Shape Functions Research Articles

Dynamic Modelling and Performance Analysis of Deployable Telescopic Tubular Mast

AbstractThis work presents the longitudinal and transverse coupling vibrations of a deployable Telescopic Tubular Mast (TTM), a multi-stepped structure integrated into a spacecraft system, while considering the rigid-flexible coupling phenomenon. The model is derived using the principle of virtual work and discretized via the variable separation method. The von Kármán strain is employed to incorporate geometric nonlinear effects. Semi-analytical results for the shape functions and natural frequencies of the quasi-static multi-stepped boom are obtained using the extended transfer matrix method (ETMM). These natural frequencies are validated against results from Nastran, confirming the ETMM's accuracy. In addition, the model accounts for the continuously changing natural frequencies and shape functions during the deployment phase. Finally, the dynamic phenomena of the longitudinal and transverse displacements are analyzed at various deploying states, including locking and restart behaviors. The influence of the structural damping on the vibration evolution is also contained in the numerical analysis.

Differential growth and shape formation of a flower-shaped structure

Morphogenesis, which is a complex interplay of biological, chemical, and physical processes, facilitates differential growth in various biological systems, particularly in plant organs, such as petals and leaves. Although recent studies have increasingly delved into the mechanical aspects of these biological structures, there remains a lack of a comprehensive quantitative understanding of shape formation induced by differential growth in plant organs. Thus, this study addressed this gap by employing a multifaceted approach encompassing theoretical analyses and comprehensive finite element analysis of the effect of differential growth on the shape of a cylinder into a flower shape. Based on the derivation of the strain energy expressions for the axisymmetric and asymmetric configurations, the shape function of the growing flower-like structures were calculated through mathematical optimization. The findings of this study shed light on the influence of the growth function, geometric characteristics, and material properties. As the wave number increased, the final configuration tended to have smaller waves, whereas a longer cylinder buckled more easily and the thickness had a minimal effect. This study offers insights that can pave the way for innovative geometrical designs, thereby providing inspiration for applications on both micro-and macroscales, such as in the realms of self-assembly of soft robotics and flexible electronics.

Emergent time scales of epistasis in protein evolution

We introduce a data-driven epistatic model of protein evolution, capable of generating evolutionary trajectories spanning very different time scales reaching from individual mutations to diverged homologs. Our in silico evolution encompasses random nucleotide mutations, insertions and deletions, and models selection using a fitness landscape, which is inferred via a generative probabilistic model for protein families. We show that the proposed framework accurately reproduces the sequence statistics of both short-time (experimental) and long-time (natural) protein evolution, suggesting applicability also to relatively data-poor intermediate evolutionary time scales, which are currently inaccessible to evolution experiments. Our model uncovers a highly collective nature of epistasis, gradually changing the fitness effect of mutations in a diverging sequence context, rather than acting via strong interactions between individual mutations. This collective nature triggers the emergence of a long evolutionary time scale, separating fast mutational processes inside a given sequence context, from the slow evolution of the context itself. The model quantitatively reproduces epistatic phenomena such as contingency and entrenchment, as well as the loss of predictability in protein evolution observed in deep mutational scanning experiments of distant homologs. It thereby deepens our understanding of the interplay between mutation and selection in shaping protein diversity and functions, allows one to statistically forecast evolution, and challenges the prevailing independent-site models of protein evolution, which are unable to capture the fundamental importance of epistasis.

Factorization for J/ψ leptoproduction at small transverse momentum

Nonrelativistic Quantum Chromodynamics (NRQCD) breaks down in the region of low transverse momentum, where the transverse momentum of the produced quarkonium state is sensitive to multiple scattering with the incoming hadron and to soft gluon radiation. In this kinematic regime, the transverse-momentum-dependent (TMD) factorization framework is required, promoting the long-distance matrix elements (LDMEs) of NRQCD to the so-called TMD shape functions (TMDShFs), which encode both the soft gluon radiation and the formation of the heavy-quark bound state. In this work, we apply an effective-field theory approach (combining NRQCD and SCET) to the photon-gluon fusion process in inclusive J/ψ leptoproduction. We derive a factorization theorem for the cross section in terms of TMDShFs, compute these quantities at next-to-leading order, establish their evolution, and study their matching onto the corresponding LDMEs in the high-transverse-momentum region. Our results are particularly relevant to the Electron-Ion Collider, where J/ψ leptoproduction can be used to probe gluon transverse-momentum-dependent parton distribution functions (gluon TMDPDFs).

Thermoelastic damping properties in hemi-ellipsoidal shells with variable thickness

Thermoelastic damping (TED) is a fundamental dissipation mechanism that inevitably exists in shell resonators with high quality factors. Based on the thermal energy method, this paper demonstrates an effective method for the TED characterization of the hemi-ellipsoidal shells with variable thickness which manifest lower TED compared with the hemispherical shells. The equation of motion of the hemi-ellipsoidal shell under clamped-free boundary conditions is established by Hamilton's principle and the assumed mode method, and the natural frequencies and mode shape functions of the hemi-ellipsoidal shell with variable thickness are obtained by solving the eigenvalue problem. The temperature field is acquired by solving the heat conduction equation along the radial direction, and an analytical model for the TED of the hemi-ellipsoidal shell with variable thickness is presented by calculating the maximum elastic potential energy and the work lost per cycle of vibration due to irreversible heat conduction. Analysis on TED at the vibration patterns of meridional wave number m = 1 and the circumferential wave number n = 2 or 3 where the shell resonators typically operate is carried out. The analytically calculated TED results are compared with those of the finite element method (FEM) to verify the feasibility and correctness of the present method. The influences of the geometrical parameters on the TED characteristics of the hemi-ellipsoidal shells with variable thickness are analyzed in detail. A meaningful discovery is that compared with the hemispherical shell, the hemi-ellipsoidal shell with variable thickness has a smaller TED when its semiminor axis is shorter than the semimajor axis, which is particularly significant for optimizing the design of the shell resonators with high quality factors.

A novel semi-analytic algorithm for evaluation of nearly singular integrals in boundary element analysis

A novel semi-analytic method is proposed to evaluate various nearly singular integrals accurately. Different from the traditional semi-analytical method, the Taylor expansion for shape functions, Jacobian, and so on in our method is based on the nearest point from a source point to an integral element rather than the projection point from the source point to the integral element. Therefore, it can more accurately approximate the distance from the source point to Gaussian integration points. Then, approximate expressions for the integrand functions of two-dimensional potential problems are derived. The effectiveness of the proposed method is verified by evaluating the calculation accuracy of physical quantities at points in different geometric models, and comparing it with the traditional semi-analytical method and distance transform method.

A new triangular thin shell element based on the absolute nodal coordinate formulation for complex surfaces

Abstract This work proposed a new Hermite triangular thin shell element based on the absolute nodal coordinate formulation to model thin shells with complex curved surfaces. Three techniques are adopted to enhance its universality and efficiency. Firstly, local numerical curvilinear coordinates are used on each node for those curved surfaces whose global curvilinear coordinates cannot be obtained analytically, and the Lie group interpolation is used for obtaining the curvilinear coordinates on the non-nodal domain. Secondly, the slope vector of the element is obtained by cross-producing the two gradient vectors only on each node; but interpolated inside the element to ensure its continuity. Additionally, this processing maintains the linear relationships between the shape functions and nodal coordinates, resulting in constant elastic constants. Thirdly, the enhanced assumed strains (EAS) and the assumed natural strains(ANS) methods are adopted respectively to accelerate the convergence speed and avoid locking problems of the element. Several numerical examples show that this new element is universal for irregularly curved surfaces without locking problems. In addition, the efficiency is much higher than the traditional triangular shell element.

Shape optimization of a non-uniform piezoelectric bending beam for human knee energy harvester

Abstract Scavenging energy from the human body to provide a sustainable source for electronic devices has gained significant attention. Recently, scientists have focused on harnessing biomechanical energy from human motion. This study was dedicated to developing and optimizing a non-uniform piezoelectric bending beam-based human knee energy harvester. The bimorph non-uniform piezoelectric bending beam consisted of a non-uniform carbon fiber substrate and piezoelectric macro fiber composites. Compared to the uniform piezoelectric bending beam, the non-uniform piezoelectric beam can optimize the shape to improve the average strain, thus improving the energy harvesting efficiency. In this study, eight shape functions, including ellipse, sin, tanh, exponential function, parabola, trigonometric line, and bell curves, were investigated and optimized. The bell curve bending beam was selected and fabricated due to its good performance. Then, a benchmark platform was developed to test the deflection curve and reaction force when the nonuniform bending beam was compressed. Finally, to validate the design, experimental testing on three subjects was conducted when they were equipped with the harvester and walked on a treadmill. Testing results indicated that the non-uniform bending beam-based energy harvester can improve the energy harvesting efficiency by 28.57% compared to the uniform beam-based energy harvester. The output power can reach 18.94 mW when walking at 7.0 km h−1.

Deriving Ritz formulation for the Static Flexural Solutions of Sinusoidal Shear Deformable Beams

This paper presents the Ritz variational method for the static bending analysis of sinusoidal shear deformable beams. The theory accounts for transverse shear deformation and satisfies transverse shear stress-free conditions at the top and bottom surfaces of the beam. The total potential energy functional for the thick beam bending problem is formulated and minimized using a Ritz procedure. The problem considered simply supported boundary conditions and two cases of loading – uniformly distributed load over the span and point load at the center. The function is a function of two unknown displacement functions constructed in terms of unknown generalized displacement parameters and shape functions that satisfy the boundary conditions. Ritz minimization of the functional is used to find the generalized displacement parameters and then the displacements w(x) and The displacements and stresses are found for the loading distributions considered. It is found that the results obtained agree remarkably well with the exact results obtained using the theory of elasticity. The differences between the present results and the exact solutions are less than 0.3% for maximum transverse displacement for both cases of loading considered. For uniform load over the beam, the result for l/t = 10 is 0.112% greater than the exact solution. For the point load at the center, the result for l/t = 10 is 4.468% greater than the exact solution. The increased difference in the point load case is due to the singular nature of the point load problem.

Potential applications of microbial genomics in nuclear non-proliferation.

As nuclear technology evolves in response to increased demand for diversification and decarbonization of the energy sector, new and innovative approaches are needed to effectively identify and deter the proliferation of nuclear arms, while ensuring safe development of global nuclear energy resources. Preventing the use of nuclear material and technology for unsanctioned development of nuclear weapons has been a long-standing challenge for the International Atomic Energy Agency and signatories of the Treaty on the Non-Proliferation of Nuclear Weapons. Environmental swipe sampling has proven to be an effective technique for characterizing clandestine proliferation activities within and around known locations of nuclear facilities and sites. However, limited tools and techniques exist for detecting nuclear proliferation in unknown locations beyond the boundaries of declared nuclear fuel cycle facilities, representing a critical gap in non-proliferation safeguards. Microbiomes, defined as "characteristic communities of microorganisms" found in specific habitats with distinct physical and chemical properties, can provide valuable information about the conditions and activities occurring in the surrounding environment. Microorganisms are known to inhabit radionuclide-contaminated sites, spent nuclear fuel storage pools, and cooling systems of water-cooled nuclear reactors, where they can cause radionuclide migration and corrosion of critical structures. Microbial transformation of radionuclides is a well-established process that has been documented in numerous field and laboratory studies. These studies helped to identify key bacterial taxa and microbially-mediated processes that directly and indirectly control the transformation, mobility, and fate of radionuclides in the environment. Expanding on this work, other studies have used microbial genomics integrated with machine learning models to successfully monitor and predict the occurrence of heavy metals, radionuclides, and other process wastes in the environment, indicating the potential role of nuclear activities in shaping microbial community structure and function. Results of this previous body of work suggest fundamental geochemical-microbial interactions occurring at nuclear fuel cycle facilities could give rise to microbiomes that are characteristic of nuclear activities. These microbiomes could provide valuable information for monitoring nuclear fuel cycle facilities, planning environmental sampling campaigns, and developing biosensor technology for the detection of undisclosed fuel cycle activities and proliferation concerns.

A quasi-3D SinZZ model-driven multi-field Chebyshev FEM for nonlinear vibration control in multilayer multiferroic composite plates

This paper presents an advanced numerical method for modeling and mitigating nonlinear vibrations in thin multilayered fiber-reinforced multiferroic composite plates, addressing complex multi-physical interactions. The proposed methodology leverages a multi-physical coupling Chebyshev finite element formulation, utilizing high-order shape functions derived from Chebyshev polynomials. By integrating the strengths of spectral element methods and Legendre spectral finite element methods, this approach effectively overcomes challenges such as shear locking and spurious zero energy modes while ensuring high convergence rates in multi-physical problems. A quasi-3D refined model, incorporating the Murakami zig-zag model and sinusoidal shear deformation theory, is employed to accurately capture the nonlinear Von Kármán strain–displacement relationship and the magneto-electro-elastic coupling in multilayer structures with thickness-dependent material properties. To suppress nonlinear vibrations, the study utilizes a closed-loop multiphysical Chebyshev finite element model for time-domain analysis of viscoelastically damped systems, employing the Golla–Hughes–McTavish model. The results underscore the significant influence of multiferroic properties and the strategic distribution of ferroelectric fibers within the substrate on the dynamic behavior of the plate. The numerical validation, supported by rigorous verification, demonstrates the robustness of the proposed method in effectively simulating and controlling multilayer fiber-reinforced multiferroic composite plates. Additionally, this research highlights the potential for significant vibration reduction through semi-active damping mechanisms, offering valuable insights for practical applications in industries where precision and stability are critical.

Spherical Magnetic Vector Forwarding of Isoparametric DGGS Cells with Natural Superconvergent Points

With the rapid advancement of satellite remote sensing technology, many scientists and organizations, including NASA, ESA, NAOC, and Roscosmos, observe and study significant changes in the geomagnetic field, which has greatly promoted research on the geomagnetic field and made it an important research direction in Earth system science. In traditional geomagnetic field research, tesseroid cells face degradation issues in high-latitude regions and accuracy limitations. To overcome these limitations, this paper introduces the Discrete Global Grid System (DGGS) to construct a geophysical model, achieving seamless global coverage through multi-level grid subdivision, significantly enhancing the processing capability of multi-source and multi-temporal spatial data. Addressing the challenges of the lack of analytical solutions and clear integration limits for DGGS cells, a method for constructing shape functions of arbitrary isoparametric elements is proposed based on the principle of isoparametric transformation, and the shape functions of isoparametric DGGS cells are successfully derived. In magnetic vector forwarding, considering the potential error amplification caused by Poisson’s formula, the DGGS grid is divided into six regular triangular sub-units. The triangular superconvergent point technique is adopted, and the positions of integration points and their weight coefficients are accurately determined according to symmetry rules, thereby significantly improving the calculation accuracy without increasing the computational complexity. Finally, through the forward modeling algorithm based on tiny tesseroid cells, this study comprehensively compares and analyzes the computational accuracy of the DGGS-based magnetic vector forwarding algorithm, verifying the effectiveness and superiority of the proposed method and providing new theoretical support and technical means for geophysical research.

Phase-field formulated meshless simulation of axisymmetric Rayleigh-Taylor instability problem

A formulation of the immiscible Newtonian two-liquid system with different densities and influenced by gravity is based on the Phase-Field Method (PFM) approach. The solution of the related governing coupled Navier-Stokes (NS) and Cahn-Hillard (CH) equations is structured by the meshless Diffuse Approximate Method (DAM) and Pressure Implicit with Splitting of Operators (PISO). The variable density is involved in all the terms. The related moving boundary problem is handled through single-domain, irregular, fixed node arrangement in Cartesian and axisymmetric coordinates. The meshless DAM uses weighted least squares approximation on overlapping subdomains, polynomial shape functions of second-order and Gaussian weights. This solution procedure has improved stability compared to Chorin's pressure-velocity coupling, previously used in meshless solutions of related problems. The Rayleigh-Taylor instability problem simulations are performed for an Atwood number of 0.76. The DAM parameters (shape parameter of the Gaussian weight function and number of nodes in a local subdomain) are the same as in the authors’ previous studies on single-phase flows. The simulations did not need any upwinding in the range of the simulations. The results compare well with the mesh-based finite volume method studies performed with the open-source code Gerris, Open-source Field Operation and Manipulation (OpenFOAM®) code and previously existing results.

Analytical Solution for Dynamic Response of a Reinforced Concrete Beam with Viscoelastic Bearings Subjected to Moving Loads.

To provide a theoretical basis for eliminating resonance and optimizing the design of viscoelastically supported bridges, this paper investigates the analytical solutions of train-induced vibrations in railway bridges with low-stiffness and high-damping rubber bearings. First, the shape function of the viscoelastic bearing reinforced concrete (RC) beam is derived for the dynamic response of the viscoelastic bearing RC beam subjected to a single moving load. Furthermore, based on the simplified shape function, the dynamic response of the viscoelastic bearing RC beam under equidistant moving loads is studied. The results show that the stiffness and damping effect on the dynamic response of the supports cannot be neglected. The support stiffness might adversely increase the dynamic response. Further, due to the effect of support damping, the free vibration response of RC beams in resonance may be significantly suppressed. Finally, when the moving loads leave the bridge, the displacement amplitude of the viscoelastic support beam in free vibration is significantly larger than that of the rigid support beam.

Developing novel wormhole metrics in finsler-randers geometry using the barthel connection and osculating-riemannian method

In this research, we focus on modelling a wormhole using Finsler-Randers geometry. By applying the Barthel connection from the range of Finslerian connections, we have developed a new wormhole metric, termed the osculating Barthel-Finsler-Randers metric, through the osculating-Riemannian method within the Finsler-Randers framework. The fundamental field equations are formulated in terms of the obtained metric tensor characterised by η(r), which plays a pivotal role in characterizing the anisotropy of the model. To explore the application of Finsler geometry in addressing the existence of a wormhole, we adopt an exponential shape function. Further, in order to streamline the computational aspects of our analysis, and to discuss the effect of anisotropy effect of Finsler Rander geometry, we adopt a specific functional form for the anisotropic parameter η(r)=arn, where α is a constant with implications for the anisotropy, among various possibilities for η(r) a non-zero analytical component of vector field in Randers metric. In addition, we consider three distinct values for the exponent n = −1, 0, and 1 and subsequently, we proceed to develop two distinct models for each of these three values of n with constant and non-constant redshift function. We analyse the physical implications of η(r) on the energy conditions. Our results demonstrate the crucial impact of anisotropy on the stability and structure of wormholes, emphasizing the requirement of exotic matter under specific conditions. This research deepens the understanding of wormhole physics within Finsler geometry, shedding light on the theoretical frameworks essential for the existence and stability of these cosmic structures.

On the use of scaled boundary shape functions in adaptive phase field modeling of brittle fracture

On the use of scaled boundary shape functions in adaptive phase field modeling of brittle fracture

A study on existence of wormhole in Lemaitre–Tolman–Bondi model

An investigation has been done for possible existence of evolving wormhole (WH) solution in the background of inhomogeneous Lemaitre–Tolman–Bondi (LTB) space-time geometry. Using separable product form of the geometric (or area) radius, the shape function can be evaluated in terms of the functional part of the radial coordinate in the area radius. The conditions for a viable WH configuration have been examined.

A numerical investigation on the effect of shape-size-number of drills on heat transfer characteristics of a circular pin fin

An increased circuit density with digitalization and miniaturization demands a compact design for the heatsink with enhanced heat dissipation capabilities. The performance of an active air-cooled pin fin heatsink depends on the geometry of the fin, which should offer more surface area for the given volume (Compact). Providing drills in a pin fin offers a more convective surface with conduction loss, and is function of place, size, shape, and number of drills. So, this investigation is focused on studying the heat transfer characteristics of a drilled pin fin of length L and diameter D to elucidate the effect of (1) shapes; circular, elliptical, and triangular, (2) locations; L/4, L/2, and 3 L/4, (3) sizes between 0.3D and 0.5D, and (4) number; 1, 2, 4, and 6 of drills on maximum fin temperature (Tmax ) and convective resistance for differential heat inputs in different convection environments. It throws light on the possible replacement of solid fins with drilled fins for enhanced heat dissipation. It offers either more heat transfer, for the given volume with reduced weight, or decreased volume for the mandated heat load. The results demonstrated that the drill location has a mere or insignificant effect on Tmax. For all the shapes considered in the study, Tmax first decreases with the enlarging drill size reaches it’s minimum at 0.5D, and increases after that. The increased number of drills from 1 to 6, of size 0.5D, brings down the Tmax by 20%, 20%, and 25% with circular, elliptical, and triangular drills, respectively.

Mechanical-electric-magnetic-thermal coupled enriched finite element method for magneto-electro-elastic structures

Abstract Magneto-electro-elastic (MEE) materials possess the ability to convert mechanical, electrical, and magnetic energies, playing a critical role in smart devices. To improve the accuracy and efficiency of solving the mechanical properties of MEE structures in mechanical-electrical-magnetic-thermal (MEMT) environments, an MEMT coupled multiphysics enriched finite element method (MP-EFEM) is proposed. Based on the fundamental equations and boundary conditions of MEE materials, the interpolation coverage function is introduced into the MEMT coupled finite element method (FEM) to construct higher-order approximate interpolation displacement shape functions, electric potential shape functions, and magnetic potential shape functions. Combined with the variational principle, MP-EFEM is proposed, and the governing equations of MP-EFEM are derived. Numerical examples validate the accuracy and high efficiency of MP-EFEM in solving the mechanical properties of MEE structures in MEMT environments. When compared to the MEMT coupled FEM (MEMT-FEM), the results show that this method offers higher accuracy and efficiency. Therefore, MP-EFEM can effectively analyze the mechanical properties of MEE structures under multiphysics coupling, providing a new method for the design and development of smart devices.

JAK inhibitor selectivity: new opportunities, better drugs?

Cytokines function as communication tools of the immune system, serving critical functions in many biological responses and shaping the immune response. When cytokine production or their biological activity goes awry, the homeostatic balance of the immune response is altered, leading to the development of several pathologies such as autoimmune and inflammatory disorders. Cytokines bind to specific receptors on cells, triggering the activation of intracellular enzymes known as Janus kinases (JAKs). The JAK family comprises four members, JAK1, JAK2, JAK3 and tyrosine kinase 2, which are critical for intracellular cytokine signalling. Since the mid-2010s multiple JAK inhibitors have been approved for inflammatory and haematological indications. Currently, approved JAK inhibitors have demonstrated clinical efficacy; however, improved selectivity for specific JAKs is likely to enhance safety profiles, and different strategies have been used to accomplish enhanced JAK selectivity. In this update, we discuss the background of JAK inhibitors, current approved indications and adverse effects, along with new developments in this field. We address the issue of JAK selectivity and its relevance in terms of efficacy, and describe new modalities of JAK targeting, as well as new aspects of JAK inhibitor action.