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Journal articles on the topic '2D Boundary Element model'

Author: Grafiati

Published: 5 June 2025

Last updated: 15 July 2025

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Chen, Leilei, Wenchang Zhao, Cheng Liu, and Haibo Chen. "2D Structural Acoustic Analysis Using the FEM/FMBEM with Different Coupled Element Types." Archives of Acoustics 42, no. 1 (2017): 37–48. http://dx.doi.org/10.1515/aoa-2017-0005.

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Abstract A FEM-BEM coupling approach is used for acoustic fluid-structure interaction analysis. The FEM is used to model the structure and the BEM is used to model the exterior acoustic domain. The aim of this work is to improve the computational efficiency and accuracy of the conventional FEM-BEM coupling approach. The fast multipole method (FMM) is applied to accelerating the matrix-vector products in BEM. The Burton-Miller formulation is used to overcome the fictitious eigen-frequency problem when using a single Helmholtz boundary integral equation for exterior acoustic problems. The continuous higher order boundary elements and discontinuous higher order boundary elements for 2D problem are developed in this work to achieve higher accuracy in the coupling analysis. The performance for coupled element types is compared via a simple example with analytical solution, and the optimal element type is obtained. Numerical examples are presented to show the relative errors of different coupled element types.

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Alaimo, Andrea, Alberto Milazzo, and Calogero Orlando. "Structural Health Monitoring of Cracked Beam by the Dual Reciprocity Boundary Element Method." Advanced Materials Research 538-541 (June 2012): 1634–39. http://dx.doi.org/10.4028/www.scientific.net/amr.538-541.1634.

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In this paper a 2D boundary element model is used to characterize the transient response of a piezoelectric based structural health monitoring system for cracked beam. The BE model is written for piezoelectric non-homogeneous problem employing generalized displacements. The dual reciprocity method is used to write the mass matrix in terms of boundary parameters only. The multidomain boundary element technique is implemented to model non-homogeneous and cracked configuration, unilateral interface conditions are also considered to prevent the physical inconsistence of the overlapping between interface nodes belonging to the crack surfaces. To assess the reliability and the effectiveness of the model numerical analyses are carried out on the modal and dynamic response of undamaged beam and results are compared with finite element calculations. Electrical response of piezoelectric sensors are then reported for different crack configurations in comparison with the undamaged case.

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Ashrafi, Hosein, M. R. Bahadori, and M. Shariyat. "Two-Dimensional Modeling of Functionally Graded Viscoelastic Materials Using a Boundary Element Approach." Advanced Materials Research 463-464 (February 2012): 570–74. http://dx.doi.org/10.4028/www.scientific.net/amr.463-464.570.

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In this paper, a 2D boundary element approach able to model viscoelastic functionally graded materials (FGM) is presented. A numerical implementation of the Somigliana identity for displacements is developed to solve 2D problems of exponentially graded elasticity. An FGM is an advanced material in which its composition changes gradually resulting in a corresponding change in properties of the material. The FGM concept can be applied to various materials for structural and functional uses. Our model needs only the Green’s function of nonhomogeneous elastostatic problems with material properties that vary continuously along a given dimension. We consider the material properties to be an exponential function of Cartesian coordinates x. As application, a numerical example is provided to validate the proposed boundary integral equation approach.

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Wilber, Michelle, and Getu Hailu. "A 2D Moving Mesh Finite Element Analysis of Heat Transfer in Arctic Soils." Thermo 3, no. 1 (2023): 76–93. http://dx.doi.org/10.3390/thermo3010005.

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Accurate soil heat transfer models are needed to predict and adapt to a warming arctic. A numerical model to accurately predict temperatures and thaw depths in soils, both with depth and with horizontal distance from features such as cliffs, was developed in Matlab using the finite element method. The model was validated against analytical solutions to simple versions of the problem and experimental temperature data from borehole thermistor strings on the north shore of Alaska. The current model is most useful for short term (on the order of days) predictions of thaw depth and near surface temperatures in homogeneous soils with existing data to allow the calibration of soil thermal parameters. These are exactly the time scales and capabilities that would integrate well with erosional models to predict the erosion during storm events and summer thaw conditions. Comparisons with analytical solutions show the model to be fairly accurate in predictions of temperatures thaw-depth and temperatures, within about 0.25 °C and 0.02 m respectively, for reasonable arctic soil parameters. Differences between predicted temperatures and thaw-depth against borehole data from Barter Island, Alaska are within about 1 °C and 0.5 m respectively. Comparison to commercial software, which does not directly track and move the phase change boundary, shows that this moving-mesh model has much better agreement. The model developed in this work is flexible and can be modified to model a wide variety of problems, but is efficiently set up to take a surface and thaw-boundary profile (not necessarily horizontal) and use soil parameters and surface boundary conditions appropriate to Arctic regions. It has been verified to appropriately model cliffs, which are particularly vulnerable to erosion.

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Petrov, Andrey, and Leonid A. Igumnov. "Dynamic Analysis of a Three-Dimensional Poroelastic Beam Using the Boundary-Element Method." Key Engineering Materials 769 (April 2018): 329–35. http://dx.doi.org/10.4028/www.scientific.net/kem.769.329.

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The problem of the effect of a normal harmonic force on a porous beam in a 3D formulation is solved using the boundary-element method. A homogeneous fully saturated elastic porous medium is described using Biot’s mathematical model. The effect of the porosity and permeability parameters on the deflection of the beam and the distribution of pore pressure over the beam thickness is investigated. The comparison of the boundary-element solution with a 2D numerical-analytical one is given.

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GUIOTTO, ANNAMARIA, ALESSANDRA SCARTON, ZIMI SAWACHA, GABRIELLA GUARNERI, ANGELO AVOGARO, and CLAUDIO COBELLI. "GAIT ANALYSIS DRIVEN 2D FINITE ELEMENT MODEL OF THE NEUROPATHIC HINDFOOT." Journal of Mechanics in Medicine and Biology 16, no. 02 (2016): 1650012. http://dx.doi.org/10.1142/s0219519416500123.

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The diabetic foot is one of the most serious complications of diabetes mellitus and it can lead to foot ulcerations and amputations. Finite element analysis quantifies the loads developed in the different anatomical structures and describes how these affect foot tissue during foot–floor interaction. This approach for the diabetic subjects’ foot could provide valuable information in the process of plantar orthosis fabrication and fit. The purpose of this study was to develop two finite element models of the hindfoot, of healthy and diabetic neuropathic subjects. These models accounts for in vivo kinematics, kinetics, plantar pressure (PP) data and magnetic resonance images. These were acquired during gait analysis on 10 diabetic neuropathics and 10 healthy subjects. Validity of the models has been assessed through comparison between the peak PPs of simulated and experimental data: root mean square error (RMSE) in percentage of the experimental peak value was evaluated. Two different finite elements analysis were performed: subject-specific simulations in terms of both geometry and gait analysis, and by adopting the complete gait analysis dataset as boundary conditions. Model predicted plantar pressures were in good agreement with those experimentally measured. Best agreement was obtained in the subject-specific case (RMSE of 13%).

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Pedroso, D. M. "Enriched Finite Element for Modelling Variable Boundary Conditions in Unsaturated Seepage Problems." Applied Mechanics and Materials 846 (July 2016): 372–77. http://dx.doi.org/10.4028/www.scientific.net/amm.846.372.

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Partial differential equations such as models for flow in unsaturated porous media are difficult to be solved when space-time variable boundary conditions are included. A general solution to this problem is discussed in this contribution and is devised in such a way that the face with variable boundary condition can be subjected to Dirichlet, Neumann or the so-called Signorini/ambiguous boundary conditions, considering the transition from one type to another. A method based on the enrichment of finite elements that is able to accurately model seepage with these complex boundary conditions is discussed. Simulations are presented illustrating the capabilities of the new method in 2D and 3D, including cases where the free surface varies due to rain.

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Florez, Sebastian, Julien Fausty, Karen Alvarado, Brayan Murgas, and Marc Bernacki. "A 2D Front-Tracking Lagrangian Model for the Modeling of Anisotropic Grain Growth." Materials 14, no. 15 (2021): 4219. http://dx.doi.org/10.3390/ma14154219.

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Grain growth is a well-known and complex phenomenon occurring during annealing of all polycrystalline materials. Its numerical modeling is a complex task when anisotropy sources such as grain orientation and grain boundary inclination have to be taken into account. This article presents the application of a front-tracking methodology to the context of anisotropic grain boundary motion at the mesoscopic scale. The new formulation of boundary migration can take into account any source of anisotropy both at grain boundaries as well as at multiple junctions (MJs) (intersection point of three or more grain boundaries). Special attention is given to the decomposition of high-order MJs for which an algorithm is proposed based on local grain boundary energy minimisation. Numerical tests are provided using highly heterogeneous configurations, and comparisons with a recently developed Finite-Element Level-Set (FE-LS) approach are given. Finally, the computational performance of the model will be studied comparing the CPU-times obtained with the same model but in an isotropic context.

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Tohti, Gulbahar, Dilinaer Mahemuti, and Mamatjan Tursun. "Finite Element Analysis to Stringer of a Semi-Trailer." Key Engineering Materials 522 (August 2012): 400–405. http://dx.doi.org/10.4028/www.scientific.net/kem.522.400.

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In this research, 2D and 3D FEM model of one stringer of a semi-trailer was built. Mesh generation and boundary conditions definition was processed on FAST software. Effective stress distribution diagram was obtained after FEM analysis to stringe structure under various working conditions. Main stress concentration area was defined and causes for stress concentration was analyzed. After all, suggestion for improvement and structure optimization was given.

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Bergfried, Christian, Samaneh Abdi Qezeljeh, Ilia V. Roisman, Herbert De Gersem, Jeanette Hussong, and Yvonne Späck-Leigsnering. "Thermal Finite-Element Model of Electric Machine Cooled by Spray." Energies 18, no. 1 (2024): 84. https://doi.org/10.3390/en18010084.

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The demand for higher power density in electrical machines necessitates advanced cooling strategies. Spray cooling emerges as a promising and relatively straightforward technology, albeit involving complex physics. In this paper, a quasi-3D thermal finite-element model of stator winding is created by the extrusion of a 2D cross-sectional finite-element model along the winding direction. The cooling effects of the spray impact are simulated as a heat flux that uses an impedance boundary condition at the surface of the winding overhang. The results confirm the advantageous performance of spray cooling, indicating that it may enable a tenfold increase in power density compared to standard air- or water-cooled machines.

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Ashrafi, Hosein, M. R. Bahadori, and M. Shariyat. "Modeling of Viscoelastic Solid Polymers Using a Boundary Element Formulation with Considering a Body Load." Advanced Materials Research 463-464 (February 2012): 499–504. http://dx.doi.org/10.4028/www.scientific.net/amr.463-464.499.

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In this work, a boundary element formulation for 2D linear viscoelastic solid polymers subjected to body force of gravity has been presented. Structural analysis of solid polymers is one of the most important subjects in advanced engineering structures. From basic assumptions of the viscoelastic constitutive equations and the weighted residual techniques, a simple but effective boundary element formulation is implemented for standard linear solid (SLS) model. The SLS model provides an approximate representation of observed behavior of a real advanced polymer in its viscoelastic range. This approach avoids the use of relaxation functions and mathematical transformations, and it is able to solve quasistatic viscoelastic problems with any load time-dependence and boundary conditions. Problem of pressurization of thick-walled viscoelastic tanks made of PMMA polymer, which subjected to a body force, is completely analyzed.

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Wang, Jian D., and Ian M. Howard. "Error Analysis on Finite Element Modeling of Involute Spur Gears." Journal of Mechanical Design 128, no. 1 (2005): 90–97. http://dx.doi.org/10.1115/1.2114891.

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Finite element analysis can incorporate two-dimensional (2D) modeling if the geometry, load, and boundary conditions meet the requirements. For many applications, a wide range of problems are solved in 2D, due to the efficiency and costs of computation. However, care has to be taken to avoid modeling errors from significantly influencing the result. When the application area is nonlinear, such as when modeling contact problems or fracture analysis, etc, the 2D assumption must be used cautiously. In this paper, a large number of 2D and three-dimensional (3D) gear models were investigated using finite element analysis. The models included contact analysis between teeth in mesh, a gear body (disk), and teeth with and without a crack at the tooth root. The model results were compared using parameters such as the torsional (mesh) stiffness, tooth stresses and the stress intensity factors that are obtained under assumptions of plane stress, plane strain, and 3D analysis. The models considered variations of face width of the gear from 5 mm to 300 mm. This research shows that caution must be used especially where 2D assumptions are used in the modeling of solid gears.

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Faye, Antoine, Paolo Perali, Benoit Augier, et al. "Fluid-Structure Interactions Response of a Composite Hydrofoil Modelled With 1D Beam Finite Elements." Journal of Sailing Technology 9, no. 01 (2024): 19–41. http://dx.doi.org/10.5957/jst/2024.9.1.19.

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_ In this paper, the hydroelastic response of a NACA0015 composite hydrofoil is studied experimentally and numerically. The foil is made of composite materials with fibers not aligned with the span of the foil, which results in the occurence of a bend-twist coupling in the material. Computations are performed using a partitioned approach. The flow problem is solved using a boundary element method. The structural response of the foil is modelled with two different finite element models. In the first one, the foil is modelled with 2D shell and 3D solid finite elements and in the second model, the foil is modelled with 1D beam finite elements. The experiments are conducted in an open circulation water channel. Hydrodynamic forces and structural displacements are measured for several angles of attack, free stream velocities and submergence depth. This paper shows that the mechanical behaviour of a composite hydrofoil submitted to hydrodynamic loads can be modelled with 1D beam finite elements. This model gives results very similar to a finite element analysis realized with 2D shell and 3D solid finite elements, which are commonly used to model composite structures. The present work also shows that the experimental results can be well predicted by numerical simulations, but it requires a precise modeling of the bend-twist coupling in the materials constituting the foil. Keywords Hydrofoil; Equivalent Beam; Fluid-Structure Interactions; Composite; Bend-Twist Coupling

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Tong, Xiaozhong, Yujun Guo, and Wei Xie. "Finite Difference Algorithm on Non-Uniform Meshes for Modeling 2D Magnetotelluric Responses." Algorithms 11, no. 12 (2018): 203. http://dx.doi.org/10.3390/a11120203.

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A finite-difference approach with non-uniform meshes was presented for simulating magnetotelluric responses in 2D structures. We presented the calculation formula of this scheme from the boundary value problem of electric field and magnetic field, and compared finite-difference solutions with finite-element numerical results and analytical solutions of a 1D model. First, a homogeneous half-space model was tested and the finite-difference approach can provide very good accuracy for 2D magnetotelluric modeling. Then we compared them to the analytical solutions for the two-layered geo-electric model; the relative errors of the apparent resistivity and the impedance phase were both increased when the frequency was increased. To conclude, we compare our finite-difference simulation results with COMMEMI 2D-0 model with the finite-element solutions. Both results are in close agreement to each other. These comparisons can confirm the validity and reliability of our finite-difference algorithm. Moreover, a future project will extend the 2D structures to 3D, where non-uniform meshes should perform especially well.

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Kant, Tarun, Sandeep S. Pendhari, and Yogesh M. Desai. "A Novel Finite-Element– Numerical-Integration Model for Composite Laminates Supported on Opposite Edges." Journal of Applied Mechanics 74, no. 6 (2007): 1114–24. http://dx.doi.org/10.1115/1.2722770.

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An attempt is made here to devise a new methodology for an integrated stress analysis of laminated composite plates wherein both in-plane and transverse stresses are evaluated simultaneously. The method is based on the governing three-dimensional (3D) partial differential equations (PDEs) of elasticity. A systematic procedure is developed for a case when one of the two in-plane dimensions of the laminate is considered infinitely long (y direction) with no changes in loading and boundary conditions in that direction. The laminate could then be considered in a two-dimensional (2D) state of plane strain in x-z plane. It is here that the governing 2D PDEs are transformed into a coupled system of first-order ordinary differential equations (ODEs) in transverse z direction by introducing partial discretization in the finite inplane direction x. The mathematical model thus reduces to solution of a boundary value problem (BVP) in the transverse z direction in ODEs. This BVP is then transformed into a set of initial value problems (IVPs) so as to use the available efficient and effective numerical integrators for them. Through thickness displacement and stress fields at the finite element discrete nodes are observed to be in excellent agreement with the elasticity solution. A few new results for cross-ply laminates under clamped support conditions are also presented for future reference and also to show the generality of the formulation.

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Jiang, Wei, Jiancheng Xu, Li Kunpeng, Ye Ouyang, and Jinzhou Yan. "Coupling Heat Conduction and Radiation by an Isogeometric Boundary Element Method in 2-D Structures." Mathematical Problems in Engineering 2022 (September 7, 2022): 1–14. http://dx.doi.org/10.1155/2022/4209720.

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We propose an efficient isogeometric boundary element method to address the coupling of heat conduction and radiation in homogeneous or inhomogeneous materials. The isogeometric boundary element method is used to construct irregular 2D models, which eliminate errors in model construction. The physical unknowns in the governing equations for heat conduction and radiation are discretized using an interpolation approximation, and the integral equations are finally solved by Newton–Raphson iteration; it is noteworthy that we use the radial integration method to convert the domain integrals to boundary integrals, and we combine the numerical schemes for heat conduction and radiation. The results of the three numerical cases show that the adopted algorithm can improve the computational accuracy and efficiency.

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Sathyan, Sabin, Ugur Aydin, and Anouar Belahcen. "Acoustic Noise Computation of Electrical Motors Using the Boundary Element Method." Energies 13, no. 1 (2020): 245. http://dx.doi.org/10.3390/en13010245.

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This paper presents a numerical method and computational results for acoustic noise of electromagnetic origin generated by an induction motor. The computation of noise incorporates three levels of numerical calculation steps, combining both the finite element method and boundary element method. The role of magnetic forces in the production of acoustic noise is established in the paper by showing the magneto-mechanical and vibro-acoustic pathway of energy. The conversion of electrical energy into acoustic energy in an electrical motor through electromagnetic, mechanical, or acoustic platforms is illustrated through numerical computations of magnetic forces, mechanical deformation, and acoustic noise. The magnetic forces were computed through 2D electromagnetic finite element simulation, and the deformation of the stator due to these forces was calculated using 3D structural finite element simulation. Finally, boundary element-based computation was employed to calculate the sound pressure and sound power level in decibels. The use of the boundary element method instead of the finite element method in acoustic computation reduces the computational cost because, unlike finite element analysis, the boundary element approach does not require heavy meshing to model the air surrounding the motor.

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Maghoul, Pooneh, and Behrouz Gatmiri. "Theory of a Time Domain Boundary Element Development for the Dynamic Analysis of Coupled Multiphase Porous Media." Journal of Multiscale Modelling 08, no. 03n04 (2017): 1750007. http://dx.doi.org/10.1142/s175697371750007x.

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This paper presents an advanced formulation of the time-domain two-dimensional (2D) boundary element method (BEM) for an elastic, homogeneous unsaturated soil subjected to dynamic loadings. Unlike the usual time-domain BEM, the present formulation applies a convolution quadrature which requires only the Laplace-domain instead of the time-domain fundamental solutions. The coupled equations governing the dynamic behavior of unsaturated soils ignoring contributions of the inertia effects of the fluids (water and air) are derived based on the poromechanics theory within the framework of a suction-based mathematical model. In this formulation, the solid skeleton displacements [Formula: see text], water pressure [Formula: see text] and air pressure [Formula: see text] are presumed to be independent variables. The fundamental solutions in Laplace transformed-domain for such a dynamic [Formula: see text] theory have been obtained previously by authors. Then, the BE formulation in time is derived after regularization by partial integrations and time and spatial discretizations. Thereafter, the BE formulation is implemented in a 2D boundary element code (PORO-BEM) for the numerical solution. To verify the accuracy of this implementation, the displacement response obtained by the boundary element formulation is verified by comparison with the elastodynamics problem.

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Tornabene, F., S. Brischetto, N. Fantuzzi, and M. Bacciocchi. "Boundary Conditions in 2D Numerical and 3D Exact Models for Cylindrical Bending Analysis of Functionally Graded Structures." Shock and Vibration 2016 (2016): 1–17. http://dx.doi.org/10.1155/2016/2373862.

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The cylindrical bending condition for structural models is very common in the literature because it allows an incisive and simple verification of the proposed plate and shell models. In the present paper, 2D numerical approaches (the Generalized Differential Quadrature (GDQ) and the finite element (FE) methods) are compared with an exact 3D shell solution in the case of free vibrations of functionally graded material (FGM) plates and shells. The first 18 vibration modes carried out through the 3D exact model are compared with the frequencies obtained via the 2D numerical models. All the 18 frequencies obtained via the 3D exact model are computed when the structures have simply supported boundary conditions for all the edges. If the same boundary conditions are used in the 2D numerical models, some modes are missed. Some of these missed modes can be obtained modifying the boundary conditions imposing free edges through the direction perpendicular to the direction of cylindrical bending. However, some modes cannot be calculated via the 2D numerical models even when the boundary conditions are modified because the cylindrical bending requirements cannot be imposed for numerical solutions in the curvilinear edges by definition. These features are investigated in the present paper for different geometries (plates, cylinders, and cylindrical shells), types of FGM law, lamination sequences, and thickness ratios.

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Guldberg, R. E., S. J. Hollister, and G. T. Charras. "The Accuracy of Digital Image-Based Finite Element Models." Journal of Biomechanical Engineering 120, no. 2 (1998): 289–95. http://dx.doi.org/10.1115/1.2798314.

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Digital image-based finite element meshing is an alternative approach to time-consuming conventional meshing techniques for generating realistic three-dimensional (3D) models of complex structures. Although not limited to biological applications, digital image-based modeling has been used to generate structure-specific (i.e., nongeneric) models of whole bones and trabecular bone microstructures. However, questions remain regarding the solution accuracy provided by the digital meshing approach, particularly at model or material boundaries. The purpose of this study was to compare the accuracy of digital and conventional smooth boundary models based on theoretical solutions for a two-dimensional (2D) compression plate and a 3D circular cantilever beam. For both the plate and beam analyses, the predicted solution at digital model boundaries was characterized by local oscillations, which produced potentially high errors within individual boundary elements. Significantly, however, the digital model boundary solution oscillated approximately about the theoretical solution. A marked improvement in solution accuracy was therefore achieved by considering average results within a region composed of several elements. Absolute errors for Von Mises stress averaged over the beam cross section, for example, converged to less than 4 percent, and the predicted free-end displacement of the cantilever beam was within 1 percent of the theoretical solution. Analyses at several beam orientations and mesh resolutions suggested a minimum discretization of three to four digital finite elements through the beam cross section to avoid high numerical stiffening errors under bending.

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PENPEN KOMGUE, LUCRECE BARBARA, FAIZ ADIL, ASSIF SAFAA, ENNAWAOUI CHOUAIB, Joël DUCOURNEAU, and ABDELOWAHED HAJJAJI. "Study of the acoustic attenuation of 2D axisymmetric models of the human ear equipped with hearing protection." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 270, no. 6 (2024): 5484–91. http://dx.doi.org/10.3397/in_2024_3599.

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The ear is the organ responsible for auditory perception. Its role is to amplify, transmit, and convert an acoustic wave present in the environment into an electrical pulse that the brain can interpret via the auditory nerve. The objective of this study was to develop two axisymmetric 2D finite element models of the human ear to predict insertion loss when a porous earplug is introduced into the ear canal. In these models, the structure-acoustic interaction was resolved by finite element analysis. For a better representation, assumptions and boundary conditions (such as fixe boundary condition, spring-mass-damping boundary condition, etc...) are considered. The tympanic ring and the earplug are assumed to be fixed, and a load of what comes after the posterior part of the tympanic ring (the ossicular chain) has been replaced by an equivalent mechanical impedance mass-spring-damper system. The first model has a regular geometry, and the second model is obtained by reconstructing a 3D model. These two models were inspired by our previous work. For each model, the insertion loss (IL) is predicted and the results obtained are compared with those of the sound attenuation measurements of hearing protection performed in the laboratory.

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Luo, Z., and N. A. Demerdash. "A finite-element ballooning model for 2D eddy current open boundary problems for aerospace applications." IEEE Transactions on Magnetics 28, no. 5 (1992): 2241–43. http://dx.doi.org/10.1109/20.179456.

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Verstraete, Matthias, W. De Waele, and Stijn Hertelé. "Development and validation of a high constraint modified boundary layer finite element model." International Journal Sustainable Construction & Design 2, no. 2 (2011): 228–36. http://dx.doi.org/10.21825/scad.v2i2.20520.

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When a notched structure is loaded, its behaviour is not only affected by the material propertiesbut also by the geometry (of both the structure and the defect) and loading condition, alternatively termedas constraint condition. Therefore, the relation between the failure behaviour of a small scale fracturemechanics test and a full scale structure needs to be elucidated.In an attempt to understand and describe such relationships, the crack tip stress fields are analysed bymeans of finite element simulations and compared for several test specimen geometries. A reference forcomparison is the crack tip stress field obtained from a high constraint reference geometry, further called amodified boundary layer model.First, this article provides some theoretical background on the modified boundary layer model. Second, thedevelopment of a 2D model is outlined in detail, focussing on the mesh design in the vicinity of the crack tipand the applied boundary conditions. Afterwards, an analytical and numerical validation is provided, basedon the level of the applied load and, on the other hand, on the magnitude of the crack tip stress fields.Finally, this validated model is used for the comparison of several constraint parameters. This comparisonindicates a weak influence of the T-stress on the Q-parameter for positive T-stresses. In contrast, negativeT-stresses result in more pronounced negative Q-values.

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Morse, Llewellyn, Zahra Sharif Khodaei, and M. H. Aliabadi. "Multi-Fidelity Modeling-Based Structural Reliability Analysis with the Boundary Element Method." Journal of Multiscale Modelling 08, no. 03n04 (2017): 1740001. http://dx.doi.org/10.1142/s1756973717400017.

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In this work, a method for the application of multi-fidelity modeling to the reliability analysis of 2D elastostatic structures using the boundary element method (BEM) is proposed. Reliability analyses were carried out on a rectangular plate with a center circular hole subjected to uniaxial tension using Monte Carlo simulations (MCS), the first-order reliability method (FORM), and the second-order reliability method (SORM). Two BEM models were investigated, a low-fidelity model (LFM) of 20 elements and a high-fidelity model (HFM) of 100 elements. The response of these models at several design points was used to create multi-fidelity models (MFMs) utilizing second-order polynomial response surfaces and their reliability, alongside that of the LFM and the HFM, was evaluated. Results show that the MFMs that directly called the LFM were significantly superior in terms of accuracy to the LFM, achieving very similar levels of accuracy to the HFM, while also being of similar computational cost to the LFM. These direct MFMs were found to provide good substitutes for the HFM for MCS, FORM, and SORM.

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Cerrolaza, M., W. Annicchiarico та M. Martinez. "Optimization of 2D boundary element models using β-splines and genetic algorithms". Engineering Analysis with Boundary Elements 24, № 5 (2000): 427–40. http://dx.doi.org/10.1016/s0955-7997(00)00006-0.

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Safuadi, M., M. Ridha, Syifaul Huzni, Syarizal Fonna, Ahmad Kamal Ariffin, and Abdul Razak Daud. "Optimization of Cathodic Protection System Design for Pipe-Lines Structure with Ribbon Sacrificial Anode Using BEM and GA." Key Engineering Materials 462-463 (January 2011): 1267–72. http://dx.doi.org/10.4028/www.scientific.net/kem.462-463.1267.

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In this paper, combination of a boundary element formulation and genetic algorithm (GA) was developed and used for analyzing of cathodic protection systems of buried pipe-lines structures. It is very important to maintain the effectiveness of the cathodic protection system for pipeline structure, in order to lengthen the lifetime of the system. However, nowadays the evaluation of the effectiveness of the system only could be performed after the system applying in the field. This study was conducted to combine 2D boundary element method (BEM) and GA in order to evaluate the effectiveness of the cathodic protection system for pipe-lines structure using ribbon sacrificial anode. Two factors i.e. the soil conductivity and the distance between pipe-lines and anode, were analyzed by using the proposed method. In this method, the potential in the domain was modeled by Laplace’s equation. The anode and cathode areas were represented by polarization curves of different metals. Boundary element method was applied to solve the Laplace’s equation to obtain any potential and current density in the whole surface of the pipe. The pipe and anode were modeled into 2D model. The numerical analysis result shows that the optimum distance between pipe-lines and anode can be determined by combining BEM and GA.

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Gabriel, Maarten, and Peter Wellens. "A two-dimensional boundary element method with generating absorbing boundary condition for floating bodies of arbitrary shape in the frequency domain." International Shipbuilding Progress 69, no. 2 (2022): 139–59. http://dx.doi.org/10.3233/isp-210007.

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A two-dimensional (2D) boundary element method is developed for the rapid assessment of the hydrodynamic performance of floating structures in waves. The boundary element method is based on potential flow and has panels along all boundaries of the fluid domain – not only along the boundary of the floater – to make the extension to second order feasible. Panels along all boundaries requires the development of generating absorbing boundary conditions for use at radiation boundaries to send incident waves into the domain while absorbing waves originating from the floating body at the same boundary, at the same time. The model is verified by means of conservation of energy of a heaving wave energy converter, and by means of the propagation of second-order waves. The performance in terms of conservation of energy with 12 panels per wave length is good, the generating absorbing boundary condition works according to expectation and the second-order wave propagation corresponds to theory.

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Juhász, Zoltán, Tamás Turcsán, Tamás Bence Tóth, and András Szekrényes. "Sensitivity analysis for frequency based prediction of crack size in composite plates with through-the-width delamination." International Journal of Damage Mechanics 27, no. 6 (2017): 859–76. http://dx.doi.org/10.1177/1056789517709893.

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This work combines modal analysis measurements with a novel 2D finite element plate model, which is capable to determine the delamination growth based on the change in the measured frequencies. The base of the presented method is a finite element model incorporating the Classical Laminated Plate Theory, and it is capable to estimate the eigenfrequencies of a rectangular plate with through-the-width delamination and straight crack front using arbitrary boundary conditions. The model contains special types of finite elements for modelling the delamination. This results a contact free model, which improves the simulation speed significantly. Using this model, the characteristic of the change of the eigenfrequencies with respect to the delamination growth can be obtained. These results can serve as reference, and according to the theoretical curves, the actual size of the delamination can be estimated based on the change in the measured frequencies. According to our measurement results, it can serve as a good reference for modal analysis. The experiment shows that the model can predict the effect of the delamination growth on the eigenfrequencies very well. Additional conclusions are drawn based on further numerical simulations, which can aid the model based modal analysis of composite plates.

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Asiri, Saeed A., Ş. D. Akbaş, and M. A. Eltaher. "Dynamic Analysis of Layered Functionally Graded Viscoelastic Deep Beams with Different Boundary Conditions Due to a Pulse Load." International Journal of Applied Mechanics 12, no. 05 (2020): 2050055. http://dx.doi.org/10.1142/s1758825120500556.

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This paper studies the dynamic viscoelastic response of functionally graded (FG) thick 2D cantilever and simply supported beams under dynamic pulse load, for the first time. A point load applied at a specific spatial point is described as a time-pulse sinusoidal load. Two-dimensional plane-stress constitutive equation is exploited to describe the local stress–strain relation through the beam. The gradation of material is depicted by generalized power law function through the layer thickness across beam thickness. The Kelvin–Voigt viscoelastic model is proposed to describe material damping of structure. Lagrange’s equation is employed to derive governing motion equation. A finite element method (FEM) is exploited to discretize the spatial domain of 2D beam structure by using 12-node 2D plane element. Numerical Newmark implicit time integration method is proposed to solve the equation of motion incrementally and get the response of beam structure. Two types of boundary conditions are considered in the numerical examples. In numerical results, effects of stacking sequence, geometry parameters and material gradation index and viscoelasticity coefficients on the displacement-time response of layered functionally graded viscoelastic deep beams for different boundary conditions.

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Fodor, E., S. Kriston, F. Nándori, L. Sárközi, and T. Szabó. "A Finite Element System for the Hierarchical Design of Agricultural Tires." Tire Science and Technology 26, no. 4 (1998): 222–40. http://dx.doi.org/10.2346/1.2135970.

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Abstract Due to the many requirements with respect to the processing and operational activities of agricultural tires, their design is not an easy task. To provide support, a special purpose nonlinear FE package called Agrotyre/2D/3D has been worked out, by which 2D asymmetric and 3D boundary problems can be solved for the case of inflation and for the case of vertical loading. In the latter situation, the whole tire is meshed into 16-noded elements including all of the lugs. By assuming the circumferential strain to be equal to zero, the asymmetric model can be analyzed for given prescribed radial displacements, and the results of the cord force distributions can be compared with that of the results of the 3D analysis. The preprocessing of the 2D and 3D meshes are on a common basis for which the data are transferred from a CAD system. In the package there is a further module by which the strength behavior of a unique lug can also be investigated. The paper presents some characteristic pictures that illustrate the usage of this new software.

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LIU, E., A. DOBSON, D. M. PAN, and D. H. YANG. "THE MATRIX FORMULATION OF BOUNDARY INTEGRAL MODELING OF ELASTIC WAVE PROPAGATION IN 2D MULTI-LAYERED MEDIA WITH IRREGULAR INTERFACES." Journal of Computational Acoustics 16, no. 03 (2008): 381–96. http://dx.doi.org/10.1142/s0218396x08003634.

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A semi-analytic method based on the propagation matrix formulation of indirect boundary element method to compute response of elastic (and acoustic) waves in multi-layered media with irregular interfaces is presented. The method works recursively starting from the top-most free surface at which a stress-free boundary condition is applied, and the displacement-stress boundary conditions are then subsequently applied at each interface. The basic idea behind this method is the matrix formulation of the propagation matrix (PM) or more recently the reflectivity method as wide used in the geophysics community for the computation of synthetic seismograms in stratified media. The reflected and transmitted wave fields between arbitrary shapes of layers can be computed using the indirect boundary element (BEM) method. Like any standard BEM methods, the primary task of the BEM-based propagation matrix method (thereafter called PM–BEM) is the evaluation of element boundary integral of the Green's function, for which there are standard method that can be adapted. In addition, effective absorbing boundary conditions as used in the finite difference numerical method is adapted in our implementation to suppress the spurious arrivals from the artificial boundaries due to limited model space. To our knowledge, such implementation has not appeared in the literature. Several examples are presented in this paper to demonstrate the effectiveness of this proposed PM–BEM method for modeling elastic waves in media with complex structure.

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Zhang, Ying, Haiyang Liu, Shikun Dai, and Herui Zhang. "Frequency-Domain Finite Element Modeling of Seismic Wave Propagation Under Different Boundary Conditions." Mathematics 13, no. 4 (2025): 578. https://doi.org/10.3390/math13040578.

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Seismic wave propagation in complex terrains, especially in the presence of air layers, plays a crucial role in accurate subsurface imaging. However, the influence of different boundary conditions on seismic wave propagation characteristics has not been fully explored. This study employs the finite element method (FEM) to simulate and analyze seismic wavefields under different boundary conditions, including perfectly matched layer (PML), Neumann free boundary conditions, and air layer conditions. First, the finite element solution for the 2D frequency-domain acoustic wave equation is introduced, and the correctness of the algorithm is validated using a homogeneous model. Then, both horizontal and undulating terrain interfaces are designed to investigate the kinematic and dynamic characteristics of the wavefields under different boundary conditions. The results show that PML boundaries effectively absorb seismic waves, prevent reflections, and ensure stable wave propagation, making them an ideal choice for simulating open boundaries. In contrast, Neumann boundaries generate significant reflected waves, particularly in undulating terrains, complicating the wavefield characteristics. Introducing an air layer alters the dynamics of the wavefield, leading to energy leakage and multi-path effects, which are more consistent with real-world seismic-geophysical models. Finally, the computational results using the Overthrust model under different boundary conditions further demonstrate that different boundary conditions significantly affect wavefield morphology. It is essential to select appropriate boundary conditions based on the specific simulation requirements, and boundary conditions with an air layer are most consistent with real seismic geological models. This study provides new insights into the role of boundary conditions in seismic numerical simulations and offers theoretical guidance for improving the accuracy of wavefield simulations in realistic geological scenarios.

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Fernandes, Gabriela R., Luis Henrique R. Crozariol, Amanda S. Furtado, and Matheus C. Santos. "A 2D boundary element formulation to model the constitutive behavior of heterogeneous microstructures considering dissipative phenomena." Engineering Analysis with Boundary Elements 99 (February 2019): 1–22. http://dx.doi.org/10.1016/j.enganabound.2018.10.018.

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Zheng, Yingcai, Adel H. Malallah, Michael C. Fehler, and Hao Hu. "2D full-waveform modeling of seismic waves in layered karstic media." GEOPHYSICS 81, no. 2 (2016): T25—T34. http://dx.doi.org/10.1190/geo2015-0307.1.

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We have developed a new propagator-matrix scheme to simulate seismic-wave propagation and scattering in a multilayered medium containing karstic voids. The propagator matrices can be found using the boundary element method. The model can have irregular boundaries, including arbitrary free-surface topography. Any number of karsts can be included in the model, and each karst can be of arbitrary geometric shape. We have used the Burton-Miller formulation to tackle the numerical instability caused by the fictitious resonance due to the finite size of a karstic void. Our method was implemented in the frequency-space domain, so frequency-dependent [Formula: see text] can be readily incorporated. We have validated our calculation by comparing it with the analytical solution for a cylindrical void and to the spectral element method for a more complex model. This new modeling capability is useful in many important applications in seismic inverse theory, such as imaging karsts, caves, sinkholes, and clandestine tunnels.

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De Vos, Leon Frederik, Nils Rüther, Karan Mahajan, Antonia Dallmeier, and Karl Broich. "Establishing Improved Modeling Practices of Segment-Tailored Boundary Conditions for Pluvial Urban Floods." Water 16, no. 17 (2024): 2448. http://dx.doi.org/10.3390/w16172448.

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Establishing appropriate boundary conditions is essential for developing high-accuracy hydrodynamic models. However, this task is particularly challenging in topographically varying urban domains without monotonous slopes due to insufficient boundary information. This study investigates five different boundary conditions and establishes modeling practices of boundary conditions in pluvial urban flood modeling. A numerical test model within the city of Berlin is used, employing the 2D hydrodynamic finite element module of the open-source TELEMAC system. It performs unsteady simulations with nodal rainfall inputs for various precipitation scenarios, excluding infiltration. The results demonstrate that the suitability of boundary conditions is critically dependent on the surrounding topography. For boundary segments with a positive slope, a stage–discharge curve is found to outperform the other boundary conditions investigated in this study. Conversely, for segments with a negative slope, a closed wall boundary condition appears clearly preferable. Additionally, a drainage reservoir boundary condition performs effectively for more complex boundary segments but necessitates extensive preprocessing. Based on these insights, simulations were repeated with segment-tailored boundary conditions. The results indicate that this combined model outperforms the global application of each individual model.

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Aslan, Ozgur, and Emin Bayraktar. "Analytical Solutions of Model Problems for Large-Deformation Micromorphic Approach to Gradient Plasticity." Applied Sciences 11, no. 5 (2021): 2361. http://dx.doi.org/10.3390/app11052361.

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The objective of this work is to present analytical solutions for several 2D model problems to demonstrate the unique plastic fields generated by the implementation of micromorphic approach for gradient plasticity. The approach is presented for finite deformations and several macroscopic and nonstandard microscopic boundary conditions are applied to a gliding plate to illustrate the capability to predict the size effects and inhomogeneous plastic fields promoted by the gradient terms. The constitutive behavior of the material undergoing plastic deformation is analyzed for softening, hardening and perfect plastic response and corresponding solutions are provided. The analytical solutions are also shown to match with the numerical results obtained by implementing a user element subroutine (UEL) to the commercial finite element software Abaqus/Standard.

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Chernyavsky, Alexander, Alexey Bereza, Leonid Frumin, and David Shapiro. "Modeling of Subwavelength Gratings: Near-Field Behavior." Photonics 10, no. 12 (2023): 1332. http://dx.doi.org/10.3390/photonics10121332.

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Subwavelength gratings have received considerable attention in the fields of photonics, optoelectronics, and image sensing. This paper presents simple analytical expressions for the near-field intensity distribution of radiation scattered by these gratings. Our proposed methodology employs a 2D point dipole model and a specialized version of perturbation theory. By validating our models via numerical techniques including boundary and finite element methods, we demonstrate their effectiveness, even for narrow slits.

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Liu, D. S., and Y. W. Chen. "Application of Craig-Bampton Reduction Technique and 2D Dynamic Infinite Element Modeling Approach to Membrane Vibration Problems." Journal of Mechanics 35, no. 4 (2018): 513–25. http://dx.doi.org/10.1017/jmech.2018.45.

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ABSTRACTAn approach is presented for solving membrane vibration problems using an integrated scheme consisting of the Craig-Bampton (CB) reduction technique and a 2D dynamic infinite element modeling (DIEM) method. In the proposed CB-DIEM scheme, the substructure domain is partitioned into multiple layers of geometrically-similar infinite elements (IEs) which use only the data of the boundary nodes. A convergence criterion based on the first invariant of the DIEM mass matrix is used to determine the optimal parameters of the CB-DIEM scheme, namely the proportionality ratio and number of layers in the DIEM partitioning process and the number of retained frequency modes in the CB reduction method. Furthermore, in implementing the CB method, the inversion of the global stiffness matrix is calculated using only the stiffness matrix of the first element layer. Having reduced the DIEM model, a coupled DIE-FE algorithm is employed to model the dynamic problems of the full structure, which removes the respective methods disadvantages while keeping their advantages. The validity and performance of the proposed CB-DIEM method are investigated by means of three illustrative problems.

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Xia, Jun, Z. Shen, and Kun Liu. "Free Vibration Analysis for Tapered Cross-Section Steel-Concrete Composite Material Beam." Materials Science Forum 893 (March 2017): 380–83. http://dx.doi.org/10.4028/www.scientific.net/msf.893.380.

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The tapered cross-section beams made of steel-concrete composite material are widely used in engineering constructions and their dynamic behavior is strongly influenced by the type of shear connection jointing the two different materials. The 1D high order finite element model for tapered cross-section steel-concrete composite material beam with interlayer slip was established in this paper. The Numerical results for vibration nature frequencies of the composite beams with two typical boundary conditions were compared with ANSYS using 2D plane stress element. The 1D element is more efficient and economical for the common tapered cross-section steel-concrete composite material beams in engineering.

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Xia, Jun, Zhi Qiang Shen, and Kun Liu. "Flexural Analysis for Tapered Cross-Section Steel-Concrete Material Composite Beam." Key Engineering Materials 703 (August 2016): 371–75. http://dx.doi.org/10.4028/www.scientific.net/kem.703.371.

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The flexural behavior of tapered cross-section steel-concrete composite material beams frequently used in structural engineering is strongly influenced by the type of shear connection between the steel beam and the concrete slab. The 1D high order finite element model for tapered cross-section steel-concrete composite material beams with interlayer slip were established in this paper. The Numerical results for deflection and interlayer slip of the composite beam with two typical boundary conditions were compared with ANSYS using 2D plane stress element. The 1D element is more efficient and economical for the common tapered cross-section steel-concrete composite material beams in engineering.

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Poklopová, Tereza, Veronika Pavelcová, Tomáš Janda, and Michal Šejnoha. "MODELING OF UNDERGROUND STRUCTURES SUBJECTED TO EARTHQUAKE BY COMBINING 1D FREE-FIELD AND 2D PSEUDO-STATIC ANALYSES." Acta Polytechnica CTU Proceedings 15 (December 31, 2018): 88–93. http://dx.doi.org/10.14311/app.2018.15.0088.

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The paper deals with the evaluation of tunnel construction subjected to earthquake using a pseudostatic analysis combined with the finite element method. The initial stage of calculation is concerned with the design of computational model and subsequent analysis of the actual excavation process. The case study of the response of a selected construction to earthquake follows next. To that end, the so called 1D free filed dynamic analysis is performed first to generate appropriate loading conditions in terms of a layered-wise constant shear strain. Therein, two particular boundary conditions, termed the fixed and absorbing boundary, are examined. The corresponding loading conditions are finally introduced in a 2D plane strain analysis to yield the internal forces developed in the tunnel lining. The results clearly show inadequacy of the fixed boundary and promote the use of absorbing boundary conditions for the present soil profile.

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Chinh, Nguyen Van, Le Cung Inh, and Le Thi Ngoc Anh. "ELASTOSTATIC BENDING OF A 2D-FGSW BEAM UNDER NONUNIFORM DISTRIBUTED LOADS." Vietnam Journal of Science and Technology 57, no. 3 (2019): 381. http://dx.doi.org/10.15625/2525-2518/57/3/13521.

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Elastostatic bending behavior of a two-directional functionally graded sandwich (2D-FGSW) beam under various types of nonuniform distributed load is studied. Based on a 3D-quasi shear deformation theory, a finite element model is derived and employed in the study. Elastostatic response of the beam is computed for the beam with different boundary conditions and aspect ratio. The effects of the material distribution and the loading type on the deflections and stresses distribution are investigated and highlighted. The influence of the aspect ratio on the behavior of the beam is also examined and discussed.

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He, Yaofeng, and Ru-Shan Wu. "One-way/one-return boundary-element method and salt internal multiples." GEOPHYSICS 75, no. 3 (2010): T63—T69. http://dx.doi.org/10.1190/1.3374463.

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Surface-related multiples or internal multiples can produce artifacts in migrated images using one-way wave-equation methods. Salt-body-related internal-multiple removal remains a challenging problem for this approach. To investigate the effects of salt-body-related internal multiples on subsalt imaging, the boundary-element method is implemented in a one-way/one-return scheme to separate the primary transmission/reflection arrivals at the salt boundaries from the internal multiples. Numerical results demonstrate that the proposed method is effective for modeling primary transmission/reflection arrivals through/from irregular interfaces between strong-velocity-contrast media. Internal multiples are obtained through straight subtraction of primary reflection arrivals from full reflected-wave data. The image from prestack depth migration of these pure internal multiples using one-way propagators is compatible with some strong artifacts in the subsalt region from migration of full-wave data using the same one-way propagators. Results suggest that a significant part of artifacts in the subsalt region in the prestack image for the 2D SEG-EAGE salt model using one-way propagators might be caused by salt internal multiples.

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Chinh, Nguyen Van. "STATIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED SANDWICH PLATES USING A THIRD-ORDER SHEAR DEFORMATION FINITE ELEMENT MODEL." Vietnam Journal of Science and Technology 57, no. 6A (2020): 77. http://dx.doi.org/10.15625/2525-2518/57/4a/14109.

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In this paper, static bending of two-direction functionally graded sandwich (2D-FGSW) plates is studied by using a finite element model. The plates consist of a homogeneous core and two functionally graded skin layers with material properties being graded in both the thickness and length directions by power gradation laws. Based on a third-order shear deformation theory, a finite element model is derived and employed in the analysis. Bending characteristics, including deflections and stresses are evaluated for the plates with classical boundary conditions under various types of distributed load. The effects of material distribution and layer thickness ratio on the static bending behavior of the plates are examined and highlighted.

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He, Ling Na, and Jian Wei Pan. "The Construction of Cerebrovascular Model and Numerical Simulation." Advanced Materials Research 562-564 (August 2012): 1382–85. http://dx.doi.org/10.4028/www.scientific.net/amr.562-564.1382.

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Medical image reconstruction technique has been an important research topic. Based on cerebrovascular CT image of actual victims, through extracting the contour of image, dividing the nodes and defining boundary, the paper reconstructed 2D grid model of blood vessel of brain. Using the finite element method to simulate and analyze the dynamics features of the medical image mesh model. Through experiment, the paper mainly compared the value of blood velocity and dynamics pressure, and analyzed the difference of hemodynamic parameters in different models. Finally, It found that the model I artery more easily alter form and induce arterial hemorrhage. This will provide the theoretical basis for analyzing the mechanism of Cerebrovascular diseases.

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Sladek, Jan, Vladimir Sladek, Michael Wünsche, and Choon Lai Tan. "Fracture Mechanics Analysis of Size-Dependent Piezoelectric Solids under a Thermal Load." Key Engineering Materials 754 (September 2017): 165–68. http://dx.doi.org/10.4028/www.scientific.net/kem.754.165.

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General 2D boundary value problems of piezoelectric nanosized structures with cracks under a thermal load are analyzed by the finite element method (FEM). The size-effect phenomenon observed in nanosized structures is described by the strain-gradient effect. The strain gradients are considered in the constitutive equations for electric displacement and the high-order stress tensor. For this model, the governing equations are derived with the corresponding boundary conditions using the variational principle. Uncoupled thermoelasticity is considered, thus, the heat conduction problem is analyzed independently of the mechanical fields in the first step. A numerical example is presented and discussed to demonstrate the effects of the strain-gradient.

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MU, LI ZHONG, HONG WEI SHAO, YING HE, TOSHIAKI ODA, and XUE MEI JIA. "CONSTRUCTION OF ANATOMICALLY ACCURATE FINITE ELEMENT MODELS OF THE HUMAN HAND AND A RAT KIDNEY." Journal of Mechanics in Medicine and Biology 11, no. 05 (2011): 1141–64. http://dx.doi.org/10.1142/s0219519411004216.

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The aim of the paper is to develop a method for generating three-dimensional (3D) models of organs from medical images (computerized tomography (CT) images, magnetic resonance imaging (MRI), etc.). There were three main steps in the development of the model: the first step was image processing. Different image-processing operators including blurring, sharpening, edge detection, region segmentation, mathematical morphology transformation, rotation, and movement of the kidney slices were performed to automatically construct the accurate boundary information. The second step was mesh generation of each slice based on the boundary information by using the transfinite interpolation (TFI) technique. In this paper, the TFI method was improved to create grids from images directly. The last step was reconstructing the models by stacking the 2D grid models and visualizing the result in the Advanced Visual System (AVS) software. In order to verify the effectiveness of this method, the finite element (FE) models of a rat kidney, human hand, and blood vessels were reconstructed and good results were obtained.

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Fahmy, Mohamed Abdelsabour, and Moncef Toujani. "A New Fractional Boundary Element Model for the 3D Thermal Stress Wave Propagation Problems in Anisotropic Materials." Mathematical and Computational Applications 30, no. 1 (2025): 6. https://doi.org/10.3390/mca30010006.

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The primary purpose of this work is to provide a new fractional boundary element method (BEM) formulation to solve thermal stress wave propagation problems in anisotropic materials. In the Laplace domain, the fundamental solutions to the governing equations can be identified. Then, the boundary integral equations are constructed. The Caputo fractional time derivative was used in the formulation of the considered heat conduction equation. The three-block splitting (TBS) iteration approach was used to solve the resulting BEM linear systems, resulting in fewer iterations and less CPU time. The new TBS iteration method converges rapidly and does not involve complicated computations; it performs better than the two-dimensional double successive projection method (2D-DSPM) and modified symmetric successive overrelaxation (MSSOR) for solving the resultant BEM linear system. We only studied a special case of our model to compare our findings to those of other articles in the literature. Because the BEM results are so consistent with the finite element method (FEM) findings, the numerical results demonstrate the validity, accuracy, and efficiency of our proposed BEM formulation for solving three-dimensional thermal stress wave propagation problems in anisotropic materials.

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Yuan, Hui, Yifeng Zhong, Yuxin Tang, and Rong Liu. "Dynamic Characteristics of Composite Sandwich Panel with Triangular Chiral (Tri-Chi) Honeycomb under Random Vibration." Materials 17, no. 16 (2024): 3973. http://dx.doi.org/10.3390/ma17163973.

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A full triangular chiral (Tri-Chi) honeycomb, combining a honeycomb structure with triangular chiral configuration, notably impacts the Poisson’s ratio (PR) and stiffness. To assess the random vibration properties of a composite sandwich panel with a Tri-Chi honeycomb core (CSP-TCH), a two-dimensional equivalent Reissner–Mindlin model (2D-ERM) was created using the variational asymptotic method. The precision of the 2D-ERM in free and random vibration analysis was confirmed through numerical simulations employing 3D finite element analysis, encompassing PSD curves and RMS responses. Furthermore, the effects of selecting the model class were quantified through dynamic numerical examples. Modal analysis revealed that the relative error of the first eight natural frequencies predicted by the 2D-ERM consistently remained below 7%, with the modal cloud demonstrating high reliability. The PSD curves and their RMS values closely aligned with 3D finite element results under various boundary conditions, with a maximum error below 5%. Key factors influencing the vibration characteristics included the ligament–rib angle of the core layer and layup modes of the composite facesheets, while the rib-to-ligament thickness ratio and the aspect ratio exert minimal influence. The impact of the ligament–rib angle on the vibration properties primarily stems from the significant shift in the core layer’s Poisson’s ratio, transitioning from negative to positive. These findings offer a rapid and precise approach for optimizing the vibration design of CSP-TCH.

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