Warping Effects Research Articles

Study of thermal stress deformation in hybrid 3D printing and milling process of PEEK material

Hybrid manufacturing can enable rapid production of personalized artificial bones that are made of Polyether-ether-ketone (PEEK) by integrating 3D printing and milling. A main challenge, however, is the thermal stress deformation that arises from the fused deposition process, leading to warping and shrinkage. As a result, the fabrication accuracy is significantly diminished. This work aims to address this challenge by investigating the thermal stress deformation behavior of PEEK in hybrid manufacturing. The main contributions of this work, therefore, include the development of a model for this thermal deformation behavior, and the identification of key parameters such as cross-section length ( Ls), printed layer thickness ( Lh), and current workpiece height ( He). Further, experiments are conducted based on response surface methodology (RSM) to explore the relationships between temperature variation rate (Δ T), end surface height difference (Δ S), and length shrinkage rate (Δ L) with critical hybrid processing parameters. Optimal parameter combinations are then identified. Our experiments demonstrate that the proposed methods effectively reduce the effects of warping and shrinkage.

Critical lateral‐torsional buckling loads of porous orthotropic rectangular beams containing warping effects

AbstractDue to their elemental porosity, porous materials display individual mechanical properties, rendering them essential components in various engineering applications. So, this study investigates the lateral‐torsional buckling (LTB) sensitivity of porous orthotropic rectangular beams subjected to a concentrated load, including the warping effects. Porosity‐dependent material properties vary along the beam's height via four different porosity distribution patterns. The constitutive equations are obtained using the principle of virtual work based on the classical beam theory containing the warping effect, and the governing equations are solved by performing the Ritz method to obtain the critical LTB load. The porous orthotropic beams and the warping effects add complexity to the analysis. So, the influence of some parameters, such as porosity coefficients, porosity distribution patterns, orthotropy, height‐to‐width ratio, slenderness ratio, and warping coefficients, on the LTB characteristics of porous orthotropic rectangular beams are investigated in detail. The novelty of this study lies in its comprehensive LTB analysis of orthotropic rectangular beams under specific effects, such as porosity and warping factors. The findings offer valuable insights into the LTB characteristics of orthotropic porous beams, contributing to an improved comprehension of their structural behavior and facilitating the design of engineering structures. This study contributes to the composite materials and structural stability analysis, offering potential applications in many engineering domains.

Green recycling of end-of-life photovoltaic modules via Deep-Eutectic solvents

Sustainable End-of-life (EOL) photovoltaic (PV) modules recycling is essential for achieving resource conservation and alleviating environmental issues. Ethylene vinyle acetate (EVA) adhesive films separation is a prerequisite for the realization of valuable component recovery of PV modules. However, the conventional wet chemical separation processes are usually accompanied by the challenges of low separation efficiency, high toxicity and difficult multiple recycling. Herein, a green, biodegradable, low-cost and recyclable deep eutectic solvent (DES) is firstly developed to efficiently separate EVA films in EOL PV modules. The high temperature stability and the acidic characteristic of DES can facilitate the separation of EVA film between component layers. At 175 ℃, the warping effect caused by the differential thermal contraction between the module component layers creates favorable conditions for the efficient reaction and separation by the DES. Additionally, the acidic medium reacts with the aluminum electrode layer of PV cells, which further enhances the separation efficiency of EVA films. The EVA separation rate reached 100%, the separation rate of the EVA containing aluminum (Al) up to 98.4% after 12.5 h at 175 ℃. Moreover, the developed DES exhibits excellent recyclable performance, the EVA separation rate remained 100% after 10 cycles. Compared to the traditional solvent toluene, DES has advantages in terms of economics, environmental impact, and efficiency. This strategy of design a green, biodegradable, low-cost and recyclable solvent to replace traditional solvents, and provides a promising route to efficiently separate EVA films in EOL PV modules.

Behavior of steel beam section under warping using BIM program

AbstractWarping not only one of the most important phenomena in steel section it is also considered as the most complicated phenomena. Ductility, bearing capacity and serviceability of steel sections may affect by increasing stress concentration of the normal stresses due to warping. In the present work, simulation of steel beam section under effect of warping is studied. Two cantilevers connected to two columns in opposite sides with a middle steel beam-column connection to create different moments on the beam to investigate the behavior of steel section under warping using building information modeling. It is found that the stress strain relationship has four groups depending on the load intensity and the angle of rotation induced due to warping.

Elastic wave spin and unidirectional routing in thin rod systems

The unusual topology of elastic waves in continuum systems has been recently uncovered. Prominently, the spin of Rayleigh-Lamb waves has been experimentally observed and used to achieve the unidirectional wave propagation. In this work, the elastic wave spin in thin rod systems is theoretically predicted and experimentally observed, for all the three basic wave modes, i.e., the zero-order flexural, longitudinal and torsional modes. By elaborately building up the subwavelength chiral sources, the spin-momentum locking has been achieved for these three modes within broad frequency range. Interestingly and surprisingly, the spin-momentum locking occurs for flexural and longitudinal modes in both circular and non-circular thin rods; the spin-momentum locking for torsional modes only exits in non-circular thin rods, due to the warping effect in non-circular cross-section rods. Our results open up the door for elastic wave spin in thin rod systems, and provide general tips for the research on basic modes in diverse thin rods, based on either the continuum media or the artificial metamaterials in future.

Long-Term Results Using “Nair Hospital Precision Carving” Technique of Rhinoplasty

Abstract Background and Objectives Convincing a patient who has undergone any aesthetic surgery to come for a long-term follow-up is extremely difficult. The result obtained after rhinoplasty usually stabilizes in the first year and it is unlikely to change after 2 years. The precision carving technique described in 2014 has been employed by us for the last several years. We wish to present long-term results (at least 2 years) obtained using this technique, now renamed as “Nair Hospital Precision Carving technique.” The unfavorable effects of warping are most apparent in the dorsum. So, we have chosen to assess results of dorsal onlay grafts only. This article presents the long-term results obtained using favorable warping technique. Materials and Methods We have followed up 45 patients in whom dorsal augmentation was done using rib grafts for various indications like aesthetic, reconstructive rhinoplasty and cleft lip nasal deformity. Grafts were carved using the precision carving technique. Results All patients were assessed at 6 weeks, 6 months, and at subsequent follow-up period of 2 to 10 years and photographs were taken at each visit. There was no major complication and all patients were satisfied with the appearance. Conclusion The Nair Hospital Precision Carving technique utilizes unbalanced yet controlled and precise carving to achieve a variety of natural shapes for the objectives of contour fill and framework reconstruction in rhinoplasty, thus ensuring good long-term results.

Is object-based warping solely object-based?

Object-based warping is a visual illusion in which dots appear farther apart from each other when superimposed on an object. Previous research found that the illusion's strength varies with the perceived objecthood of the display. We tested whether objecthood alone determines the strength of the visual illusion or if low-level factors separable from objecthood also play a role. In Experiments 1-2, we varied low-level features to assess their impact on the warping illusion. We found that the warping illusion is equally strong for a variety of shapes but varies with the elements by which shape is defined. Shapes composed of continuous edges produced larger warping effects than shapes defined by disconnected elements. In Experiment 3, we varied a display's objecthood while holding low-level features constant. Displays with matched low-level features produced warping effects of the same size even when the perceived unity of the elements in the display varied. In Experiments 4-6, we tested whether displays with low-level features predicted to be important in spatial warping produced the visual illusion even when the display weakly configured into a single object. Results showed that the presence of low-level features like contour solidity and convexity determined warping effect sizes over and above what could be accounted for by the display's perceived objecthood. Our findings challenge the view that the spatial warping illusion is solely object-based. Other factors like the solidity of contours and contours' position relative to reference dots appear to play separate and important roles in determining warping effect sizes. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Hexagonal warping effects on Bloch oscillations in proximitized Rashba systems

Bloch oscillations (BOs) in Rashba systems, taking into account the effects of hexagonal warping and proximity-induced band gap, are reported. We find that in addition to real-space trajectories, the group and Berry velocities of Bloch electrons exhibit novel BOs which strongly depend on the crystal momentum. This oscillatory motion is affected significantly by variations in the strength of hexagonal warping and the proximity-induced band gap, originating from the substantial changes in the energy spectrum induced by these factors. In addition, it is shown that the Bloch oscillations are modified considerably under the influence of applied uniform in-plane electric and transverse magnetic fields, which allow for a geometric visualization of the Bloch dynamics. Interestingly, when the system is subjected to these fields simultaneously, it undergoes a dynamic phase transition between confined and de-confined states. This phase transition is tuned by the relative strength of the applied fields and is further influenced by variations in the strength of hexagonal warping and proximity-induced band gap. The appearance of such a transition is attributed to the interplay between the external fields and the intrinsic properties of the crystal lattice. Moreover, we find that the direct-current drift velocity shows negative differential conductivity, which is a characteristic feature of the BO regime.

Left Ventricular Segmentation, Warping, and Myocardial Registration for Automated Strain Measurement

The left ventricular global longitudinal strain (LVGLS) is a crucial prognostic indicator. However, inconsistencies in measurements due to the speckle tracking algorithm and manual adjustments have hindered its standardization and democratization. To solve this issue, we proposed a fully automated strain measurement by artificial intelligence-assisted LV segmentation contours. The LV segmentation model was trained from echocardiograms of 368 adults (11,125 frames). We compared the registration-like effects of dynamic time warping (DTW) with speckle tracking on a synthetic echocardiographic dataset in experiment-1. In experiment-2, we enrolled 80 patients to compare the DTW method with commercially available software. In experiment-3, we combined the segmentation model and DTW method to create the artificial intelligence (AI)-DTW method, which was then tested on 40 patients with general LV morphology, 20 with dilated cardiomyopathy (DCMP), and 20 with transthyretin-associated cardiac amyloidosis (ATTR-CA), 20 with severe aortic stenosis (AS), and 20 with severe mitral regurgitation (MR). Experiments-1 and -2 revealed that the DTW method is consistent with dedicated software. In experiment-3, the AI-DTW strain method showed comparable results for general LV morphology (bias − 0.137 ± 0.398%), DCMP (− 0.397 ± 0.607%), ATTR-CA (0.095 ± 0.581%), AS (0.334 ± 0.358%), and MR (0.237 ± 0.490%). Moreover, the strain curves showed a high correlation in their characteristics, with R-squared values of 0.8879–0.9452 for those LV morphology in experiment-3. Measuring LVGLS through dynamic warping of segmentation contour is a feasible method compared to traditional tracking techniques. This approach has the potential to decrease the need for manual demarcation and make LVGLS measurements more efficient and user-friendly for daily practice.

Large rotation isogeometric shell model for alternating stiff/soft curved laminates including warping and interlayer thickness change

The mechanics of laminates made up of elastic alternating stiff/soft layers is dominated by bending and membrane actions in the stiff layers, while transverse shear deformations concentrate in the soft interlayers producing significant zigzag warping effects. Additionally, curved geometry and large deformations can induce an interlayer thickness strain affecting the overall response of the laminate. This work presents a rotation-free Total Lagrangian large deformation curved shell model to accurately capture such a structural response. Each stiff layer is modeled as a Kirchhoff–Love shell. Without additional DOFs, each soft interlayer is modeled as a solid-shell by expressing, in finite kinematics, the displacement of top and bottom interfaces as a function of the mid-surface displacement of the upper and lower stiff layers it couples. The model is characterized by a sparse stiffness matrix compared to high-order theories and requires a small number of DOFs (3 per stiff layer) to reproduce the 3D solution. A NURBS discretization meets the high continuity of the weak form with a patch-wise reduced quadrature to avoid locking and enhance efficiency. All thickness integrals are pre-computed just once.

Bending-bending-torsion coupled wave propagation in thin-walled asymmetric metabeam: An analytical and experimental analysis

The primary focus of this paper is to analyze the impact of the periodic resonators on the wave dispersion phenomenon of a thin-walled asymmetric beam. An analytical framework has been developed to study the triply coupled flexural and torsional wave propagation in an asymmetric metabeam. The resonators are modeled as a beam with a lumped mass at the center and placed eccentrically from the shear center. Their periodicity allows them to generate a subwavelength attenuation band in the beam. The governing equations for the coupled bending-bending-torsion vibration of a metabeam having an asymmetric cross-section are considered for generating the dispersion phenomenon, including the warping effect. Applying the Bloch-Floquet principle, the dispersive characteristics of the asymmetric metabeam are obtained by using the transfer matrix method. The modal characteristics of an asymmetric beam without a resonator are computed using the spectral element method and are validated with previously published results. Subsequently, the attenuation band is investigated due to the presence of a resonator and followed by the transmittance spectrum to verify the suppression of the elastic waves in the attenuation band. The experimental analysis is carried out to validate the analytical framework by obtaining the modal frequencies from the frequency response function. The detailed parametric investigation reveals that the resonator’s position and characteristics significantly impact the occurrence of the band gap. A substantially wide attenuation band gap is attained by considering a continuous beam-mass resonator instead of a discrete spring-mass type resonator. This type of novel structure has the potential for the application of vibration control and acoustics.

Torsional vibration behavior of a restrained non-circular nanowire in an elastic matrix

This study introduces an approach to analyze torsional vibration in non-circular nanowires within magnetic fields, considering various boundary conditions on an elastic foundation. Analytical formulas for natural angular frequencies are obtained using nonlocal strain gradient theory. The analysis covers three non-circular cross-sections, incorporating the warping effect. Elastic springs at the wire ends simulate support conditions, restricting rotation around the wire’s axis. The torsion function around the axis is represented by a Fourier series, discretized at the spring points and linked using the Stokes’ transform alongside the boundary values. This leads to an eigenvalue problem that includes higher-order material size parameters (strain gradient, nonlocal), spring parameters, and the warping function. The study’s novelty lies in effectively solving torsional vibration for non-circular sections, addressing warping function, elastic medium, and size effects under both deformable and non-deformable boundary conditions. The presented solution is capable of determining vibration frequencies for both rigid and deformable boundary conditions. This is accomplished by specifying the torsional spring stiffness values, thereby obviating the necessity for additional recalculations. In order to verify the obtained results and compare them with the existing literature, nanowires with free and clamped boundary conditions are solved numerically by changing the spring parameters in the eigenvalue problem. In the formulation of natural angular frequency; length scale parameters, warping, magnetic field, elastic medium effects are included. In addition, since the support conditions are modeled with elastic springs, the resulting formulas are quite general and can be used to solve different types of torsional vibration problems.

Anisotropic Josephson Diode Effect in the Topological Hybrid Junctions with the Hexagonal Warping

Recently the diode effect in superconductivity became an active area of research. In particular, the three-dimensional topological insulators may be one of the most suitable materials to implement the superconducting diodes. It is common to consider only linear and quadratic terms of the topological insulator Hamiltonian in the low energy expansion. Typically the effect of the hexagonal warping is neglected. However, the hexagonal warping can be very significant in consideration of the transport properties of the TI materials, such as Bi2Se3 or Bi2Te3. In this theoretical work we present the study of the Josephson diode effect based on the topological insulator weak link. We address the question of the hexagonal warping influence on the Josephson diode effect. We argue that the warping term leads to the anisotropy of the Josephson diode effect.

In-plane and out-of-plane vibration analysis of laminated composite frames with warping effects

This paper addresses the free vibration analysis of a general planar frame structure, consisting of an assembly of laminated composite beam members. A mathematical model is established for the beams by introducing a novel displacement field, which encompasses the influence of shear deformation, rotary inertia, material coupling, warping phenomenon, as well as in-plane and out-of-plane deformations. By incorporating these various factors, a comprehensive representation of the beam's behavior is achieved. The continuity equations for displacements and rotations of two adjacent members are formulated to derive the equations for the entire frame structure. The assembled equations are solved using the Finite Element Method (FEM). The numerical results obtained are compared with existing results in the literature and new results from 3D models in ANSYS. The present results for torsional modes are closer to the ANSYS results than the results of previous studies. An extensive analysis is performed to investigate the impact of various parameters, including stacking sequence, frame angle, relative frame length, and anisotropy ratios on the system response.

Wavefronts Dislocations of Friedel Oscillations in Graphene: Trigonal Warping Effect

The electron waves of a host system exhibit an oscillating response to an external impurity, namely Friedel oscillations (FOs), extensively studied in two‐dimensional materials. Recently, wavefront dislocations, a new feature of FOs, have been revealed in graphene. However, previous analytical works have been limited to the linear dispersion of graphene. Herein, the fate of wavefront dislocations is investigated numerically in FOs beyond the linear regime. The wavefront dislocations are robust against the trigonal warping effect, crucial for high doping graphene, due to the invariant winding number of the tight‐binding energy band. Furthermore, the opening of the gap, increasing the electronic Fermi wavelength, can highlight the wavefront dislocations blurred by intravalley scattering‐induced short‐range oscillations. These results should be observable using current experimental technology. Therefore, this study not only demonstrates the robust existence of wavefront dislocations in FOs over a wide range of energies but also deepens the understanding of intervalley scattering in graphene and other two‐dimensional valleytronic materials.

Application and Experimental Validation of Seven-Degree-of-Freedom Beam Element for Girder Bridges during Deck Construction

During bridge deck construction, the deck finishing machine and the fresh concrete often produce large vertical loads and torsional moments acting on the bridge girder system. In some cases, these loads can cause excessive vertical deflection and transverse rotation in the bridge girders, leading to many maintenance and safety problems, such as changes in deck thickness and local and global instabilities during construction. To minimize the potential problems caused by deck construction, the AASHOTO LRFD Bridge Design Specification requires consideration of these torsional moments during the design procedure, and a detailed three-dimensional finite element analysis may be conducted. However, for bridge girders with open-section thin-walled sections, only the solid or shell element can be used to recognize the warping of the girder since the torsional warping effect is not included in the classical beam element. In this research, a warping degree of freedom was added to a beam element, and a three-dimensional beam element with seven degrees of freedom (7-DOF) at each node was derived as an alternative method for analyzing girder bridges during deck construction. A computer program based on the 7-DOF beam element was also developed in MATLAB. To assess the 7-DOF beam element, one bridge was selected to measure the transverse rotation, vertical deflection, and stress of the exterior girder and the first interior girder during deck construction. Also, three full-scale numerical models using solid elements, classical three-dimensional beam elements, and 7-DOF beam elements were created based on the geometries and loads of the experimental bridge. A comparative study was conducted by comparing the results from the numerical models and experimental monitoring data to evaluate the 7-DOF beam element. The results showed that the 7-DOF beam element had excellent behavior in analyzing the girder bridges under construction load, especially in the torsional analysis of bridge girders. Also, unlike the solid element model, which also provided reasonable results, the 7-DOF beam element model can compute the internal forces of the cross-sections along the bridge, which allows the 7-DOF beam element to be an alternative approach for design and research requiring less modeling effort and computational complexity.

Refined beam finite element model for thin-walled multi-cell box girders considering distortion and secondary distortional moment deformation effect

In this paper, a novel one-dimensional refined beam finite element model (FEM) accounting for non-uniform distortional warping and secondary distortional moment deformation effect (SDMDE) is formulated for the distortional analysis of thin-walled multi-cell box girders with cantilevered flanges. The extra distortional angle is introduced to incorporate SDMDE, and the validity of which is proved through rigorous theoretical derivation. The in-plane and out-plane deformations at any point around the edge of transverse section built upon the distortional center are unified in the same form and described in detail. The governing differential equations in terms of two generalized displacements, distortional angle χ and primary distortional angle curvature Θ, are derived based on the principle of minimum potential energy (MPE) and solved exactly so as to provide non-polynomial shape functions for the establishment of element stiffness matrix and nodal load vector. A series of multi-cell rectangular hollow section (RHS) girders are analyzed and particular extensions are given to single-cell and multi-cell bridge girders with cantilevered flanges. Comparisons to the results generated from corresponding ones provided by pioneering work or shell FEM analyses not only validate the correctness and reliability of the present beam element formulations but also highlight the significance of the inclusion of SDMDE when the cantilevered flanges are arranged.

Nonlinear Free Vibration of Spinning Pre-Twisted Functionally Graded Material Plates in Thermal Environment

This paper investigates the nonlinear free vibration of spinning pre-twisted functionally graded material (FGM) plates in thermal environment. Based on the Kirchhoff plate theory and von Kármán large-deformation theory, the nonlinear dynamic model is established via the Lagrange equation, where the warping effect is taken into account. The material properties are related to temperature and change according to a power-law exponent distribution. The theoretical solution of nonlinear-free vibration is obtained using the multiple scale method. The effects of power-law exponent, temperature difference, spinning speed, hub radius ratio, and twist angle on nonlinear-free vibration characteristics of the spinning pre-twisted cantilever FGM plates are discussed. The results show that the spinning pre-twisted cantilever FGM plate exhibits nonlinear hardening-spring vibration behavior, while the characteristics weaken with the increase of spinning speed. The twist angle and setting angle have coupling effects on the nonlinear vibration characteristics of spinning pre-twisted FGM plates.

Mesoscale Structure and Properties of the Terrestrial Magnetotail Plasma Sheet From the Magnetospheric Multiscale Mission

AbstractUsing Magnetospheric Multiscale mission (MMS) orbits in the Earth's magnetotail from 2017 to 2020, plasma conditions and the 3D spatial structure of inner‐magnetotail plasma environments (with a focus on the plasma sheet (PS)) are studied with different approaches. Threshold conditions for distinguishing the PS, PS boundary layers, and lobes are derived from the statistical properties of background plasma parameters. Our results support previous studies that employed similar methods using Cluster data. However, stronger currents are observed in both the lobes and PS, likely due to the smaller spacecraft separation (≲70 km) that can resolve thin electron‐scale currents. Threshold conditions are used together with magnetic field and electric field measurements to image the spatial structure of the PS. Results are in good agreement with a global neutral sheet model based on solar wind conditions and magnetospheric configurations. Furthermore, the Earth's dipole tilts toward the Sun around June solstice, which warps the magnetotail as much as ∼2–4 RE in Z geocentric solar magnetospheric. This warping effect is relaxed toward September equinox. Consequently, as MMS travels through the magnetotail from dawn to dusk during this period, there is an apparent dawn‐dusk asymmetry in plasma conditions between June and September. Kink‐like flapping waves and interplanetary magnetic field twisting are other mesoscale processes attributed with a few RE of flaring near the flanks. These findings reveal important insights into the mesoscale structure and dynamics of the magnetotail.

Lateral-torsional buckling performance of high strength steel rectangular hollow section beam-columns

A new approach namely Plate-Beam theory was employed to perform the investigation into the lateral torsional buckling (LTB) performance of high strength steel (HSS) rectangular hollow section (RHS) beam-columns. Firstly, the total strain energy corresponding to the LTB failure mode of the beam-columns was established, and then the equilibrium differential equation was developed, through the variation of energy functional. Based on the Plate-Beam theory, the equivalent restrained torsional rigidity (warpage constant) that can simultaneously accounted for the secondary warping effect was derived, and the formulation process did not involve any sectoral coordinate operation. The deducing process of the total strain energy of RHS beam-columns was further discussed and recommended to describe the torsion performance of composite and irregular thin-walled members. Based on the FE program verified against test data and theoretical solution, the accuracy of the provisions of HSS RHS beam-columns given in Eurocode3 and GB50017-2017 was assessed. The comparison of numerical program against codified design provisions revealed that the resistance prediction in Eurocode3 was still serviceable for HSS RHS beam-columns, in conjunction with the torsional rigidity according to the Plate-Beam theory.