Warping Deformation Research Articles

A Thermomechanical Model for Time-Varying Deformations of Spigot Interference Connection under Shrink-Fitting Assembly

The interference fit connection structure is widely employed in various industries. Different from the conventional connection structure, the aero-engine rotor connection has a spigot-bolt structure. The quality of the shrink-fitting assembly process directly affects the final assembly performance of the rotor. The complexity of the connection structure and the time-varying thermal deformation bring great challenges in analyzing the formation patterns of connection performance. However, existing methods of interference connection analysis are mainly used in the wide range of interference connection structures, which makes them difficult to apply in low height interference connection for aero-engine rotors. This paper introduces a thermomechanical interference fit pressure model. First, a theoretical model for interference fit pressure considering temperature-variable loads is established to obtain the time-varying pressure during the assembly process. Second, a finite element model is established to explore the influence of interference and temperature loads on the spigot pressure and the mounting edge deformation. Finally, the experiments validate the accuracy of both the theoretical model and the finite element analysis. The results indicate that during the shrink-fitting assembly process, the interference fit pressure exhibits a nonlinear evolution trend, and the warping deformation of the mounting edge is a result of the combined influence of temperature and interference fit pressure. The law found in this paper has an application prospect in the process parameter setting of shrink-fitting assembly for special structures.

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.

Residual Stress Testing and Simulation Analysis of Crystal Structures of Electronic Device Materials

In this paper, we analyze the residual stress of different components of the crystal structures of electronic device materials following exposure to elevated temperatures using a combination of experimental tests and finite element simulations. X-ray diffraction (XRD) and LXRD micro-area residual stress analyzer were employed to determine the residual strain and stress of the CBGA sample encapsulation cover and solder joints. Subsequently, the experimental data were utilized to verify the accuracy of the simulation. The discrepancy between experimental measurements and simulation outcomes of the residual stress following reflow soldering of CBGA-assembled micro-solder joints is below 14%. The analysis also included thermal warping deformation of the CBGA encapsulation cover and how the residual stress was influenced by the diameter, spacing, and height of the solder joints. The study reveals that the residual stress following reflow soldering of BGA solder joints is non-uniformly distributed within the array. Within a single solder joint, residual stress gradually increases in distribution from its middle to the point where it make contact with the PCB and chip, with the highest level of residual stress observed where the solder joint contacts the chip. The variation in material parameters, such as the coefficient of thermal expansion, is the primary cause of thermal warping deformation on the surface of CBGA encapsulation covers. Three primary factors significantly impact the residual stress on BGA solder joints: solder joint diameter, spacing, and height. The maximum value is inversely proportional to the height of the solder joints and the residual stress. Conversely, the diameter and spacing of the joints are positively proportional to the highest value. When the diameter of the solder joint is increased from 0.55 mm to 0.75 mm, the maximum residual stress in the BGA solder joint increases from 37.243 MPa to 36.835 MPa. Conversely, increasing the height of the solder joint from 0.36 mm to 0.44 mm reduces the stress from 39.776 MPa to 36.835 MPa.

Development of Warp Deformation Prediction Method for Weight Reduction of Vehicle Resin Parts

Development of Warp Deformation Prediction Method for Weight Reduction of Vehicle Resin Parts

Investigating the failure behaviour of aluminium alloy gusset joints under impact loading: An experimental and numerical study

The AAG joint, also known as the Temcor joint, is a well-established method for constructing long-span spatial grid structures using aluminium alloys. This joint system has been widely used and tested is considered a mature technology in the field. This paper investigates the tensile properties of 15 stainless-steel bolt connections for aluminium alloy plates at room temperature. Through testing, the load–displacement curve was obtained and two failure modes of the connection were identified. Test results show that the increase in the number of bolts and the thickness of aluminium alloy plate increases the ultimate bearing capacity of the connection. The thickness of the aluminium alloy plate was found to have a significant impact on the slippage effect of the bolts and the warping deformation of the contact surface. Based on the test results of the connection, three specimens of AAG joints were designed to study their dynamic behaviour under different impact loads. Our findings detail the dynamic response behaviour of joints subjected to varying impact times, including stress, acceleration, and displacement, as well as the resultant joint failure phenomenon. The test results show that AAG joints have good impact resistance. The refined FE model of the AAG joint was established using ANSYS/LS-DYNA, and its effectiveness was verified by comparing the stress, displacement, and acceleration between the numerical model and the experimental model. By comparing and analysing the final deformation of AAG joints obtained through test and numerical simulation, three distinct failure modes of AAG joints under impact load were identified. Finally, based on the stress nephogram and impact force time-history curve obtained by numerical simulation, the stiffness degradation law of AAG joints is discussed. This paper also discuss the energy dissipation mechanism of AAG joints during impact load, based on the strain energy time-history curve of each component.

Insights of the vehicle-track-girder system dynamic response changes caused by the thermal deformation of CRTS III ballastless track in the natural environment

The regularity of the high-speed railway track plays an important factor in ensuring the stability and safety of vehicle operation. The study of the influences of the slab warping deformation on the dynamic response of the vehicle-track-bridge is of great engineering significance. Currently, in relevant research work, only the impacts of track irregularity caused by the track or bridge warping deformation on the dynamic responses are considered, but the influence of structural modal changes induced by the thermal deformation is commonly ignored. This article focuses on the temperature deformation of the CRTS III track on the elevated bridge and the deformation-induced vehicle-track-girder dynamic response changes. Firstly, based on the CRTS III slab temperature deformation monitoring experiment and theoretical analysis, the warping deformations of the CRTS III track and girder in natural environments were studied. Secondly, the deformation-induced modal changes of the track-girder were fully considered, and the dynamic response changes of the vehicle-track-girder were analyzed when the warping deformation of the slab reached the maximum. Through a comparative analysis of three scenarios: no structural temperature deformation, only track irregularity caused by the deformation, and the combined effects of deformation-induced irregularity and modal changes, it was found that the time–frequency domain variation characteristics of wheel-rail force and rail acceleration can be acceptably simulated in the case of only deformation-induced track irregularity, but the dynamic response changes of the slab and girder will be underestimated. Therefore, in the study of the dynamic responses of the vehicle-track-girder with temperature effects, full consideration should be given to the deformation-induced track irregularities and structural modal changes.

Early warping deformation of high-speed railway CRTS III track slabs

Excessive flatness deviation issues in the track slabs of railway tracks make it difficult to achieve precise adjustments for both the track slabs and rails. This study aimed to analyze the deviation in flatness of the high-speed railway CRTS III track slabs. Experimental measurements were conducted on the warping deformation of the track slabs before water curing during the maintenance period. Six improved designs were implemented for the steaming process and structural construction. A numerical model was established to predict the warping deformation of the track slab before water curing, considering the temperature and humidity fields as driving forces. Using the sequential coupling method, the warping deformation of CRTS III track slab was calculated under the combined action of temperature field, shrinkage strain field, and prestressed tendons. Based on the results, it is concluded that: (1) High-temperature steam curing of the track slab increases the effective maintenance time and accelerates its strengthening rate. (2) Early shrinkage of the track slab is the primary factor causing warping deformation. (3) During the steam curing period, the warping deformation of the track slab can be controlled economically and effectively by employing secondary water spraying and presetting a reverse arch of 0.5 mm–0.8 mm.

Maximum Likelihood Coordinates

AbstractAny point inside a d‐dimensional simplex can be expressed in a unique way as a convex combination of the simplex's vertices, and the coefficients of this combination are called the barycentric coordinates of the point. The idea of barycentric coordinates extends to general polytopes with n vertices, but they are no longer unique if n > d+1. Several constructions of such generalized barycentric coordinates have been proposed, in particular for polygons and polyhedra, but most approaches cannot guarantee the non‐negativity of the coordinates, which is important for applications like image warping and mesh deformation. We present a novel construction of non‐negative and smooth generalized barycentric coordinates for arbitrary simple polygons, which extends to higher dimensions and can include isolated interior points. Our approach is inspired by maximum entropy coordinates, as it also uses a statistical model to define coordinates for convex polygons, but our generalization to non‐convex shapes is different and based instead on the project‐and‐smooth idea of iterative coordinates. We show that our coordinates and their gradients can be evaluated efficiently and provide several examples that illustrate their advantages over previous constructions.

Weak form quadrature element analysis of spatial geometrically exact composite beams with torsional warping

Spatial thin-walled laminated composite beams under large deformations with torsional warping effects are studied. A novel two-dimensional cross-section model for composite beams with shear and torsion-warping deformations is proposed wherein the three-dimensional warping and coupling effects caused by inhomogeneous anisotropic materials are considered. A weak form quadrature element formulation is established for nonlinear analysis of geometrically exact composite beams with torsional warping and shear deformations. By combining the two-dimensional cross-section model and the nonlinear one-dimensional beam model, the three-dimensional stress and strain fields can be obtained. Numerical examples are provided to investigate the torsional warping effects and verify the effectiveness of the present formulation. Results of the present beam formulation which are achieved at a significantly lower computational cost are in excellent agreement with those of shell and solid models of commercial codes.

Interdependent evolution of deformation, fracture and recovering deposition during laser powder bed fusion

Common defects such as fracture and deformation seriously affect the quality of laser powder bed fusion (PBF) components. This work focuses on the understanding and the in situ monitoring of structural fracture and deformation during laser PBF. The transient interactive processes of normal deposition, fracture, severer warping deformation and recovering deposition during laser PBF are explored via a series representative cantilever structures. The interdependent evolutions of the critical factors are revealed via a novel model with validations of critical experimental results. The inherent strain and the cohesive force methods are integrated and the coupled stress-deformation-fracture processes can be computed by the model. It was found that the parts experienced different stages of the four interdependent processes of deposition, stresses, deformation, and fracture, depending on the structural features, input energy densities, and intermediate layer-wise processes. A typical phenomenon was discovered that components can exhibit a near-flat top surface but a curved bottom delaminated from the substrate, which implied the misleading monitoring information from the printing plane. The revealed mechanisms and visualized processes provide a useful guidance for the determination of the optimum time window for in situ monitoring which can judge the underneath fracture and deformations from the surface features.

Theoretical Method to Predict Internal Force of Crossbeam in Steel–Concrete Composite Twin I-Girder Bridge under Torsional Loading

During the operational phase of a bridge, the crossbeam, acting as a supporting member, plays an important role in keeping the cross-sectional shape constant in addition to resisting against various lateral and longitudinal loads and distributing the dead and the live loads to the adjacent main girders. The complex functional requirements lead to a complex internal force composition of the crossbeam. When subjected to torque, the two main beams of the twin I-girder bridge will have deformation in opposite longitudinal directions (known as warping deformation) to counteract the torque. The existing research has not considered the impact of main beam warping deformation on the internal force of the crossbeam. Based on the existing research, this article further considers the impact of main beam warping deformation on the internal force of the crossbeam, making the calculation of the internal force of the crossbeam more accurate. The results show that the torsional characteristics of the continuous twin I-girder bridge can be calculated using Vlasov’s theory of thin-walled structures combined with the displacement method. As for the effect of the crossbeam on the torsional stiffness of the structure, it can be managed by making the crossbeam stiffness continuous; however, in general, the equivalent stiffness is small compared to the stiffness of the main beam and it can be ignored. The crossbeam can be simplified to a bar with two solid ends for the internal force calculation whose formula is proposed in this paper, based on the existing frame model, and it can further consider the influence of warping deformation of the main beam on the internal force of the beam, and the calculation accuracy is high.

In-plane and out-of-plane free vibration analysis of thin-walled box beams based on one-dimensional higher-order beam theory

In this paper, the accurate free vibration characteristics of thin-walled box beam are discussed and the kinematic model is established by using fine shear deformation theory. The model adopts the in-plane and out-of-plane displacement fields including extension, torsion, warping and distortion, as well as the transverse shear due to bending and warping due to torsion. One-dimensional high-order beam theory is applied to the dynamic solution of thin-walled box beam, and the analytical solution of high free vibration modes of multi-deformation coupled modes under different boundary conditions is derived. The results show that warping, distortion and shear deformation play an important role in the free vibration characteristics of thin-walled box beam, and the validity of the model is verified. In addition, finite element software (ANSYS) is used for finite element simulation. The application of vibration mode in the structure design of thin-walled box beam is summarized, especially in the case of higher natural frequency. The calculation method is in good agreement with the finite element results.

Warping included mixed finite elements for bending and stresses of functionally graded exact curved beams

This study presents a warping included mixed finite element formulation for the static and stress analyses of functionally graded (FG) exact curved beams. Another distinctive feature of this study is to present the range of geometric and material parameters where the first-order shear deformation theory lacks necessary precision. The constitutive equations are derived from the 3D elasticity theory of an elastic continuum. The couple effects are considered in addition to the variations of FG material constituents through the transverse/axial directions. The mixed finite element formulation is enhanced by the cross-sectional warping deformations over a displacement-type finite element formulation. The two-noded curved mixed finite elements with 12 degrees of freedom at per node are derived over exact curvature and length. Satisfactory results are obtained for the static responses and stresses of axially FG-sandwich and transversely FG exact curved beams with power-law dependence compared to the 3D behavior of brick finite elements. Finally, the influences of ellipticity, width to thickness ratio, FG material constituents, and material gradient index on the static response of FG exact curved beams are investigated.

Identification of Cement Pavement with Temperature Effect and Evaluation of Polymer Grouting Effect.

The falling weight deflectometer (FWD) detection system benefits from its outstanding characteristics of no damage, fast speed, and high precision. The warping deformation of cement concrete pavement occurs due to the temperature difference along the depth of the slab, which makes FWD detect different results under different temperature fields. In this study, we systematically carried out the cement pavement's temperature field and deflection test. The experimental data were analyzed to obtain the temperature variation law of the top and bottom of the pavement slab every day. By establishing a three-dimensional finite element model of cement pavement with a multi-layer elastic foundation type, the influence of the temperature difference at the bottom of the slab on the deflection of the center point of the slab corner load under different working conditions, different seasons, different loads and whether there is polymer filling in the void area was studied. We summarize the correlation between the temperature difference and the influence coefficient and propose the cement pavement void identification and polymer grouting effect evaluation method considering the temperature effect.

Research on warping optimization of automobile mesh based on artificial intelligence algorithm

Automobile mesh is a typical large plastic part prone to warping deformation in the manufacturing process, which seriously affects the quality of products. The traditional method is to find the optimal combination parameters to reduce warping deformation in the forming process through repeated trial or mold flow analysis with high cost. In this study, An optimization method based on an artificial intelligence algorithm is proposed to optimize the warping deformation of the automobile mesh. In the optimization method, artificial intelligence regression algorithm-support vector machine regression was used to establish the nonlinear function relationship (prediction function) between the molding process parameters and the warpage of automobile mesh, and the performance of the prediction function was optimized by a genetic algorithm. The optimized prediction function was taken as the fitness function, the warping value was regarded as the fitness value, and genetic algorithm is used again to obtain a set of optimal process parameters and minimum warpage values. Finally, the reliability of the optimization method is verified by the modal flow analysis software.

Unsupervised Template Warp Consistency for Implicit Surface Correspondences

AbstractUnsupervised template discovery via implicit representation in a category of shapes has recently shown strong performance. At the core, such methods deform input shapes to a common template space which allows establishing correspondences as well as implicit representation of the shapes. In this work we investigate the inherent assumption that the implicit neural field optimization naturally leads to consistently warped shapes, thus providing both good shape reconstruction and correspondences. Contrary to this convenient assumption, in practice we observe that such is not the case, consequently resulting in sub‐optimal point correspondences. In order to solve the problem, we re‐visit the warp design and more importantly introduce explicit constraints using unsupervised sparse point predictions, directly encouraging consistency of the warped shapes. We use the unsupervised sparse keypoints in order to further condition the deformation warp and enforce the consistency of the deformation warp. Experiments in dynamic non‐rigid DFaust and ShapeNet categories show that our problem identification and solution provide the new state‐of‐the‐art in unsupervised dense correspondences.

A novel method to combine fused deposition modelling and inkjet printing in manufacturing multifunctional parts for aerospace application

Nowadays, the fabrication of smart product with sensing capability is still an arduous task due to the difficulties in integrating multifunctional materials using conventional method. To address this problem, this study presents a novel method to manufacture the multifunctional parts using fused deposition modeling (FDM) and inkjet printing (IJP) technologies. Firstly, the influence of process parameters on building time (BT), surface roughness (SR) and ultimate tensile strength (UTS) of poly-ether-ether-ketone (PEEK) samples manufactured by FDM was studied. Then, IJP was used to fabricate conductive lines on the surface of printed PEEK substrates. Finally, the process-structure–property relationship of PEEK parts before and after printing the conductive line was investigated. It is concluded that the BT and the SR of PEEK parts are significantly increased with an increased layer thickness, while the UTS increases steadily with an increase of nozzle temperature. Moreover, the maximum SR of 35.352 μm and the maximum UTS of 73.649 MPa are obtained at the infill angle of 45°. Furthermore, the warping deformation of PEEK samples will greatly affect SR during the real manufacturing, especially at both ends of the printed parts. Printed lines showing good aesthetic quality and the lowest electrical resistance (6.838 Ω/cm) are obtained on PEEK samples with the infill angle of 90°. This study demonstrates the possibility of manufacturing structure-integrated antenna by the combination of FDM and IJP processes.

Simulation and analysis of sintering warping and thermal stress for a cermet half-cell of solid oxide fuel cells

Warping deformation often appears due to internal thermal stress generated during sintering process of solid oxide fuel cell (SOFC) functional layers composed of metal and ceramic composite materials. In this study, a model is developed for a half-cell of an anode-supported design SOFC to simulate warping displacement and thermal stress generated at the highest sintering temperature of 1673 K. A sensitivity analysis is further conducted, and the orthogonal experimental method is applied for parameter optimization. The predicted results reveal that the warping displacement is reduced by 64.3%, while the maximum thermal stress decreases by 55.8% as combined parameters are optimized. In addition, the effects of thickness and fillet treatment on the thermal stress and deformation are also investigated. It is found that the anode support layer is a dominant factor, and its thickness should not be less than 550 μm; the thickness of the electrolyte layer should be maintained at 20 μm; while the treatment of 10 mm fillets on the 10 × 10 cm2 scaled half-cells is favorite.

A thermo-elastic-hydrodynamic model for air foil thrust bearings considering thermal seizure and failure analyses

This study aims to investigate the thermo-elastic performance of an air-lubricated thrust bearing under the thermal failure effect. A thermo-elastic-hydrodynamic model was established using temperature-dependent alloy material properties. The thermo-elastic deformation characteristics were analyzed based on the fluid-thermal-structure interaction approach. The mechanisms of bearing thermal seizures and failure behavior were studied. The results show that the rotor thermal warping deformation at low rotating speed plays a leading role in the increase of the film thickness. The rotor-foil thermal seizure occurs in a high rotating speed. The additional forced cooling conditions effectively reduce the risk of thermal failure.

Calculating the ultimate strength of a tube–gusset KT joint with 1/4 ring stiffener plates

In this study, experiments, numerical simulations, and theoretical analyses were performed on tube–gusset KT joints with 1/4 ring stiffener plates, which are frequently used in electrical transmission line towers. The failure modes and mechanisms of the joint were determined to comprise either ‘chord failure’, in which the chord exhibits obvious deformation while the stiffener plate exhibits little deformation, or ‘stiffener plate failure’, in which the chord exhibits obvious concave deformation and the stiffener plate exhibits obvious warping deformation. An increase in chord axial compression caused the ultimate bearing capacity of the joint to decrease, though when the ratio of axial chord force to plastic limit was less than 0.2, this effect of was not obvious. Furthermore, an equation for the ultimate strength of a joint was proposed based on the conservation of energy, which was subsequently verified against test and finite element model results. In this equation, the influence of the chord axial compression on the bearing capacity of the joint is considered using the coefficient β, which is dependent on the ratio of the chord diameter to the chord thickness. Finally, the proposed bearing capacity calculation method was shown to reproduce the numerical analysis results more accurately than the Japanese code or CIDECT code. Thus, the proposed calculation method can be confidently used to guide joint design in electrical transmission line tower projects.