Three-dimensional Finite Element Method Research Articles

Size dependent scaling law of plastic flow in FCC Nanolattices: A Dislocation Dynamics Study

Micro- and nanolattices can achieve simultaneously both lightweight and ultra-high strength due to a combination of resilient architecture and enhanced mechanical properties of small-scale unit constituents. However, understanding the fundamental deformation mechanism for these novel materials remains intriguing due to the intricate interplay of various geometric characteristics and intrinsic microscopic defects. Here, we investigate the fundamental mechanism of plastic deformation in terms of dynamic evolution of defects and corresponding mechanical responses in aluminum nanolattices using a mesoscale defect dynamics model which couples three-dimensional dislocation dynamics and finite element method. Our concurrently coupled model could capture detailed dislocation motion under complex loading conditions and predict the plastic flow stress of the nanolattices. We demonstrate that the size of individual constituent beam plays a critical role in the properties of nanolattices through small-scale strengthening, showing the strength of the nanolattices increases with decreasing beam size with the scaling law of σ∝db−0.89. As a result, the scaling law of plastic yielding with material density drastically increases from the continuum prediction. In addition, our modeling could allow us to study the geometric effect with various nanolattices. These findings establish a foundation for the fundamental understanding of the governing mechanism of plastic deformation, allowing access to a new regime in designing optimal structures using nanolattices.

Influence of Subsoil and Building Material Properties on Mine-Induced Soil–Structure Interaction Effect

Soil–structure interaction (SSI) refers to the dynamic interaction between a structure and the surrounding soil on which it rests. The behavior of the soil can significantly affect the response of the building structure. In the context of civil engineering and structural analysis, SSI becomes particularly important when considering the response of structures to dynamic loads such as earthquakes or so-called paraseismic loads, e.g., mining tremors. Several factors contribute to SSI. Soil and building structure material properties, foundation type, and loading conditions are the most important parameters. The article concerns SSI in the case of mining rock bursts in Poland. The influence of changes in site material conditions and building material properties on the SSI phenomenon was investigated. A few variants of different properties of typical construction materials (brick, reinforced concrete, and cellular concrete) in the case of selected representative building structure were considered. The subsoil material properties from the wide range were also taken into account. Numerical three-dimensional finite element method (FEM) analysis was applied. The adopted models of the soil-structure system were verified by data from in situ experimental vibration measurements. A significant influence of the subgrade material and the building structure material on the SSI was demonstrated.

Examination of Precast Concrete Movement Subjected to Vibration Employing Mass-Spring Model with Two Convective Masses

This article investigates the movement of concrete subjected to vibration employing mass-spring model. For this purpose, two different prefabricated concrete-formworks, on which experimental work was done before, were analysed analytically. The theoretical modeling of precast formworks employed in experiments has been made by the three-dimensional finite element method employing the SAP2000 program. Modeling of mortar is performed to resolve the interaction between the fresh concrete and formwork using the mass-spring model. Considering the dynamic behavior of the fluid, it is possible to define multiple oscillation (convective) masses with different frequency values in addition to the impulse mass. Thus, one impulse mass and two convective masses were used in the mass-spring model. This study is essentially theoretical, and its accuracy has been strengthened by experimental work. The time-dependent results of concrete movement obtained from the dynamic mass-spring model were compared with the measured ones. The matches indicate that the findings are consistent.

In-plane behaviour of masonry infill walls with openings strengthened using textile reinforced mortar

A numerical study was carried out to simulate the in-plane behaviour of a 1:2.5 scaled one-storey one-bay masonry-infilled reinforced concrete (RC) frame retrofitted with textile-reinforced mortar (TRM). The study used ABAQUS finite element analysis (FEA) software and a three-dimensional (3-D) finite element method. Using a ductile design and details, the TRM-reinforced structure encountered in-plane displacement-control cyclic loads during the test. This study assesses how accurately a representative numerical model can replicate the results of an experimental test. Parametric research was conducted following the numerical model's calibration. To develop a suitable numerical model, suitable constitutive models based on the concrete damage plasticity (CDP) approach were used to characterize the nonlinear response of TRM, masonry infill, and concrete. The experimental findings, which aggrandize the response simulation, served as the basis for calibrating the models. Using a finite element framework and the simplified micro model technique, the masonry structure is simulated at the infill component level. The numerical model demonstrated accurately the ability to simulate the in-plane behaviour of the modified RC frame with infill walls, including its initial stiffness, deterioration, deformation-resisting ability, and failure patterns. Furthermore, a parametric study was conducted to determine the significance of the full-bond scenario between the RC frame infilled with masonry and the TRM considering: (1) the location of the strengthening material on the specimen and (2) the number of layers of the strengthening material. All retrofitted wall specimens showed a considerable improvement in in-plane performance; some features of the wall's behaviour were found to be strongly influenced by the parameters under examination. It can be observed that the specimen with two layers of TRM on both sides of the infill wall exhibit the maximum lateral load carrying capacity and maximum deflection resisting characteristics while the other retrofitted specimens controlled the deflection to some extent and significantly enhancing the load carrying capacities of the masonry system.

Precise regulation of surface plasmonic hotspots in an Au split nanoring coupled system

The signal enhancement in plasmon-enhanced spectroscopy is primarily contributed by hotspots generated through the surface plasmon resonance effect. Precise control of hotspot positions within nanostructures is of great significance in surface-enhanced Raman spectroscopy (SERS) and high spatial resolution imaging. However, predicting the positions of hotspots is challenging due to the small nanogaps and complex plasmonic interactions. In this study, we theoretically investigate the localized surface plasmonic properties of split ring nanostructure. The effects of variations in the inner radius, gap distance and thickness of the split ring on the hotspot distribution at the nanogaps are systematically analyzed using a three-dimensional finite element method. The results demonstrate that precise control over the positions and quantities of hotspots can be achieved by choosing the excitation wavelength and the gap size of the split rings. The calculated maximum Raman enhancement obtained at the hotspots can reach nine orders of magnitude. Our findings not only contribute to a deeper understanding of the SERS enhancement mechanism, but also provide theoretical insights for further development of surface-enhanced fluorescence, plasmonic sensors, and super-resolution imaging in the field of interface spectroscopy.

Experimental and numerical analysis of the behavior of rehabilitated aluminum structures using chopped strand mat GFRP composite patches

PurposeThis paper comprehensively addresses the influence of chopped strand mat glass fiber-reinforced polymer (GFRP) patch configurations such as geometry, dimensions, position and the number of layers of patches, whether a single or double patch is used and how well debonding the area under the patch improves the strength of the cracked aluminum plates with different crack lengths.Design/methodology/approachSingle-edge cracked aluminum specimens of 150 mm in length and 50 mm in width were tested using the tensile test. The cracked aluminum specimens were then repaired using GFRP patches with various configurations. A three-dimensional (3D) finite element method (FEM) was adopted to simulate the repaired cracked aluminum plates using composite patches to obtain the stress intensity factor (SIF). The numerical modeling and validation of ABAQUS software and the contour integral method for SIF calculations provide a valuable tool for further investigation and design optimization.FindingsThe width of the GFRP patches affected the efficiency of the rehabilitated cracked aluminum plate. Increasing patch width WP from 5 mm to 15 mm increases the peak load by 9.7 and 17.5%, respectively, if compared with the specimen without the patch. The efficiency of the GFRP patch in reducing the SIF increased as the number of layers increased, i.e. the maximum load was enhanced by 5%.Originality/valueThis study assessed repairing metallic structures using the chopped strand mat GFRP. Furthermore, it demonstrated the superiority of rectangular patches over semicircular ones, along with the benefit of using double patches for out-of-plane bending prevention and it emphasizes the detrimental effect of defects in the bonding area between the patch and the cracked component. This underlines the importance of proper surface preparation and bonding techniques for successful repair.Graphical abstract

Correction: An enhanced flux continuity three-dimensional finite element method for heterogeneous and anisotropic diffusion problems on general meshes

Correction: An enhanced flux continuity three-dimensional finite element method for heterogeneous and anisotropic diffusion problems on general meshes

Cross-sectional analysis of initially curved composite beams with rectangular and circular sections using an asymptotic meshless method

An analytical meshless cross-sectional dimensional reduction method is developed to perform structural analysis of initially curved composite beams. By introducing the Pascal polynomials in the Cartesian coordinates system for beams with rectangular cross-sections and in the polar coordinates system for the beams with circular cross-sections to the warping field, a three-dimensional beam problem can be split into a two-dimensional cross-sectional analysis and a one-dimensional along the reference line of the beam. The obtained cross-sectional stiffness matrix based on higher-order of the strain energy can be incorporated into a one-dimensional finite element solution for initially curved composite beams, for the purpose of strain and stress analysis. Finally, the three-dimensional strain through the thickness of the beam can be achieved by the recovery analysis. The present method takes advantage of Pascal polynomials so that the solution procedure will be more simplified and computationally more efficient compared to three-dimensional finite element (3D FE) method. The proposed method for different isotropic and anisotropic beams is examined and compared with the literature, 3D FE, and Variational Asymptotic Beam Sectional (VABS) package which is a finite element based cross-sectional analysis tool for composite beams.

Numerical Simulation of Cathode Nodule Local Effects

As one of the main factors decreasing current efficiency and product quality, the growth of nodules deserves attention in the copper electrorefining process. Three-dimensional (3D) Finite Element Method models combining tertiary current distribution and fluid flow were established in this study to investigate the details of the growth of columnar nodules, including the electrolyte flow around the nodule and its effects. Compared with an inert nodule, a significant impact of the electrochemical reaction of an active nodule has been observed on the fluid flow, which may be one of the reasons for the formation of small nodule clusters on the cathode. Furthermore, the local current density is not even on the nodule surface under the comprehensive influence of local electrolyte flow, local overvoltage, and the angle with the anode surface. Thus, the head of an active nodule grows faster than the root, and the upper parts grow faster than the lower parts, leading to asymmetric growth of the nodules.

Analytical Model for Non-linear $$\user2{M - }\,\,{\varvec{\theta}}$$ Relationships of Dowel-Type Timber Connections Exposed to Fire

AbstractRecent experimental evidence has shown that wood–steel–wood dowel-type connections exhibit a semi-rigid behaviour even after 90 min of fire exposure. Because a semi-rigid behaviour influences the bending moment distribution among structural members, considering the moment–rotation relationships within frame analyses in which structural members are modelled as beam elements can enable a realistic fire response analysis that is significantly simpler than the three-dimensional finite element method. This study proposes an analytical methodology that accounts for the thermo-mechanical behaviour of timber and dowels, enabling the simulation of the non-linear moment–rotation relationships under fire conditions. The proposed analytical model divides dowels into a series of elements on an elastoplastic foundation and performs a direct stiffness method in a time-incremental procedure using an element stiffness matrix derived from beam-on-elastic-foundation theory. This study also presents the results of load-carrying tests on timber frames with dowel-type connections performed under ambient and fire conditions. The analytical results were consistent with the fire test results. Additionally, the analyses were also performed under three conditions in which the dowels were rigid, linear elastic, and elastoplastic bodies. These three results converged to the same value after 65 min of heating, which suggests that the ultimate states of beams with dowel-type connections exposed to fire can be modelled by assuming that dowels are rigid bodies.

A Three-Dimensional Finite Element Analysis of A Two-Axially Pre-Loaded Plate Exposed To A Dynamic Force

In this paper, the forced vibration analysis by a harmonically time-dependent force of an elastic plate covered rigidly by a rigid half-plane is given. The plate layer is subjected to bi-axial normal initial force, into lateral sides separately. Here, the preloading state is exactly static and homogeneous. To eliminate the disadvantage of such a nonlinear model, the problem formulation is modeled in terms of the fundamental consideration of the theory of linearized wave in elastic solids under a pre-loaded state (TLWESPS) in a plane-stress case. For this purpose, considering Hamilton’s principles, the system of the partial equations of motion and the boundary-contact conditions are found. Based on the virtual work and the fundamental theorem of calculus of variation, the three-dimensional finite element method (3D-FEM) is used to understand the dynamic behavior of the plate. A numerical validation process is established. Next, influences of certain problem parameters such as Young’s modulus, aspect ratio, thickness ratio, pre-loaded parameter, etc. on the frequency mode of the pre-stressed system are given.

Finite element analysis (FEA) of stress distribution in platform-switched short dental implants.

The distribution of stress on short platform switched dental implants is of interest. Hence, the mandibular posterior molar area was modelled using a three-dimensional finite element method (FEM) with a continuous 1.5 mm cortical bone thickness and an inner cancellous bone core. The implants used in the study were 5 mm long, 4.5 mm wide and 3.5 mm wide at the abutments. 120 N of force was applied in both the vertical and oblique (20° and 35°) directions to create a realistic simulation. ANSYS Workbench was generated for each model. Von Mises stress was assessed in the cortical and cancellous bones at varying depths. Ten noded tetrahedron elements with three degrees of freedom per node were employed to interpret translations on the x, y, and z axes. The stress-based biomechanical behaviour of platform switched short osseo-integrated implants varied across all 5 positions in FEM simulations, based on the depth of implant placement, the direction of applied force, and the shape of the bone. Data shows that opposite forces to the vertical forces caused more damage. Thus, the implantation of subcrestal implants resulted in reduced stress on the cortical and cancellous bone.

Effects of electric and magnetic fields on the electronic properties in the asymmetrical biconvex lens-shaped GaAs/GaAlAs quantum dots

Theoretical investigation of electronic properties in asymmetric biconvex lens-shaped GaAs/GaAlAs quantum dots is considered in the presence of the external magnetic and electric fields. In addition, the effects of the dot size and the asymmetry of the structure on the electronic properties are also investigated. The shape of this quantum dot corresponds to the intersection of two differently centered spheres. The energy levels and wave functions of the shallow hydrogenic impurity in the structure with a finite potential are calculated numerically in cylindrical coordinates with the effective mass approach using a complex eigenvalue formalism through a two-dimensional axisymmetrical and three-dimensional finite element methods. The results reveal significant dependence of the calculated physical properties on lens dimensions, axial impurity position, and intensities of applied electric and magnetic fields.

An enhanced flux continuity three-dimensional finite element method for heterogeneous and anisotropic diffusion problems on general meshes

An enhanced flux continuity three-dimensional finite element method for heterogeneous and anisotropic diffusion problems on general meshes

Three-dimensional finite element analysis on stress distribution after different palatoplasty and levator veli palatini muscle reconstruction.

To establish a three-dimensional finite element model of the upper palate, pharyngeal cavity, and levator veli palatini muscle in patients with unilateral complete cleft palate, simulate two surgical procedures that the two-flap method and Furlow reverse double Z method, observe the stress distribution of the upper palate soft tissue and changes in pharyngeal cavity area after different surgical methods, and verify the accuracy of the model by reconstructing and measuring the levator veli palatini muscle. Mimics, Geomagic, Ansys, and Hypermesh were applied to establish three-dimensional finite element models of the pharyngeal cavity, upper palate, and levator veli palatini muscle in patients with unilateral complete cleft palate. The parameters including length, angle, and cross-sectional area of the levator veli palatini muscle etc. were measured in Mimics, and two surgical procedures that two-flap method and Furlow reverse double Z method were simulated in Ansys, and the area of pharyngeal cavity was measured by hypermesh. A three-dimensional finite element model of the upper palate, pharyngeal cavity, and bilateral levator veli palatini muscle was established in patients with unilateral complete cleft palate ; The concept of horizontal projection characteristics of the palatal dome was applied to the finite element simulation of cleft palate surgery, vividly simulating the displacement and elastic stretching of the two flap method and Furlow reverse double Z method during the surgical process; The areas with the highest stress in the two-flap method and Furlow reverse double Z method both occur in the hard soft palate junction area; In resting state, as measured, the two flap method can narrow the pharyngeal cavity area by 50.9%, while the Furlow reverse double Z method can narrow the pharyngeal cavity area by 65.4%; The measurement results of the levator veli palatini muscle showed no significant difference compared to previous studies, confirming the accuracy of the model. The finite element method was used to establish a model to simulate the surgical procedure, which is effective and reliable. The area with the highest postoperative stress for both methods is the hard soft palate junction area, and the stress of the Furlow reverse double Z method is lower than that of the two-flap method. The anatomical conditions of pharyngeal cavity of Furlow reverse double Z method are better than that of two-flap method in the resting state. This article uses three-dimensional finite element method to simulate the commonly used two-flap method and Furlow reverse double Z method in clinical cleft palate surgery, and analyzes the stress distribution characteristics and changes in pharyngeal cavity area of the two surgical methods, in order to provide a theoretical basis for the surgeon to choose the surgical method and reduce the occurrence of complications.

The effect of excitation current on radial electromagnetic force wave of tangential magnetizing parallel structure hybrid excitation synchronous motor

To study the influence of the magnitude of the excitation current on the radial electromagnetic force wave of the tangential magnetizing parallel structure hybrid excitation synchronous motor (TMPS-HESM) under different working conditions. Firstly, the basic structure of the motor and the rotor magnetic circuit model is introduced. Secondly, considering the influence of excitation current, the Maxwell stress tensor method is used to analyze the radial electromagnetic force wave of the motor and the source, frequency and order of the radial electromagnetic force wave that has a great influence on the electromagnetic vibration of the motor are qualitatively obtained. Then, the three-dimensional finite element method is used to calculate the variation law of the radial electromagnetic force wave when different excitation currents are applied under no-load and load conditions, revealing that the DC excitation will increase the amplitude of the radial electromagnetic force wave of a specific order. Meanwhile, the influence of load torque variation on the radial electromagnetic force wave is discussed, and it is found that the (2f, 8) and (6f, 24) order electromagnetic force waves are greatly affected by the armature reaction. The work provides a theoretical basis for further suppressing the electromagnetic vibration of this type of hybrid excitation motor.

Three-Dimensional Finite Element Modeling of Spray-Applied Pipe Liners Repaired Corrugated Metal Pipes Buried Under Shallow Cover

Corrugated metal pipes (CMPs) corrode over time. To maintain structural performance, deteriorated CMPS must be replaced or rehabilitated. Spray-applied pipe liners (SAPLs) are one of the quickest ways to rehabilitate deteriorated CMPs among other ways. Only a few lab tests and finite element studies from the past have been done on this new method. The calibration of a three-dimensional (3D) full-scale finite element method model using test results obtained at the Center for Underground Infrastructure Research and Education laboratory at the University of Texas at Arlington is covered in this paper. The tests were carried out on circular invert cut CMPs that had been rehabilitated with polymeric SAPLs. To repair the invert-cut CMPs, three different thicknesses were used: 0.25, 0.5, and 1-in. The removal of an 18-in. invert from the intact CMP represented the deterioration of the CMP. A full 3D corrugated model was developed to represent the test setup in the FE model using ABAQUS. To perform the calibration process, the load–displacement curves, earth pressure distribution, and strain around the liner were compared to the test results. The comparison of these parameters showed the capability of the model for verification. The verified FE model was used to generate the load–displacement graphs for other thicknesses and elastic modulus of the liner. In addition, the role of the embedment depth is also considered in the analyses in which the maximum deformation of the rehabilitated pipe has decreased by 58.9% with increasing the burial depth of the pipe from 0.4D (D = external pipe diameter) to 1.0D.

Numerical study of transient supercooling performance and thermal stress analysis of segmented annular thermoelectric cooler

A multiphysics-coupled numerical simulation of a segmental annular thermoelectric cooler (SATEC) was performed using a three-dimensional finite element method. A coupling model of the temperature, stress, and electric fields was established based on the three-dimensional transient states. Moreover, the effects of different pulse width (τ), pulse current amplitude (Pa), pulse current shape parameter (m), heat transfer coefficient (h), angle (θ), and length (H) of the thermoelectric leg on the SATEC transient properties and von Mises stress were studied. The results show that τ and Pa are the key influencing factors of SATEC. The larger the h, the more optimized the heat transfer effect of the SATEC hot end. However, when h increased to a certain value, the changes in the transient performance were insignificant. The optimal pulse can be achieved when the input pulse current Iop = 6.47 A and pulse width τ = 20 s. When the length of the thermoelectric leg H4 was 3 mm and the thermoelectric leg angle θ2 was 7°, the performance of SATEC was optimal, with Tc,min being 249.57 K, Tc,max being 279.50 K, thold being 5.5 s, and the maximum von Mises stress being 37.48 MPa. The results show that different supercooling indices and von Mises stresses could be obtained for different pulse current shapes. Geometric optimization of SATEC can improve the cooling performance and reduce the von Mises stress, thereby providing a theoretical reference for practical engineering applications and thermoelectric cooling research.

Analysis of competition and interference mechanisms of multiple hydraulic fractures in deep-sea hydrate reservoirs in the South China Sea

Improving the fundamental theory of hydraulic fracturing in deep-sea hydrate reservoirs is of great significance in enhancing the efficiency of gas hydrate mining. In this paper, a multi-cluster fracturing model for a horizontal well was established with a three-dimensional extended finite element method and the measured geo-mechanical data from hydrate reservoirs in the South China Sea. The performance, fracture initiation, and expansion mechanisms of multi-hydraulic fractures are investigated under different fracturing sequences, hydrate saturation and cluster deployment patterns. Some interesting results have been discovered: In the case of three-cluster, the fractures produced by sequential fracturing are notably more affected by pre-existing fractures. Furthermore, the effect of fracture interference between simultaneous and sequential fracturing is reflected in the middle fracture is compressed by the fractures on its left and right sides. The increase in hydrate saturation enhances the cementing ability of the sediments and results in an increased difficulty of fracture initiation for the five-cluster simultaneous fracturing. It also results in a decrease in the geo-stress field, where the interaction between fractures plays a dominant role in the process of fracture expansion, leading to non-uniform expansion.

Micromechanical Analysis of GFRP Composite with Micro-Level Defects

Fiber-reinforced plastic (FRP) composites are subjected to micro-level defects such as fiber-matrix debond and/or matrix cracks after a period of their service due to the increasing brittleness of matrix material. Prediction of the degraded elastic properties of a lamina through micromechanical studies by incorporating micro-level defects gives an idea of the health condition of such structures. Due to the limitations of classical mathematical approaches in solving complex structures, numerical mathematical methods like the finite element method (FEM) can be employed. The present investigation deals with the micromechanical analysis of Glass fiber-reinforced plastic (GFRP) composite with micro-level defects to predict some of the elastic properties. The composite is idealized as an array of square unit cells, and the micromechanical behavior of one such unit cell is simulated in ANSYS software using the three-dimensional finite element method to predict Young’s moduli and Poisson’s ratios in principal material directions. The converged finite element solution for longitudinal modulus is validated by the rule of mixtures and the other properties using the Maxwell–Betti reciprocal theorem. Variations of Young’s moduli and Poisson’s ratios due to an incremental internal failure of composite such as low-level, medium-level, and high-level defects at an expected range of fiber volume fractions (50% - 60%) are evaluated and estimated the percentage degradation with respect to a corresponding defect-free composite.