Three-dimensional Displacement Field Research Articles

Introducing a computer simulation to model flexural vibrations of sandwich structures reinforced by advanced nanocomposites surrounded by auxetic concrete foundation

This study introduces a computer simulation framework aimed at analyzing the flexural vibrations of sandwich structures comprising a polymer core sandwiched between two face sheets reinforced with graphene oxide powder (GOP) nanocomposites. The sandwich structures are situated on an auxetic concrete foundation, incorporating sophisticated theoretical formulations to approximate the three-dimensional displacement fields of GOP-reinforced rectangular plates under varying loading conditions. The research addresses the complex interplay of material properties and geometric configurations, crucial for optimizing the structural performance of advanced composite materials in practical applications. The computational model integrates analytical techniques to predict the dynamic behavior of the sandwich structure’s flexural vibrations. Key parameters such as the dispersion of GOP within the polymer matrix, and the auxetic properties of the concrete foundation are systematically varied and analyzed to understand their impact on the overall structural response. Results from the simulations provide insights into the natural frequencies of the GOP-reinforced sandwich structures, offering valuable data for design engineers and materials scientists. The study underscores the potential of graphene oxide powder nanocomposites in enhancing the mechanical performance of sandwich structures, particularly when supported by innovative foundation materials like auxetic concrete. Future research directions include validation and further refinement of the computational model to accommodate additional complexities and real-world conditions.

Introducing a computer simulation to model flexural vibrations of sandwich structures reinforced by advanced nanocomposites surrounded by auxetic concrete foundation

This study introduces a computer simulation framework aimed at analyzing the flexural vibrations of sandwich structures comprising a polymer core sandwiched between two face sheets reinforced with graphene oxide powder (GOP) nanocomposites. The sandwich structures are situated on an auxetic concrete foundation, incorporating sophisticated theoretical formulations to approximate the three-dimensional displacement fields of GOP-reinforced rectangular plates under varying loading conditions. The research addresses the complex interplay of material properties and geometric configurations, crucial for optimizing the structural performance of advanced composite materials in practical applications. The computational model integrates analytical techniques to predict the dynamic behavior of the sandwich structure’s flexural vibrations. Key parameters such as the dispersion of GOP within the polymer matrix, and the auxetic properties of the concrete foundation are systematically varied and analyzed to understand their impact on the overall structural response. Results from the simulations provide insights into the natural frequencies of the GOP-reinforced sandwich structures, offering valuable data for design engineers and materials scientists. The study underscores the potential of graphene oxide powder nanocomposites in enhancing the mechanical performance of sandwich structures, particularly when supported by innovative foundation materials like auxetic concrete. Future research directions include validation and further refinement of the computational model to accommodate additional complexities and real-world conditions.

A data-driven procedure for one-dimensional dynamic analysis of thin-walled beams with arbitrary cross-sections

This paper develops a one-dimensional dynamic model for thin-walled beams with arbitrary complex cross-sections in a data-driven way. In order to consider complicated deformations in the framework of a beam theory, a universal node system is first created to fit the deformed shape of a thin-walled cross-section, whether prismatic or curved, with or without symmetry. This helps to reduce the three-dimensional displacement field of the thin-walled beam to one dimension, and results in a preliminary higher-order beam model with limited precision loss. For the purpose of largely condense DOFs of the new model, a data-driven approach is proposed to identify cross-section deformation modes through the principal component analysis of free vibration deformation data of an unconstrained thin-walled beam. As a result, a compact set of core deformation modes are obtained and selected to update the preliminary model, leading to the refined higher-order beam model of high accuracy and efficiency. Examples are presented to illustrate the concrete implementation and check the effects of data-related controlling parameters of the proposed procedure. We also verify through numerical examples that the proposed model agrees well with plate/shell and other beam theories, and has remarkable advantages in physical interpretation, modeling simplicity and computation efficiency.

Measurement of three-dimensional volumetric displacement fields in structural porous adhesive joints, under tensile and tensile-shear load, by means of in-situ X-ray microtomography

Nowadays, structural bonding is increasingly used for its advantages over conventional joining methods such as riveting or welding. Bonding defects (incomplete polymerization, gradient of mechanical properties, and presence of pores, among others.) can significantly impact the mechanical behavior of these assemblies. Among these defects, the presence of pores, detectable by means of X-ray microtomography measurements, could have a significant influence on the mechanical strength of a bonded structure (reduction of the useful section, questioning of the continuity of the joint, and stress concentration, among others). The study of these pores populations by means of microtomographic measurements, as well as their evolution under mechanical stress, can therefore provide valuable information regarding the mechanical behavior. These data can provide information on (i) the mechanical behavior on a microscopic scale, (ii) the identification of mechanisms of damage and failure of the adhesive joint, or (iii) the measurement of volume displacement fields. In this work, a method for calculating volume displacement fields in an adhesive joint is presented, using the detected pores as markers. The robustness, limits, and effects of different parameters (noise, voxelization, among others.) on this algorithm are identified on synthetic data representative of an adhesive joint. Finally, the validation of the method is based on interrupted tests on relatively small bonded specimens (called mini-Scarf) under tensile and tensile-shear loads.

Three-dimensional surface deformation from multi-track InSAR and oil reservoir characterization: A case study in the Liaohe Oilfield, northeast China

Oil productions can result in pore pressure drop in the reservoir, generating an increase in effective stress and leading to reservoir compaction. The compaction in the subsurface reservoir translates to the earth's surface, which is manifested as a loss of elevation (land subsidence), causing damages to oil production facilities and surface infrastructures. The Liaohe oilfield, located in Liaohe River Delta (LRD), northeast of China, is one of the most significant subsidence areas in China as a direct consequence of oil extraction from the reservoir. Previous studies carried out in this area assumed the oil production-induced displacement retrieved from Interferometric Synthetic Aperture Radar (InSAR) corresponds only to vertical deformation. In this work, for the first time, we proposed a method to retrieve the full three-dimensional (3D) displacement field over the oilfield. We retrieved the vertical and east-west displacement components by combining the multiple-geometry InSAR line-of-sight (LOS) observations and retrieved the north-south component based on the assumption of a physical relationship between the horizontal and vertical displacement. Two ascending and two descending datasets from Sentinel-1 satellite covering the area were processed by an InSAR time series analysis over the 2017 to 2021 period, providing consistent displacement rate maps and displacement time series in the LOS direction. Spatial local-scale land subsidence was found in several producing fields over the deltaic region, including Shuguang, Huanxiling, and Jinzhou oilfields. The 3D displacement decomposition was then conducted in Shuguang oilfield. The derived 3D displacement field exhibit a circular subsidence bowl with a maximum subsiding rate reaching 212 mm/year, accompanied by a centripetal pattern of horizontal displacements with maximum rates up to 50–60 mm/year moving towards the subsidence center. The retrieved 3D displacements are in good agreement with predictions from the geomechanical modeling by assuming a disk-shaped reservoir subject to a uniform reduction in pore fluid pressure. Finally, we show the importance of knowing both the vertical and horizontal displacement in characterizing the lateral boundary of the subsurface reservoir.

The response of dry and wet silica sand to high velocity impact

Understanding the mechanisms governing the interaction of high-velocity projectiles and sand targets is important for numerous applications and industries. The high-velocity penetration of sand targets is known to be controlled by micromechanical phenomena; however, our quantification of these phenomena and our understanding of water saturation effects on target response is presently limited. To help improve our understanding of these phenomena, we performed impact experiments on wet and dry sand with in-situ and post-mortem analysis in a two-stage gas gun with varying impact chamber pressures. For in-situ analysis, we developed and used a novel experimental method for measuring projectile depth and three-dimensional displacement fields from orthogonal flash X-ray images acquired during the penetration process. We also employed in-situ high-speed imaging of ejecta. For post-mortem analysis, we examined final depths of penetration, particle size distributions, and permanent penetrator deformation. We found that impacts into wet sand targets featured enhanced sand displacements around projectiles, enhanced ejecta, and enhanced intermediate and final depths of penetration as compared to impacts into dry targets. We also found that impacts into wet targets led to less particle breakage than impacts into dry targets. Target chamber pressure was found to significantly influence final depth of penetration, likely through a fluidization process as air and fluid escaped the sample’s pores to equilibrate with the surrounding chamber pressure after initial impact. We discuss our findings in the context of existing literature and discuss the hypothesized origin of several of our observations with support from modeling efforts described elsewhere.

Free vibrations of axially loaded thin-walled shaft-disk rotors subjected to non-uniform temperature field

Research on vibrations of shaft-disk rotors in non-uniform thermal field is essential for the design of rotating machinery. In this paper, the dynamic model of axially loaded thin-walled shaft-disk rotors in axial non-uniform temperature field is developed, considering three-dimensional displacement fields of the shaft and disk. This model introduces the temperature-dependent properties of materials, and gyroscopic and centrifugal effects. Based on the Euler-Bernoulli beam theory and the Kirchhoff plate theory, Lagrange's equation is used to derive the differential equations of motion. By comparing with the results of the existing reference and finite element results, the accuracy of the present model is verified. The effects of the axial displacement of shaft, temperature-dependent material property, temperature difference, temperature distribution, disk position and axial preload on the free vibration of shaft-disk rotors are discussed. Results show that the present model can effectively predict free vibrations of shaft-disk rotors in axial non-uniform temperature field. The effect of thermal field on vibrations of shaft-disk rotors is affected by the rotational speed and disk location as well.

Fracture toughness evaluation of a nuclear graphite with non-linear elastic properties by 3D imaging and inverse finite element analysis

Effective small specimen tests are needed to obtain fracture toughness and elastic properties as the limited availability of irradiated graphite restricts the quantity and dimensions of test specimens. Both properties have evaluated simultaneously in a crack propagation test with the double cleavage drilled compression (DCDC) specimen geometry of a fine-grained graphite (SNG742) that has non-linear elastic properties in the unirradiated condition. Three-dimensional displacement fields were obtained by digital volume correlation of in situ laboratory X-ray computed tomographs, and the 3D crack geometry (crack tip position, crack opening displacements and angle) was determined objectively by a wavelet variance method. The tensile softening of the Young modulus was determined by inverse analysis of the strain field using the finite element model updating (FEMU) method. The strain energy release rate of the quasi-static propagating crack was calculated using the contour integral method in a finite element model with the derived non-linear elastic properties and the measured displacements as boundary conditions. The critical strain energy release rate was constant with crack length (118 ± 14 J m−2) and equivalent to a fracture toughness of 1.13 ± 0.07 MPa m1/2.

Three-dimensional analytical solution of free vibrations of a simply supported composite plate in contact with a fluid

Background:The quantification of fluid–structure interactions is critical for the design and optimization of marine structures. As composite materials gain more traction in naval construction, there is a dire need of modeling tools to detail the dynamic response of composites in contact with fluids. Current structural theories and finite-element simulations offer promising pathways, but their strong hypotheses on through-the-thickness deformations and high computational cost challenge their practical feasibility. Methods:We propose an analytical three-dimensional solution to the free vibration of a bidirectional composite, separating a fluid column from vacuum. We leverage Pagano’s method to describe the three-dimensional displacement field in each ply of the composite plate and the fluid potential in the form of a Fourier series. Results:An analytical solution to the coupled fluid–structure problem is derived by imposing the continuity of displacement and stress at the ply interfaces, as well as boundary conditions on dry and wetted plies. We specialize the solution to sandwich structures of naval interest, offering insight on how the interactions with water can dramatically affect mode shapes and through-the-thickness profiles of displacement and stress. Discussion:The proposed approach provides the foundations for the design of thick composite plates for use in marine structures.

Nonlinear transient response of graphene platelets reinforced metal foams annular plate considering rotating motion and initial geometric imperfection

Investigating the nonlinear transient responses of rotating annular plate is a worthy subject in aerospace and aeronautic fields. In this paper, the nonlinear transient response induced by pulse loads for the graphene platelets reinforced metal foams (GPLRMF) annular plate with rotating motion is illustrated by time history curves and phase trajectory. Three-dimensional displacement field is captured by employing the first-order shear deformation theory (FSDT). The modeling accuracy of nonlinear transient response for the annular plate resting on viscoelastic foundation is enhanced by using von-Kármán's nonlinearity. The assumed mode method is used to solve the highly coupled nonlinear governing equations, and the fourth order Runge-Kutta iterative algorithm is applied to track the nonlinear transient response path. Detailed parametric studies are performed to investigate the effects of initial geometrical imperfection, dispersion and weight fractions of graphene platelets (GPLs), distribution types and coefficients of porosity, geometric dimensions of annular plates, viscoelastic foundation, thermal effect, types and properties of uniformly distributed pulse loads as well as rotating motion on nonlinear transient response of the annular plates. It turned out that, the blast load can significantly affect the dynamic behavior of the annular plate. Additionally, the annular plate with larger initial geometric imperfection has better deformation resistance, and the presence of the rotating motion can increase the maximum vibration amplitude of the annular plate.

Phase retrieval ofelectron rocking curves using total variation andtotal squared variation regularizations.

In this study, a new method for the phase retrieval of electron rocking curves observed using convergent-beam electron diffraction, which is applicable to the determination of three-dimensional lattice displacement fields along the beam direction, is proposed. Total variation and total squared variation regularizations are introduced for phase retrieval to suppress overfitting to noise or background signals in the rocking curves and to reproduce the sparse characteristics of displacement fields, which exist only near lattice defects. The results show that the proposed algorithm is effective for rocking curves modulated by the dynamical effect of electron diffraction. The accuracy of phase reconstruction using the proposed method is also discussed. Phase retrieval of the experimental rocking curves obtained from a stacking fault in stainless steel is demonstrated.

Radial Gradient Seismic Metamaterials with Ultra-Low Frequency and Ultra-Wide Band Gap

In this paper, a radial gradient seismic metamaterial (RGSM) is proposed. The structural unit cell is composed of an external square soil embedded with a triangular-cross-sectioned steel ring, which is filled at different angles of multiple steel rings to form a supercell. The dispersion curve and attenuation spectrum of the unit cell are calculated by the finite element method, and the opening mechanism of the band gap is explained by analyzing the modes at the band gap boundary. The influence of geometric parameters and material parameters on the band gap is further studied, and the optimized supercell radial gradient seismic metamaterial (OS-RGSM) structure is designed through structure and parameter optimization. The ultra-low broadband excellent band gap in the range of 2.35–20 Hz for seismic Lamb waves is realized, and its three-dimensional frequency response and displacement field diagram are calculated. In addition, the attenuation characteristics of the optimized supercell seismic metamaterial on the seismic surface wave are calculated and analyzed. It is found that the attenuation can reach more than 50% in the ultra-low frequency range of 3.5–9 Hz. The seismic wave barrier is verified by the vibration transmission characteristics of RGSM under finite period and dynamic time history analysis. The results show that RGSM can effectively shield from seismic Lamb waves in the ultra-wideband with the starting frequency of 2.35 Hz and can also effectively attenuate the seismic surface wave in semi-infinite space.

Research on the Dynamics of the Space Tubular Expandable Structure Driving Deployment Unit

The limitations associated with traditional screw-based and cable-based deployment mechanisms for space deployable structures, such as deployment stiffness, accuracy, and distance, are effectively overcome by introducing the concept of a variable diameter internal drive device. To enhance stability during the discontinuous surface transition phase inside the tubular structure, a thin-walled flexible beam structure is adopted for the driving deployment unit. The analysis employs the spatial absolute nodal coordinate formulation, integrating the pose states of each node into the global coordinate system. The three-dimensional displacement field and rotational angle changes at different time intervals are obtained using the unit shape function matrix and Kirchhoff theory. Subsequently, a dynamic model of the corresponding spatial nodes is established using the virtual work principle. This significant improvement enhances the dynamic characteristics of the coupled rigid-flexible deformation of the driving deployment unit under radial and axial external forces, surpassing the previously used flexible beam structure. The dynamic simulation analysis is performed using the finite element method and validated through experimental tests. The experimental results confirm the driving deployment unit’s stability and successful achievement of the desired functionalities, as demonstrated by the endpoint displacement, three-dimensional centroid displacement, and trajectory rotation angle.

Finite element models with node-dependent kinematics based on Legendre polynomials for the global–local analysis of compact and thin walled beams

In the present work, enhanced one-dimensional finite elements with node-dependent kinematics are proposed for the static analysis. Finite element governing equations are derived by applying the Carrera Unified Formulation. This framework subdivides the three-dimensional displacement field into a cross-section domain and an axis domain. The dimension along the beam is discretized by using Lagrange-based shape functions. At each node of the element, an independent structural theory can be imposed, thus obtaining a node-dependent kinematic model. This method permits to focus on the finite element node. In this way, several combinations of kinematics can be used together. In particular, Taylor-based and Legendre-based expansions have been adopted in this paper to create global–local models without using special coupling methods. The results have been compared with well-established benchmarks from the literature. Compact section and thin-walled beams have been taken into account. Results have been given in terms of displacements and stresses. It is shown that the present model provides high accuracy with a reduced number of degrees of freedom.

Experimental study on the spatial fracture behaviour of red sandstone containing weak inclusions with non-unitary geometric features under uniaxial compression

The failure of weakly filled rock masses is an important factor in the safety and stability of rock engineering. To investigate the spatial fracture behaviour of red sandstone with non-unitary geometric weakly filled joints, uniaxial compression experiments were carried out. The 3D DIC and acoustic emission (AE) technology were used to obtain the three-dimensional spatial deformation information and AE parameters of specimens containing both planar and circular weak inclusions, respectively. The main results are as follows: (1) The results show that the ductility of planar weak inclusions has a certain deterioration effect on the bearing capacity of the specimens, and the extent of this deterioration effect is not constant. (2) When the ductile length of the planar weak inclusions increases, the three-dimensional spatial displacement and strain fields of the specimens are divided by the planar weak inclusions, showing different degrees of deformation behaviour and different distribution patterns in the upper and lower parts. (3) The three-dimensional spatial fracture characteristics of specimens with different ductile lengths of planar weak inclusions will be dominated by the ductility, and the main failure mode of the specimen will gradually evolve from shear failure to splitting failure. The “guiding effect” of circular hole weak inclusions on the main crack is no longer evident when the ductility of planar weak inclusions is at its maximum. (4) The growth trend of the cumulative AE counts can be divided into four stages, and the stage characteristics are significantly influenced by the ductile length of the planar weak inclusions; different failure modes show different AE signal distribution characteristics. In addition, the key points of stability control of rock masses containing weak inclusions in practical engineering are discussed.

Investigation of carbon-aramid hybrid braided composites using digital volume correlation

Hybrid braided composites combine two or more reinforcing fibres in a matrix. Limited research on hybrid braided composites has been conducted. The Digital Image Correlation (DIC) method has been used to understand hybrid braided composites' external deformation and strain. However, DIC measurements do not provide sufficient information on the internal behaviour of hybrid braids. Therefore, this study focuses on understanding the behaviour of hybrid braids Digital Volume Correlation (DVC). DVC is a micro-computed tomography (Micro-CT) based volumetric strain measurement technique that allows for the internal strain fields of an object. Tensile loading of the Carbon-Aramid hybrid braided samples is achieved using an integrated material testing stage. DVC is used to generate three-dimensional displacement and strain fields and understand the internal strain behaviour of hybrid braided composites. The peak and strain observed for the sample was around −0.065 (µm/µm) and 0.017 (µm/µm), respectively. The effect of contrast-enhancing tracking particles on the DVC resulting DVC strain fields were also examined. Samples with and without contrast particles were subjected to in-situ loading and then analyzed using the DVC process. From this comparison, it was found that the addition of contrast-enhancing particles improves the volumetric strain results from the DVC measurements.

3D numerical modeling for thermo-mechanical behavior of additively manufactured titanium alloy parts with process-induced defects

The defects due to the rapid heating and cooling in powder bed fusion affect significantly the mechanical properties of additively manufactured as-built parts. However, the effect of process-induced defects on the thermo-mechanical behaviors of as-built parts is still unclear. In this paper, considering the process-induced interfacial lack of fusion (LoF) and pores, we developed a coupled thermo-mechanical model of titanium alloy parts in the powder bed fusion process. The equivalent temperature-dependent thermal properties of the parts with defects are calculated based on mixture theory. The three-dimensional thermal, mechanical, and displacement fields are predicted based on the differential quadrature method (DQM). The accuracy of the proposed model is verified by the comparison with the predictions and experimental data in the references. The effect of crucial parameters on the thermo-mechanical responses of as-built parts is analyzed, including energy densities, scan patterns, preheating temperature, LoF dimension, porosity, and powder layer thickness. The predicted results show that the process and geometry parameters play a vital role in the temperature distribution, residual stress buildup, and deformation of the printed parts. In addition, the LoF defect triggers the stress jump at the interface of the defect/powder bed and powder bed/substrate. The predicted results can be beneficial to provide a guideline for the design and additive manufacturing of titanium alloys.

Transmission of Vibrations from Windings to Tank in High Power Transformers

This article presents a step-by-step methodology for calculating transformer tank vibrations caused by electromagnetic forces. This approach uses 3D finite element models for both magnetic and structural calculations. Particular attention was paid to the description of momentum transfer between structural and fluid areas of the transformer. The actual geometry of the coils in the phase windings was taken into account. The dominant role of the axial component of the Lorentz force is the main conclusion of the article. The results are given in the form of three-dimensional displacement fields of the transformer tank presented together with the acoustic pressure field in the oil. The theoretical analysis is verified by laser-scanned vibration patterns on the tank wall.

Complex surface displacements of the Nanyu landslide in Zhouqu, China revealed by multi-platform InSAR observations

The Zhouqu County of Gansu Province in northwestern China is a geological hazard-prone area with frequent landslide and debris flow events. As a recent example, the Jiangdingya landslide, a smaller landslide within the larger ancient Nanyu landslide, was reactivated and partially collapsed to block the Bailong River near the Nanyu Township on 12 July 2018. Previous studies have shown that heavy rainfall is the major triggering factor of the failure event, but the spatio-temporal pattern of surface displacements of the landslide remains unknown due to a lack of in-situ measurements on the slope. In this study, we retrieved the surface displacements of the Nanyu landslide before the slope failure event using time-series Synthetic Aperture Radar Interferometry (InSAR) analysis of Sentinel-1 and ALOS-2 PALSAR-2 data. Our results show that the ancient Nanyu landslide has been in an unstable state prior to the failure event. To investigate the spatial patterns in displacement, we inverted a quasi three-dimensional (3D) surface displacement field using multi-orbit InSAR measurements combined with the surface parallel flow model, which showed a significant spatial heterogeneity in displacement patterns across the ancient landslide. In particular, a sign of local reactivation was observed on the upper slopes, which might be related to recent road construction activities. Furthermore, the detectability of unstable slopes near the Nanyu landslide with Sentinel-1 and ALOS-2 PALSAR-2 observations was analyzed to deepen our knowledge on the optimal choice of SAR data for geohazards detection and monitoring.

Global/local buckling analysis of thin-walled I-section beams via hierarchical one-dimensional finite elements

Buckling instability is one of the factors that limit the ultimate load-carrying capacity of I-section beams, and the coupling of global buckling and local buckling makes it difficult to predict the mechanical behavior of I-section beams. Hierarchical one-dimensional finite elements for the global/local buckling analysis of I-section beams are presented in this paper. Within the framework of Carrera’s Unified Formulation (CUF), a model is built by using Lagrange polynomials to describe the three-dimensional displacement field as an arbitrary order approximation by displacement variables over the beam cross-section. One-dimensional finite elements are obtained by discretizing the governing equation along the beam length. Due to its high efficiency and step length adaptability, the Asymptotic Numerical Method (ANM) is adopted to solve the nonlinear governing equations. Several typical buckling problems in I-section beams, including global buckling, local buckling and global–local coupled buckling, are investigated. The numerical results demonstrate the validity and efficiency of the proposed model. The critical buckling load and displacement field can be precisely predicted, and a good agreement is found in comparison with results obtained via three-dimensional finite element solutions.