide thin film transistors with the top-gate (TG) coplanar structure are used to realize the proposed pixel circuit on the glass substrate. It is shown that the pulse width of micro-LED current can be linearly modulated by the data voltage. Furthermore, the measured rising time and falling time of the PWM signal are 15.6 μs and 25.5 μs, respectively, which are much smaller than that of the PWM signal in the conventional analog PWM pixel circuits.

Molecular insights into codon usage analysis of mitochondrial fission and fusion gene: relevance to neurodegenerative diseases.

Mitochondrial dysfunction is the leading cause of neurodegenerative disorders like Alzheimer's disease and Parkinson's disease. Mitochondria is a highly dynamic organelle continuously undergoing the process of fission and fusion for even distribution of components and maintaining proper shape, number, and bioenergetic functionality. A set of genes governs the process of fission and fusion. OPA1, Mfn1, and Mfn2 govern fusion, while Drp1, Fis1, MIEF1, and MIEF2 genes control fission. Determination of specific molecular patterns of transcripts of these genes revealed the impact of compositional constraints on selecting optimal codons. AGA and CCA codons were over-represented, and CCC, GTC, TTC, GGG, ACG were under-represented in the fusion gene set. In contrast, CTG was over-represented, and GCG, CCG, and TCG were under-represented in the fission gene set. Hydropathicity analysis revealed non-polar protein products of both fission and fusion gene set transcripts. AGA codon repeats are an integral part of translational regulation machinery and present a distinct pattern of over-representation and under-representation in different transcripts within the gene sets, suggestive of selective translational force precisely controlling the occurrence of the codon. Out of six synonymous codons, five synonymous codons encoding for leucine were used differently in both gene sets. Hence, forces regulating the occurrence of AGA and five synonymous leucine-encoding codons suggest translational selection. A correlation of mutational bias with gene expression and codon bias and GRAVY and AROMA signifies the selection pressure in both gene sets, while the correlation of compositional bias with gene expression, codon bias, protein properties, and minimum free energy signifies the presence of compositional constraints. More than 25% of codons of both gene sets showed a significant difference in codon usage. The overall analysis shed light on molecular features of gene sets involved in fission and fusion.

Effects evaluation of different exercises on subclinical left ventricular dysfunction in obese rats by speckle-tracking echocardiography

ObjectiveTo identify subclinical left ventricle dysfunction (LVD) in obese rats by speckle-tracking echocardiography, and to evaluate the effects of 12-week Moderate-Intensity Continuous Training (MICT) or High-Intensity Interval Training (HIIT) on LV geometry, histology and function in obese rats. MethodsEighteen male standard or obese Sprague-Dawley rats were randomly divided into the Control group, the MICT group, and the HIIT group. Exercise interventions were conducted for 12 weeks, with equal total load and increased intensity gradient. Using dual-energy X-ray, two-dimensional speckle-tracking echocardiography, pulse Doppler, and HE staining to evalucate body shape, LV morphology, structure, and myocardial mechanics function. Results(1) Both MICT and HIIT have good weight loss shaping effect. (2) The LV of obese rats underwent pathological remodeling, with decreased longitudinal contractility and synchrony, and increased circumferential contractility and synchrony. (3) Exercise can inhibit LV pathological remodeling, improve myocardial mechanical function. HIIT is superior to MICT. (4) The global longitudinal strain of obese rats in the HIIT group showed a significant correlation with Fat% and Lean%. ConclusionObesity can induce LV pathological remodeling and subclinical dysfunction. Compared with MICT, 12-week HIIT can effectively inhibit the pathological remodeling of LV and promote the benign development of myocardial mechanical function in obese rats.

Casimir wormhole solutions in [formula omitted] gravity

In this paper, we study the Casimir effect on the wormhole geometry in f(R,Lm) gravity. We derive the field equations for the generic f(R,Lm) function by assuming static and spherically symmetric Morris–Thorne wormhole metric. Then we consider two non-linear f(R,Lm) models, specifically, f(R,Lm)=R2+Lmβ and f(R,Lm)=R2+(1+αLm)Lm where α and β are free parameters. We derive the shape functions for wormholes by utilizing the Casimir effect and examining their existence. Subsequently, we analyse the obtained wormhole solutions for each scenario, assessing the energy conditions at the wormhole throat with a radius of r0. Our findings reveal that for some arbitrary quantities, there is a violation of classical energy conditions at the wormhole throat. Additionally, we delve into the behaviour of the equation of state (EoS) for each case. Furthermore, we explore the stability of the Casimir effect wormhole solutions by employing the generalized Tolman–Oppenheimer–Volkoff (TOV) equation. Finally, we utilize the volume integral quantifier to determine the amount of exotic matter required near the wormhole throat for both models.

РАСПАРАЛЛЕЛИВАНИЕ ВЫЧИСЛЕНИЙ НА ГРАФИЧЕСКОМ ПРОЦЕССОРЕ ДЛЯ УСКОРЕНИЯ ГРАНИЧНО-ЭЛЕМЕНТНЫХ РАСЧЕТОВ В МЕХАНИКЕ

In solving problems of computer modeling using various methods, accuracy and computational efficiency questions always arise. This study explores the application of two modifications of the boundary element method to solve the problem of potential distribution within a closed two-dimensional domain with a uniform potential distribution on its boundary. The first modification involves using three nonlinear shape functions instead of one. The second modification applies the Galerkin method to the boundary element approach with three nonlinear shape functions. The essence of this modification lies in the fact that the system of equations is formulated in integral form over the entire boundary element, rather than at collocation points. In addition to this, the paper describes and investigates the advantages and disadvantages of the smoothing modification applied to these approaches. Since the influence matrix consists of independently computable elements, parallelization of calculations using NVIDIA CUDA technology has been proposed to enhance computational efficiency, significantly accelerating the calculation of interaction matrix. The choice of this technology is advantageous due to the prevalence of NVIDIA graphics accelerators in almost every personal computer or laptop, as well as it is easy to use. The study presents an approach to the application of this technology and demonstrates the results, showing the acceleration of parallelized calculations which show the dependence on the number of boundary elements. A comparison of the efficiency of the selected technology when applied to two methods, collocation and Galerkin, is also presented, indicating a significant speedup of up to 22 times by computing the influence matrix of the boundary elements.

Non-commutative Wormhole geometries in presence of modified Chaplygin–Jacobi gas and Anton–Schmidt fluid

In this work, we have found Wormhole (WH) solutions in isotropic cosmology in the backdrop of general relativity while utilizing the “Modified Chaplygin–Jacobi Gas” and “Anton–Schmidt fluid” equations of state. As a starting point for our calculations, we have also considered two matter distributions, namely the Gaussian distribution and the Lorentzian distribution. All four energy conditions (i.e. strong, weak, null and dominant) are calculated, and their respective graphs are plotted as well. The shape function and redshift function associated with the wormhole structure are also derived and plotted graphically. After that, the embedding diagram of our wormhole models and proper radial distance are presented graphically. Finally, we have discussed the stability of the wormhole solutions obtained using the generalized Tolman–Oppenheimer–Volkov (TOV) equation and have examined the aspect of vanishing sound speed inside the wormhole throat to study the role of perturbations of the system.

Reduction of Boundary Value Problem using Shape Function

This research looks at the MHD flow of a power-law fluid on a stretched sheet with a uniform heat source. The boundary shape function technique translated the resulting Couple of Nonlinear Ordinary Differential equations (BVP) with boundary conditions into a related initial value problem (IVP). The BVP's solution is represented by the boundary shape function (BSF), and a further new variable is the free function. With the right method, the initial value of the problem may be numerically solved.’

Ubiquitous filter feeders shape open ocean microbial community structure and function.

The mechanism of mortality plays a large role in how microorganisms in the open ocean contribute to global energy and nutrient cycling. Salps are ubiquitous pelagic tunicates that are a well-known mortality source for large phototrophic microorganisms in coastal and high-latitude systems, but their impact on the immense populations of smaller prokaryotes in the tropical and subtropical open ocean gyres is not well quantified. We used robustly quantitative techniques to measure salp clearance and enrichment of specific microbial functional groups in the North Pacific Subtropical Gyre, one of the largest ecosystems on Earth. We discovered that salps are a previously unknown predator of the globally abundant nitrogen fixer Crocosphaera; thus, salps restrain new nitrogen delivery to the marine ecosystem. We show that the ocean's two numerically dominant cells, Prochlorococcus and SAR11, are not consumed by salps, which offers a new explanation for the dominance of small cells in open ocean systems. We also identified a double bonus for Prochlorococcus, wherein it not only escapes salp predation but the salps also remove one of its major mixotrophic predators, the prymnesiophyte Chrysochromulina. When we modeled the interaction between salp mesh and particles, we found that cell size alone could not account for these prey selection patterns. Instead, the results suggest that alternative mechanisms, such as surface property, shape, nutritional quality, or even prey behavior, determine which microbial cells are consumed by salps. Together, these results identify salps as a major factor in shaping the structure, function, and ecology of open ocean microbial communities.

Enhancing the landing guidance of a reusable launch vehicle by improving genetic algorithm-based deep reinforcement learning using Hybrid Deterministic-Stochastic algorithm.

The PbGA-DDPG algorithm, which uses a potential-based GA-optimized reward shaping function, is a versatiledeep reinforcement learning/DRLagent that can control a vehicle in a complex environment without prior knowledge. However, when compared to an established deterministic controller, it consistently falls short in terms of landing distance accuracy. To address this issue, the HYDESTOC Hybrid Deterministic-Stochastic (a combination of DDPG/deep deterministic policy gradient and PID/proportional-integral-derivative) algorithm was introduced to improve terminal distance accuracy while keeping propellant consumption low. Results from extensive cross-validated Monte Carlo simulations show that a miss distance of less than 0.02 meters, landing speed of less than 0.4 m/s, settling time of 20 seconds or fewer, and a constant crash-free performance is achievable using this method.

A unified framework for equivalent single layer theories of composite beams, plates, and shells: a review

This article presents a comprehensive review of the unified framework for the equivalent single layer theories of composite beams, plates and shells. First, the approach to unified displacement fields has two main categories: one is to start from the assumption of linear displacement field variables. And the another is to start from the assumption of transverse strains and transverse displacement variable. In terms of unified shape functions, the shape function is defined as the function that exist in the transverse strain rather than the in-plane displacement variables. Moreover, the basic requirements for the choose of shape functions are also given and analysed in this paper. The unified shape functions are introduced in terms of the several functions and the unified polynomial model. In addition, a construction method for new shear strain shape functions is described in this review. Finally, the current research progress and future prospects are also given.

A Boundary Node Method for Solving Interior and Exterior Acoustic Problems

The Boundary Node Method (BNM) is a meshfree scheme for solving Boundary Integral Equations (BIE). BNM simplifies the problem at two levels. Primarily, as BNM aims to solve the integral form of the governing equation, dimensionality of the problem is reduced by one order. Additionally, the mesh-free scheme eliminates the need for meshing, proving particularly beneficial for problems involving complex geometries. In this study, BNM is formulated using Element Free Galerkin (EFG) scheme to solve interior and exterior problems in acoustics. A 3-dimensional linear basis is used to construct moving least square shape functions. This eliminates the need to define additional local or parametric coordinate systems, making the method easily applicable to any arbitrary geometry. To illustrate the capabilities of the proposed method, four example problems are solved. An open pipe at resonance and a simple expansion muffler are analyzed to validate BNM’s performance in solving interior problems. Radiation from a pulsating sphere and radiation from a sphere with harmonic velocity excitation are analyzed as examples of exterior problems. Results from all four sample problems indicate that the BNM scheme proposed for solving acoustic problems is accurate and robust.

Free vibration behaviour of composite laminated skew cylindrical shells reinforced with graphene platelets

Current Investigation deals with the free vibration response of composite laminated shells which are reinforced with graphene platelet. Shell is in the form of skew cylinder where rectangular and skew plates and cylindrical shell are considered as especial cases. Each layer of the shell may be enriched with different amount of graphene platelets which results in a functionally graded pattern of reinforcements. The basic governing equations of the shell are obtained by means of the first order shear deformation shell theory. To implement the boundary conditions, it is more preferred to use an oblique coordinate system. Consequently, definition of strains and stresses are provided in an oblique coordinate system. After that, total kinetic and strain energies of the shell are established. Following the idea of Ritz method where the basic shape functions are Chebyshev polynomials, the motion equations of the shell associated to free vibrations are established. Results of this research are compared with the available data in the open literature and after that novel numerical results from the present study are provided to explore the effects of skew angle, opening angle, shallowness, side to thickness ratio, boundary conditions, graphene platelet weight fraction and profile. It is shown that all of these factors are important for the free vibration response of such structure.

STODOLA-VIANELLO ITERATION METHOD FOR FREE TORSIONAL VIBRATION ANALYSIS OF MONOSYMMETRIC BOX-BEAM BRIDGES

Box-beam bridges are used in large spans and wider decks due to their high strength and greater torsional and flexural stiffness. They are usually prone to vibration due to moving vehicular traffic. Their eigenfrequency analysis is a crucial aspect of their design in order to ensure that the natural frequency is not close to the excitation frequency to avert resonance failures. The free torsional vibration equation is a fourth order partial differential equation (PDE) with variable parameters. For prismatic cross-sections, homogeneous and isotropic materials the governing PDE have constant parameters. This paper explores the Stodola-Vianello iteration method (SVIM) for solving the PDE for isotropic, homogeneous prismatic box-beams. Harmonic response is assumed, decoupling the PDE to two equations, one in terms of time and the second an ordinary differential equation (ODE) in terms of space coordinates. The Stodola-Vianello method is used by the method of four successive integrations to express the ODE as an algebraic iteration problem with four constants of integration. The four boundary conditions are used to solve for the four constants of integration, thus making the problem determinate. Application of the boundary conditions results in the full determination of the iteration equations. For simply supported boundaries studied in the work, a trigonometric buckling shape function that satisfies all the boundary conditions is employed in the SVIM formula to obtain the next bucking modal shape function. The requirement for convergence is then used to establish the characteristic buckling equation from which the eigenvalues are obtained. The solution to the characteristic buckling equation gave the exact mathematical expression for the natural torsional frequency at the nth vibration mode. The frequencies are determined for the first eight vibration modes and compared with previously obtained values. It was found that the natural frequencies are identical with previously found values of the exact natural frequencies. The natural frequency obtained is exact because it satisfies the PDE and the boundary conditions at all points in the domain.