Element Length Research Articles

Geometric nonlinear analysis of planar frames constituted of nonprismatic Timoshenko-like elements referred to their noncentroidal axis

This paper proposes a geometric nonlinear formulation to solve 2D frames modeled with Timoshenko-like elements defined by their noncentroidal axis. The kinematics of deformation of the element and the cross-sectional constitutive relationships are referenced to any given axis. Thus, the element axes may be any simple straight-line segments intersecting the element's cross-sections at any position. Knowing the element's centroidal axis is of no relevance. As a consequence, the interaction between axial and flexural effects must be consistently taken into consideration. The methodology consists of using a flexibility-type method based on the principle of virtual forces to determine the structural property coefficients. Such a method is convenient for determining the exact solutions of nonprismatic Timoshenko beams because they avoid solving awkward differential equations governing the frame elements. In addition, the exact Timoshenko’s shape functions (TSFs) for nonprismatic elements result as a by-product of the formulation. Thus, the exact deformed shape of the element may be determined at any load level in the nonlinear analysis. Polynomials of different orders may be used to interpolate the variable rigidities along the element length. Moreover, we adopt boundary integrals to compute the cross-sectional rigidities along the element, which facilitates the modeling of cross sections of complex shapes. Regular, low-order Gauss-Legendre quadratures are required to evaluate all integrals involved in the analyses. The proposed formulation is validated by comparing our responses with the ones determined by using highly refined 3D ANSYS models. Nonlinear equilibrium paths, stresses, and internal forces are observed in the comparison of results.

Comparison of Soil Modeling Strategies with Springs in Free-Span Submarine Pipelines

The fatigue life of submarine pipelines is significantly influenced by structural parameters and environmental conditions to which they are exposed. Numerous studies have focused on modeling this issue using the Finite Element Method to determine frequencies and natural modes of vibration. The models consist of pipeline sections, with some segments in free spans and others supported by soils that can be represented by contact surfaces or sets of springs constituting an elastic foundation. This work aims to evaluate different strategies for representing soil stiffness using springs in a finite element model. Additionally, we investigate the incorporation of the solution for a semi-infinite beam on an elastic foundation to calculate the stiffness of the modeled endpoints. We analyze different element lengths in a free-spanning pipeline model to quantify the influence of various approaches on frequencies and natural modes of vibration. Therefore, this work emphasizes the relevance of parametric studies in modeling submarine pipelines, with particular emphasis on accounting for soil stiffness.

Space truss finite elements applied to actuated structures and origami – implementation and discussions

In the various branches of engineering, dynamic analysis of structures is always a relevant topic and the training of future professionals and researchers in this area is always important. Nowadays, with the evolution of materials and topological dispositions, structural elements and structures are becoming increasingly lighter and slender, increasing the amplitude of movements in such a way that nonlinear geometric analysis is necessary. regarding actuated structures or origami mechanisms, there is a natural mobility between planes defined by the relative rotation in the creases that makes it possible to create foldable devices of great interest such as the production of retractable roofs, retractable antennas, wheels for light vehicles, biomechanical devices , among others. This work introduces the presence of actuators in spatial structures by directly controlling the initial length of truss elements (actuation). At the same time, to define origami or “flat” 3D structures, it is necessary to introduce the strain energy associated with the folds at the junction between flat panels (creases). To introduce this energy, vectors orthogonal to the adjacent origamic planes are defined and fictitious spring elements are introduced to oppose the change in the anglebetween the planes. Illustrative examples and discussions of future work are presented.

Use of hyperelastic models and sliding connections to model the mechanical behavior of musculoskeletal structures

The generation of movement and force produced by the musculoskeletal system in various parts of the body is a topic of high interest in academic research. The increasingly detailed and precise knowledge of the biomechanical behavior of these structures is required to meet the demands of health care and human well-being. The use of structural analysis tools is essential for that purpose. In some situations, in vivo or in vitro tests present a series of inconveniences; therefore, computational simulations prove to be complementary to experimental tests to analyze human movements and generally offer advantages in terms of cost and time. To contribute to the construction of a more precise understanding of the mechanical behavior of biological structures, this work aims to numerically simulate the planar behavior of the upper limb of the human body through the action of skeletal muscles and the movement of adjacent joints. The mechanical simulation is performed through a computational code developed based on the Positional Finite Element Method (PFEM), capable of performing geometric nonlinear analyses directly in its formulation. The proposed modeling treats the muscle tissue as a composite material made of a three-dimensional matrix and embedded simple bar elements, which represent the muscle fibers. Despite the three-dimensional nature of the model, it is important to emphasize that the work aims at a two-dimensional application, simulating the mechanical behavior of musculoskeletal structures on a single plane. The Saint-Venant-Kirchhoff hyperelastic constitutive model is used to define the relationship between stresses and strains in the materials, highlighting its potential and limitations. Additionally, the active muscle behavior is considered through a numerical strategy that represents fiber contraction by allows controlling the initial length of the bar element. The joint studied in the model is the elbow, modeled through the formulation of sliding connections, allowing relative movement between connected surfaces. Since the mechanical simulation is planar, only flexion and extension movements are reproduced. The kinematic conditions imposed on the system to promote sliding are introduced into the problem using Lagrange multipliers. The proposed model has the potential to describe the mechanical response of human body members in a simplified manner.

Research on the sensitivity of various factors influencing the molding performance of PSC damage elements through orthogonal design

Abstract To investigate the forming characteristics of the damage element in a plane symmetric shaped charge structure, the geometric design of an oil perforating charge was undertaken. The shaping process of this damage element was then numerically simulated using LS-DYNA. By analyzing the factors influencing the molding performance of the PSC damage element, the orthogonal design method was employed to identify three key factors: groove wall thickness, groove width, and groove height. Additionally, five evaluation indices were established: head velocity, tail velocity, velocity gradient, length, and width of the damage element. The sensitivity of each factor to these evaluation indices was examined. The findings reveal that groove wall thickness and height are the primary factors influencing head velocity, tail velocity, head-tail velocity difference, and the length of the damage element. Except when the wall thickness is 0, where a monotonic increase is observed, the groove width is the primary determinant of the damage element’s width. Other evaluation indicators demonstrate contrasting trends relative to other factors. Ultimately, the combination parameter b4δ2h1, which exhibits superior cutting performance, was optimized.

Enhanced Phase Coherence in Series‐Fed Patch Array Antenna: A Design Method for Uniform Element Spacing With Low Sidelobe Levels

ABSTRACTMicrostrip series‐fed patch array antenna (SFPA) is increasingly prominent in millimeter‐wave radar systems. Especially, SFPA with tapered amplitude using Dolph–Chebyshev, Taylor, and Binomial distribution has been developed to reduce a sidelobe level (SLL), which is critical to radar resolution. Even though reported designs of SFPA have achieved notable reductions in SLLs, the patch element and inter‐element spacing optimized by simulation over the entire array design can't guarantee perfect in‐phase radiation. Consequently, for nonuniform SFPA designs, achieving precise in‐phase radiation necessitates a theoretical approach and a thorough phase analysis of each element. In this article, we present a noniterative design method to ensure in‐phase feeding to each patch element by accurately compensating for the phase difference encountered in nonuniform SFPA. This approach begins with designing the electrical length of each patch element to be equal to 35 GHz. Subsequently, delay lines are then designed to provide in‐phase feeding across the array while maintaining uniform spacing between elements. Consequently, we fabricated three 8‐element SFPAs operating at 35 GHz and compared their performance, and the proposed design shows an SLL of –20.7 dB with a radiation angle of .

Signature of viral fossils: a comparative genomics approach to understand the diversity of endogenous retroviruses in bats

Endogenous retroviruses (ERVs) are traces of past viral infections commonly found in vertebrate genomes. Many ERVs are tightly regulated by the host genomes and co-opted for various functions within the hosts. Bats are the only true volant mammals, with the smallest mammalian genomes and a high fraction of ERVs within the genomes. They are important hosts for various zoonotic viral pathogens and can effectively modulate their immune response to tolerate viral infections. Integrations of retroviruses have been implicated as one of the mechanisms by which bats have co-evolved strategies to combat viral infections. In this study, we investigated the diversity of ERVs in over 40 publicly available bat genomes to understand the distribution and the evolution of ERVs within bats. We observed all classes of ERVs within bat genomes including even the complex lenti retroviruses. Alpha and spuma retroviruses which are generally considered rare in mammals, were common within bats. We observed a positive correlation between bat genome size and length of ERV elements. Interestingly, nearly 30 % of the ERVs within bats are intact suggesting a recent origin or co-option by the host genome. Future studies focusing on comparative genomic and experimental data will be critical to understand the role of these ERVs in host genome evolution.

SUBSTANTIATION OF THE REGULARITIES OF THE SUBGRADE STRESS-STRAIN STATE AFTER THE IMPLEMENTATION OF THE EUROPEAN TRACK

Purpose. The implementation of the European track (1435 mm) on the existing subgrade, built on the territory of Ukraine, is a factor that leads to a change in the stress-strain state. The purpose of the article is to substantiate the regularities of the stress-strain state of the subgrade based on the results of numerical analysis of finite-element models. Methodology. For numerical analysis based on the finite element method, a 6 m high subgrade model for the combined track was developed. The developed model reproduces all the real geometric characteristics of the subgrade, the upper structure of the track, as well as the sleeper for the combined track. The developed model allows to vary the application of the train load with the setting of a couple of forces on the rails, which have the Ukrainian value of the track gauge (1520 mm), as well as the European one. The model also simulates the reinforcement of the subgrade for four options (without pile, with pile length of 2.0, 4.0 and 6.0 m). Findings. The results of the numerical analysis made it possible to obtain the values of horizontal and vertical stresses, as well as to obtain the regularities of the stress-strain state of the subgrade before the introduction of the European track. Qualitative analysis of the train position shows that the reduction of the track gauge and its asymmetric location on the sleeper increases vertical deformations. The biggest problem is precisely the asymmetric distribution of vertical displacements. It was found that the increase in the length of the vertical reinforcement element provides a reduction in displacements by 1.1 … 1.2 times. It was found that the patterns of changes in the displacements of the subgrade, when the length of the vertical reinforcement element is varied, are linear for the horizontal component and polynomial of the second degree for the vertical component. Originality. For the first time, based on the regularities of the stress-strain state of the subgrade, a picture of the stresses formation and the distribution of deformations before and after the implementation of the European track was obtained. Practical value. Based on the results of the numerical analysis, it was found that increasing the length of the vertical reinforcement element by 2.0 m provides a reduction in displacements by 10 … 20 %. This data makes it possible to create a methodology for the initial selection of the reinforcement element parameters.

Multi-Objective Optimization of MEMS-based Box Pattern Microheaters Using Response Surface Method

We present a response surface method to evaluate multi-objective optimization for MEMS-based microheater design. Box pattern, the standard microheater shape, was selected in this study since it has a uniform temperature distribution compared to other patterns. The optimum parameters are used to obtain the maximum total current density and Joule heat. Based on a hybrid of the Response Surface Method and Central Composited Design, the model simulation emerged with 25 sets of Design Experiments. As expected, the voltage is proportional to the increased output temperature and Joule heat of the microheater. Material thermal conductivity, anchor length and thickness of the heating element are included as design variables for the optimization. The microheater thicknesses of 4.23 - 4.55 µm, length of 40 µm and thermal conductivity of materials of approximately between 52 to 66 Wm-1K-1 became the optimized results at 1 V input voltage to obtain a maximum Joule heat of 4.9x105 W/mm3 and total current density of 5.6x107 mA/mm2.

Wheeler-DeWitt canonical quantum gravity in hydrogenoid atoms according to de Broglie-Bohm and the geodesic hypothesis. Einstein’s Quantum Field Equation

We explore the geodesic hypothesis of orbital trajectories of the electrons in hydrogenoid atoms, in the frame of de Broglie-Bohm quantum theory. It is intended that the space-time can be curved, at very short distances, by the effect of the joint action of the energy content of the atomic system and the contribution of the electric and quantum potentials. The geodesic hypothesis would explain the non-lose of energy in the electron orbital trajectories. So we explore a conception where particles and waves interact in a closed system: the waves guide the particles and the particles generate the spacetime perturbation that acts as a wave, beyond the pilot-wave theory. We establish the equivalence, in a local neighborhood, between the electron trajectory of an hydrogenoid atom in the Minkowskian space where the de Broglie-Bohm can be cast with its movement in a Lorentzian manifold, according to the concept of metric tangent. Through the geodesic condition and the invariance of the elemental length, we establish a relationship between some components of the metrics. But as the particles in microphysics do not follow the Einstein’s field equation, we consider the 3+1 decomposition according to ADM and the quantization in the Wheeler De Witt theory and with a so-called quantum Einstein field equation, with a decomposition of spacetime into three-dimensional sheets of a spatial character. Then we derive from the moment-energy tensor a further equation between the components of the metrics. It opens the avenue to characterize the metric by an exact solution of the Einstein’s field equations.

КРАЙОВІ ЕФЕКТИ В БАЛКАХ ІЗ КОМПОЗИТІВ

Beams made of composites are widely used in aircraft structures, various machines and mechanisms. The experience of operation and repair of such objects shows that when designing beams and spars, one must take into account such effects as the influence of thermal stresses and the additional contribution of Poisson's coefficients to the stressed state of beam elements both in the length direction and along the width beam elements. Scientific studies devoted to the assessment of the stress-strain state of load-bearing structures made of composites demonstrate the conclusions that the effects of thermal expansion (contraction) of heterogeneous connected elements and the influence of Poisson's ratios give significant increases in stress. The value of these increases can be up to dozens of percents of the base load (that is, without taking these effects into account).The paper proposes an engineering mathematical model that allows estimating the value of normal and shear stresses from thermal loading and Poisson stresses. An analysis of the distribution of these stresses along the length and width of the beam elements was carried out.When using the structural-technological solution of beams with sub-shoulders, the proposed method allows you to reasonably choose adhesive or binder for reliable connection of the cap with sub-shoulder, as well as more correctly justify the geometric dimensions of the beam elements. Also, this technique can be used to develop new structural and technological solutions for beams and other load-bearing elements (ribs, walls, webs, doublers, overlapping joints of composite parts).Another applied direction of using the developed methodology can be considered the development and optimization of existing technological processes for the production of parts and units of composites, in which the so-called hot polymerization of the binder (at elevated temperatures) is used. The method makes it possible to estimate the level of thermal stresses that occur during the manufacture of the unit.In general, the proposed technique makes it possible to understand the principles of additional stresses occurrence, to estimate their absolute values, and to increase the accuracy of estimating the stress-strain state of beam elements.

Quantifying the Vices and Virtues of Snakes and Ladders Through Time

Abstract The game of Gyan Chaupar or ‘Snakes and Ladders’ exists in many forms throughout history as a board game of varying size, structure, and game elements of snakes and ladders associated with various vices and virtues inscribed within the board. Three boards were analyzed via simulation in Python, including the 1998 Milton Bradley version, the 72-square Vaisnava board, and the 84-square Jaina board, with the goal of understanding the relationships between board design and associated behaviors and spiritual concepts. Game play on each board was simulated 100,000 times with variations that included individual removal of a snake or ladder, thereby quantifying the importance of that element towards achieving victory. Comparison of the weighted importance of each game element and associated vice and virtue permitted quantification of their importance for the game designer and their associated culture, with each game board component being assigned a contribution towards victory. Historical values inscribed within the class of Gyan Chaupar games were interpreted quantitatively via simulation allowing for comparison of different variations of the game and their associated cultures in different locations and time. The hypothesis that game element contribution towards victory could not be assessed by players a priori via element board length was supported by simulation data that identified many snakes and ladder game elements whose importance towards victory deviated significantly from proportionality with their game element length.

Bayesian Inference for the Calibration of Progressive Damage Model of Dovetail Specimens from Laminated Composite Fan Blade

Abstract Composite fan blades are the preferred alternative for the fan stage of most advanced high bypass ratio turbofan engines. The ability of the dovetail to safely bear this load is one of the key points of the multi-level “test pyramid” approach of compliance demonstration for special airworthiness regulation. Debonding between adjacent layers is the main damage mode of laminated composite fan blades. However, there is difficulty in measuring the as manufactured interlaminar mechanical properties used in finite element models. In this study, tensile loading was applied to simulate the interacting centrifugal force and capture mixed mode damage evolution. Structural responses and material damages were calibrated with measured tensile loads through Bayesian inversion. Posterior probability distributions of maximum interface tractions and contact stresses were solved using Markov chain Monte Carlo sampler. Results indicated the two bilinear cohesive material models had a capacity of predicting empirical means of longitudinal reaction forces as that in test considering additional discrepancy term (0.035 kN and 0.96 kN respectively), while they made an significant impact on the prediction of tensile load history especially when two delamination cracks initiated and propagated. Interface elements provided a higher matching quality in predicting loading history and capturing damage mechanism in association with in-plane progressive damage analysis. This calibrated parameter set could be functioned as benchmark in numerically determining the ultimate tensile load of dovetail elements and reducing the necessary number of physical tests at elemental length level.

Morpho-Anatomical Variations in Sisymbrium irio L. Plants Raised from Seeds Treated with γ Radiation.

This study determines the effect of γ irradiation on seed germination, growth, and morpho-anatomical traits of the Sisymbrium irio L. (London rocket) plant. Seeds irradiated with 2.5, 5, 10, 15, and 20 kGy of γ radiation showed a reduced germination percentage (13.68-56.84%) with reference to the control, showing an inverse relationship with radiation dose. Observations recorded at preflowering, flowering, and postflowering stages of plant growth showed a significant (P < 0.05%) dose-dependent decline in many growth parameters, such as root length, shoot length, shoot dry weight, number of leaves, and pods per plant, due to the radiation effect. However, root dry weight, leaf length, leaf dry weight, number of branches, and number of flowers per plant increased at the lowest dose (2.5 kGy) and then declined steadily with the increasing level of radiation. Likewise, several anatomical features (length of fibers and vessel elements, diameter of vessel elements, proportion of cortex, and vasculature in the stem) showed a consistent decrease with increasing γ irradiation in treated plants compared with the control. However, the pith area and the number of vessels per microscopic field decreased significantly with the lowest radiation dose (2.5 kGy) and then increased gradually with higher doses at each ontogenetic stage. The vulnerability factor in the control as well as treated plants increased with increasing plant age. In treated plants, vulnerability was higher under the effect of low-level radiation than in the control, but it showed an inverse relationship with the increasing level of radiation, thus being the lowest at 20 kGy radiation dose. Mesomorphy also showed an almost similar variation pattern with reference to the radiation dose.

Adaptive ray tracing in freeform gradient-index media using an index directional derivative.

Freeform gradient index (F-GRIN) media are increasingly used in optical systems. The existing ray tracing methods for F-GRIN have low calculation efficiency and require manual adjustment of step size, making the design process complex. To address this, we propose an adaptive ray tracing (ART) method for F-GRIN. ART obtains an initial step size based on an index directional derivative and the element's length. During the subsequent transmission process, the step size is adaptively adjusted. The accuracy and speed of ART were verified through multiple comparison tests. ART can reduce manual participation and significantly improve efficiency in the optical design of F-GRIN.

Evaluation of stresses on the surface of production columns equipped with sand filters when downing into a horizontal well

Relevance. The need to estimate the time of formation sand accumulation near the annulus of a horizontal well and the unit length of filter elements in the bottom of production strings and to determine the stresses on the surface of production strings equipped with sand filters when lowering into the well. Aim. Based on a study of the reasons for the continued flow of sand into wells equipped with anti-sand filters, to develop and propose measures related to the need to choose a reduction in the number of filters that provide the design flow rate of a horizontal well or a significant increase in the length of the filtering surface of the filters in order to reduce erosive wear of the wire winding. Objects. We are considering a well with a horizontal section, equipped with sand filters, the same size as the casing strings. It was assumed that the integrity of the surface of the filter elements would be preserved and the conditions for their destruction would be eliminated when lowering into the horizontal shaft. This presupposes the necessary efficient operation of the well throughout the entire operational period. The section of the first set of curvature and the forces arising during this are considered as wellas stability of a pipe string during possible stops. Centralizers are evenly located along the length of the column, then in some sections we will have a multi-span statically indeterminate beam, in each section of which a radial load acts. Methods. When studying the time of formation sand accumulation in the annular space of a horizontal well and a unit length of filter elements in the bottom of production strings, it is necessary at the first stage to determine the stresses on the surface of production strings equipped with sand filters when lowering into the well. Studying the assessment of the existence time of the transition period is of particular interest. This is, in other words, during what operational period there is a complete accumulation of formation sand in the annular space and the transition of formation drainage along the entire length of the horizontal wellbore to drainage of only zones adjacent to the filters. To calculate the fluid flow rate when the annular space of the horizontal well is completely filled with sand, the design values ​​of the AC4.8 formation parameters were used. The maximum value of depressions used in the calculations is assumed to be 1.5 MPa. Results. Consideration of situations that arise when filters are lowered into horizontal wells indicates that the outer surface of the filter elements is not protected from destruction as a result of contact stresses with the walls of the drilled wellbore. To protect against destruction and rubbing open gaps by clay-containing rocks, rigid centralizers should be installed along the edges of the filter elements, the maximum allowable distances between which should not exceed 4.0–4.5 m.

Comparison between experimental and numerical results for piezoelectric signals generated in water-saturated cancellous bone by ultrasound irradiation

Abstract The bone formation is considered to be accompanied by the piezoelectric effects in bone. Therefore, the piezoelectric effect under ultrasound irradiation should be elucidated to realize the effective healing. Then, the piezoelectric properties in cancellous bone have been attempted to clarify by complementing experiments and simulations with each other. In this paper, the piezoelectric signals generated in water-saturated cancellous bone by ultrasound irradiation were experimentally and numerically observed, and the effect of the trabecular orientation was investigated. The experimental observation was performed by the piezoelectric cell (PE-cell), which corresponds to an ultrasound receiver using the cancellous bone specimen as a piezoelectric element. The numerical observation was performed by the piezoelectric finite-difference time-domain (PE-FDTD) method, which is an elastic FDTD method with piezoelectric constitutive equations. In both the experimental and simulated results, the piezoelectric signal amplitude increased with the mean intercept lengths (MILs) of the trabecular elements and the pore spaces or the strength of the trabecular orientation. From the fact that the ultrasound propagation in water-saturated cancellous bone can depend on the trabecular orientation, it was considered that the ultrasound properties could be largely associated with the piezoelectric properties.

On finitely generated Engel branch groups

AbstractWe construct finitely generated Engel branch groups, answering a question of Fernández‐Alcober, Noce and Tracey on the existence of such objects. In particular, the groups constructed are not nilpotent, yielding the second known class of examples of finitely generated non‐nilpotent Engel groups following a construction by Golod from 1969. To do so, we exhibit groups acting on rooted trees with growing valency on which word lengths of elements are contracting very quickly under section maps. Our methods apply in principle to a wider class of iterated identities, of which the Engel words are a special case.

Progressive failure analysis of laminar composites under compression using smeared crack-band damage model and full layerwise theory

This paper presents an original finite element (FE) model that integrates the smeared crack band (SCB) approach and full layerwise plate theory (FLWT). The model enhances the computational efficiency of progressive failure analysis (PFA) of laminar composites in compression, by utilizing the layerwise approach which reduces a 3D model to a 2D one. The model distributes damage throughout the FE domain, with fracture mechanisms represented by material stiffness degradation controlled by damage variables (based on equivalent strains specifically defined for each failure mode). Mesh dependency issues are addressed by scaling fracture energy using a characteristic element length, and failure initiation and modes are determined using the 3D Hashin failure criterion.Accurately describing lamina response in fiber direction under compression requires linear-brittle softening with a stress plateau. The study showed that a model considering 30 % of residual stress accurately predicts maximum stress regardless of mesh refinement, demonstrating results’ minor dependence from the selected element size.The model accuracy has been confirmed by comparing the obtained results against experimental and benchmark data from the literature. The size effect study demonstrated a decrease in maximum stress of the open-hole laminates in compression with increasing specimen in-plane size. This trend is consistent with experimental and reference numerical observations, confirming the model accuracy and applicability even for relatively coarse meshes. Therefore, computational efficiency is improved, with preserved accuracy of conventional solid finite element models.

Shapovalov elements for U q ( s l ( N + 1 ) )

For a simple Lie algebra, Shapovalov elements give rise to highest weight vectors in Verma modules. The usual construction of these elements uses induction on the length of a certain Weyl group element. If g = s l ( N + 1 ) explicit expressions for Shapovalov elements were given in I. M. Musson [Explicit expressions for Shapovalov elements in type A, J. Algebra 623 (2023), 358–394]. Here we adapt the argument to the quantized enveloping algebra of g .