Статті в журналах: "Linear FEM analyse"

1

Ptaszny, Jacek, and Marcin Hatłas. "Evaluation of the FMBEM efficiency in the analysis of porous structures." Engineering Computations 35, no. 2 (April 16, 2018): 843–66. http://dx.doi.org/10.1108/ec-12-2016-0436.

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Purpose The purpose of this paper is to evaluate the efficiency of the fast multipole boundary element method (FMBEM) in the analysis of stress and effective properties of 3D linear elastic structures with cavities. In particular, a comparison between the FMBEM and the finite element method (FEM) is performed in terms of accuracy, model size and computation time. Design/methodology/approach The developed FMBEM uses eight-node Serendipity boundary elements with numerical integration based on the adaptive subdivision of elements. Multipole and local expansions and translations involve solid harmonics. The proposed model is used to analyse a solid body with two interacting spherical cavities, and to predict the homogenized response of a porous material under linear displacement boundary condition. The FEM results are generated in commercial codes Ansys and MSC Patran/Nastran, and the results are compared in terms of accuracy, model size and execution time. Analytical solutions available in the literature are also considered. Findings FMBEM and FEM approximate the geometry with similar accuracy and provide similar results. However, FMBEM requires a model size that is smaller by an order of magnitude in terms of the number of degrees of freedom. The problems under consideration can be solved by using FMBEM within the time comparable to the FEM with an iterative solver. Research limitations/implications The present results are limited to linear elasticity. Originality/value This work is a step towards a comprehensive efficiency evaluation of the FMBEM applied to selected problems of micromechanics, by comparison with the commercial FEM codes.

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2

Wang, Xiang Qiu, Zhi Guo Zhou, and Yu Hong Zhang. "Non-Linear FEM Analysis for the Layered Rock-Mass Tunnel Based on the Twin Shear Strength Criterion." Advanced Materials Research 168-170 (December 2010): 152–55. http://dx.doi.org/10.4028/www.scientific.net/amr.168-170.152.

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According to the geotechnical conditions, A FEM model has been established to analyse the mechanical characteristics of the highway tunnel in the layered rock mass. In this model the layered rock mass and the soften joint are simulated by the transversal isotropic material, the interfaces between layers are simulated by the element of rotational Goodman interface, but the interface between the lining structure and surrounding mass is proposed to simulate by an interface element with thickness, and the supporting of tunnel is simulated by the straight beam element. In the meantime, based on the twin shear strength criterion, the mechanical characteristics of rock, the stiff matrix of element for the layered rock mass, soften joint and interface have been discussed. The analytical model has been demonstrated by comparing the results of layered surrounding rock-mass FEM with the test data in situ.

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3

Akinpelu, Mutiu Adelodun, Bilyamin Adeoye Ibitoye, Samson Olalekan Odeyemi, and Kabir Opeyemi Olorede. "Numerical Verification of Strut and Tie Models and Failure Modes of Reinforced Self-Compacting Concrete Deep Beams." International Journal of Engineering Research in Africa 53 (March 2021): 76–100. http://dx.doi.org/10.4028/www.scientific.net/jera.53.76.

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This study utilized Finite Element Method (FEM) to analyse the structural behaviour and failure modes of Reinforced Self Compacting Concrete (RSCC) deep beams. Eighteen deep beam specimens subjected to four-point loadings were modelled and analyzed using Abaqus modelling tool. Damage plasticity model was used to characterised the nonlinear behaviour of concrete material while linear elastic, linear-plastic-hardening model represented the reinforcing steel material behaviour. The results of the finite model were compared with four different Strut and Tie Models (STMs) using one-way Analysis of Variance (ANOVA). Results of the numerical study revealed that the concrete strength and shear span to depth ratio mostly affect the load-deflection response of the beams. Also, the failure modes of the studied deep beams were influenced by shear span to depth ratio, concrete strength as well as web reinforcement distribution. The ANOVA results also showed that the FEM outperformed the existing STMs.

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4

Maleska, Tomasz, and Damian Beben. "Behaviour of corrugated steel plate bridge with high soil cover under seismic excitation." MATEC Web of Conferences 174 (2018): 04003. http://dx.doi.org/10.1051/matecconf/201817404003.

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The design codes and calculation methods related to the corrugated steel plate (CSP) bridges and culverts say only on the minimum soil height. This value is connected with the bridge span and shell height. In the case of static and dynamic loads (like passing the vehicles), such approach seems to be reasonable. However, it is important to know how the CSP bridges with high the soil covers behave under the seismic loads. This paper is presented the result of numerical study of CSP bridge with different high cover under seismic excitation. The analysed CSP railway bridge in the cross section has two closed pipe-arches. The span of shells is 4.40 m and the height of shells is 2.80 m. The load-carrying structure was constructed as two shells assembled from CSP sheets, designed with a depth of 0.05 m, pitch of 0.15 m, and plate thickness of 0.003 m. The real soil cover depth over the CSP structure (including ballast, blanket and backfill) equals 2.40 m. In this study two heights of soil cover were analysed (2.40 m and 5.00 m). Numerical analysis was conducted using the DIANA program based on finite element method (FEM). A linear model with El Centro records and Time History was used to analyse the problem.

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5

Plaitano, Francesco, Aurel Stratan, and Elide Nastri. "Simplified Modelling of Failure in High Strength Bolts under Combined Tension and Bending." Journal of Composites Science 6, no. 10 (October 11, 2022): 302. http://dx.doi.org/10.3390/jcs6100302.

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Bolted connections are widely adopted in steel structures and their behaviour affects to a large extent the global response of the system. High-strength bolts of type HV are commonly employed. Under pure tension, these bolt assemblies usually fail by thread stripping. However, it was observed experimentally that, under combined tension and bending, the failure mode changes to fracture of the shank. The former loading condition commonly occurs in the case of thick extended end plate connections and the latter in the case of flush end plates. In order to analyse the behaviour of the structure, the finite element method (FEM) is usually employed. While there is a wealth of information on FEM modelling of bolts for standard loading conditions (e.g., tension), the authors are unaware of a model able to replicate both tension-only and combined tension and bending conditions. In this paper, a simplified approach to be used in the framework of FEM is proposed to model the behaviour of high-strength HV bolts which can replicate the failure mechanism of bolts under tension only and combined tension and bending. The bolt assembly is modelled with continuum elements, supplemented by a non-linear spring connecting the nut to the bolt shank. The spring captures the stiffness, resistance, and ductility of the bolt-to-nut threaded connection, reproducing the experimentally observed failure mode in the case of pure tension conditions. A simplified damage model is applied to the continuum finite elements used to model the bolt, which replicates shank failure under combined tension and bending as a result of large local stresses and strains occurring under these conditions. The proposed model captures with good accuracy the actual behaviour of high-strength HV bolts under tension only as well as under combined tension and bending.

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6

Calderon Arenas, Jose Antonio. "Axisymmetric modelling of transient thermal response in solids for application to infrared photothermal radiometry technique." Revista Mexicana de Física 65, no. 1 (December 31, 2018): 54. http://dx.doi.org/10.31349/revmexfis.65.54.

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To induce temperature changes on the sample surface by the incidence of a monochromatic modulated light beam and detect the changes produced in the thermal radiation emission is the basic principle of the infrared photothermal radiometry technique. Until now, in order to analyze the thermal response mathematical models based in an one-dimensional model were used considering a sample with a finite thickness and an infinite incidence surface, as well as, the linear approximation of the Stefan-Boltzmann Law in the calculus of the heat losses due to thermal radiation. In this work, analytical and numerical models for the 2D heat diffusion in homogenous finite solid samples, are presented. These models were obtained by solving the heat diffusion equation, under cylindrical symmetry, considering mixed boundary conditions to include radiation and convection heat losses through the surfaces of the sample, and a monochromatic Gaussian excitation beam impinging on the front of the sample. The analytical models were obtained by solving the governing equations, considering the well-known linear approximation of the Stefan-Boltzmann law in the calculus of the heat losses due to thermal radiation. To analyse the effects of the non-linearity of the heat losses by thermal radiation on the thermal transient response, in the numerical model it was taken into account the full expression of the Stefan-Boltzmann law, and the transport equation was solved numerically by means of the Finite Element Method (FEM). The analytical solution for the oscillatory thermal response reveals the close dependence of the thermal response on the ratio of thickness to the radius of the sample, represented by the form factor sf. Both, the analytical and the numerical solutions were employed to simulate the thermal response of homogenous materials, and compared with experimental results reported elsewhere by part of our same research group. Finally, the difference between the thermal response predictions, from the analytical and numerical models, were analyzed.

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7

Devaud, Denis. "Petrov–Galerkin space-time hp-approximation of parabolic equations in H1/2." IMA Journal of Numerical Analysis 40, no. 4 (October 16, 2019): 2717–45. http://dx.doi.org/10.1093/imanum/drz036.

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Abstract We analyse a class of variational space-time discretizations for a broad class of initial boundary value problems for linear, parabolic evolution equations. The space-time variational formulation is based on fractional Sobolev spaces of order $1/2$ and the Riemann–Liouville derivative of order $1/2$ with respect to the temporal variable. It accommodates general, conforming space discretizations and naturally accommodates discretization of infinite horizon evolution problems. We prove an inf-sup condition for $hp$-time semidiscretizations with an explicit expression of stable test functions given in terms of Hilbert transforms of the corresponding trial functions; inf-sup constants are independent of temporal order and the time-step sequences, allowing quasi-optimal, high-order discretizations on graded time-step sequences, and also $hp$-time discretizations. For solutions exhibiting Gevrey regularity in time and taking values in certain weighted Bochner spaces, we establish novel exponential convergence estimates in terms of $N_t$, the number of (elliptic) spatial problems to be solved. The space-time variational setting allows general space discretizations and, in particular, for spatial $hp$-FEM discretizations. We report numerical tests of the method for model problems in one space dimension with typical singular solutions in the spatial and temporal variable. $hp$-discretizations in both spatial and temporal variables are used without any loss of stability, resulting in overall exponential convergence of the space-time discretization.

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8

HLADÍK, I., M. B. REED, and G. SWOBODA. "ROBUST PRECONDITIONERS FOR LINEAR ELASTICITY FEM ANALYSES." International Journal for Numerical Methods in Engineering 40, no. 11 (June 15, 1997): 2109–27. http://dx.doi.org/10.1002/(sici)1097-0207(19970615)40:11<2109::aid-nme163>3.0.co;2-1.

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9

Różyło, P. "Experimental-numerical test of open section composite columns stability subjected to axial compression." Archives of Materials Science and Engineering 84, no. 2 (April 2, 2017): 58–64. http://dx.doi.org/10.5604/01.3001.0010.0979.

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Purpose: The aim of the work was to analyse the critical state of thin-walled composite profiles with top-hat cross section under axial compression. Design/methodology/approach: The purpose of the work was achieved by using known approximation methods in experimental and finite element methods for numerical simulations. The scope of work included an analysis of the behavior of thin-walled composite structures in critical state with respect to numerical studies verified experimentally. Findings: In the presented work were determined the values of critical loads related to the loss of stability of the structures by using well-known approximation methods and computer simulations (FEM analysis). Research limitations/implications: The research presented in the paper is about the potential possibility of determining the values of critical loads equivalent to loss of stability of thin-walled composite structures and the future possibility of analyzing limit states related to loss of load capacity. Practical implications: The practical approach in the actual application of the described specimen and methodology of study is related to the necessity of carrying out of strength analyzes, allowing for a precise assessment of the loads upon which the loss of stability (bifurcation) occurs. Originality/value: The originality of the research is closely associated with used the thinwalled composite profile with top-hat cross-section, which is commonly used in the fuselage of passenger airplane. The methodology of simultaneous confrontation of the obtained results of critical loads by using approximation methods and using the linear eigenvalue solution in numerical analysis demonstrates the originality of the research character. Presented results and the methodology are intended for researchers, who are concerned with the topic of loss of stability of thin-walled composite structures.

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10

Zhang, Yunpeng, Dorival M. Pedroso, and Ling Li. "FDM and FEM solutions to linear dynamics of porous media: stabilised, monolithic and fractional schemes." International Journal for Numerical Methods in Engineering 108, no. 6 (March 11, 2016): 614–45. http://dx.doi.org/10.1002/nme.5231.

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11

Viale, Nicola, Giulio Ventura, Paulo B. Lourenço, and Javier Ortega. "Linear and non-linear FEM analyses to assess a shear flat-jack test for masonries." Journal of Building Engineering 43 (November 2021): 103169. http://dx.doi.org/10.1016/j.jobe.2021.103169.

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12

Annasiwaththa, Buddhika, and Koichi Oka. "B206 Initial design and FEM analysis of a non-contact power transfer method for magnetically levitated linear slider." Proceedings of the Symposium on the Motion and Vibration Control 2015.14 (2015): 297–301. http://dx.doi.org/10.1299/jsmemovic.2015.14.297.

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13

Chekhov, V. V. "Tensor-based matrices in geometrically non-linear FEM." International Journal for Numerical Methods in Engineering 63, no. 15 (2005): 2086–101. http://dx.doi.org/10.1002/nme.1343.

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14

De Luycker, E., D. J. Benson, T. Belytschko, Y. Bazilevs, and M. C. Hsu. "X-FEM in isogeometric analysis for linear fracture mechanics." International Journal for Numerical Methods in Engineering 87, no. 6 (January 24, 2011): 541–65. http://dx.doi.org/10.1002/nme.3121.

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15

GHERMAN, Laurian, and Raluca GHICIUC. "Linear electromagnetic accelerator." Safety & Defense 5, no. 2 (January 24, 2020): 17–21. http://dx.doi.org/10.37105/sd.50.

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Over time, the weapons have been based on mechanical energy (bows, catapults) and chemical energy (guns, missiles), however, at the moment, more and more weapons are designed using electromagnetic energy (railgun, coilgun). The focus of this paper is to obtain the desired muzzle velocities of a projectile according to the existent current. In the first part of the paper, the railgun and coilgun design are presented along with their most important advantages. Based on these observations, a new design of an electromagnetic launch system is presented. Next, Maxwell interactive software package was used that applies the finite element method (FEM) to analyze and solve 3D electromagnetic field problems in order to analyze the variation of acceleration force, speed in time. All simulation data shows that this design has a great potential, because of the adaptability to different applications.

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16

Staneva, Nelly, Yancho Genchev, and Desislava Hristodorova. "Strength Investigation of an Upholstered Furniture Frame with Side Plates of PB, OSB and PLY by Finite Element Method." Drvna industrija 71, no. 3 (July 10, 2020): 253–59. http://dx.doi.org/10.5552/drvind.2020.1921.

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Comparative analysis of the strength characteristics of one-seat upholstered furniture frame with rails of Pinus Sylvestris L. and side plates of PB, OSB and PLY boards was carried out. 3D geometric model of the upholstered furniture frame was created by Autodesk Inventor Pro®. Linear static analyses were carried out by the method of finite elements (FEM) simulating light-service loading. The orthotropic material characteristics of the used materials were considered in the analyses. Two variants of corner joints in the frame (model A – staples and PVAc; model B - staples, PVAc and strengthening elements under the rail of the seat) were considered. The laboratory established coefficients of rotational stiffness of used staple corner joints in the skeleton were considered in finite element analysis (FEA). As result, the distribution of the maximum and minimum principal stresses in the 3D model of upholstered furniture frame side plates were derived and analysed. The worst failure indexes according to Tsai-Wu failure criteria were calculated at heavy-service load. The study provided database of strength values that can help in the engineering of upholstered furniture frames with side plates of PB, OSB and PLY.

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17

Barrientos, Mauricio A., Gabriel N. Gatica, and Matthias Maischak. "A posteriorierror estimates for linear exterior problemsviamixed-FEM and DtN mappings." ESAIM: Mathematical Modelling and Numerical Analysis 36, no. 2 (March 2002): 241–72. http://dx.doi.org/10.1051/m2an:2002011.

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18

Ferretti, Patrich, Gian Maria Santi, Christian Leon-Cardenas, Elena Fusari, Giampiero Donnici, and Leonardo Frizziero. "Representative Volume Element (RVE) Analysis for Mechanical Characterization of Fused Deposition Modeled Components." Polymers 13, no. 20 (October 15, 2021): 3555. http://dx.doi.org/10.3390/polym13203555.

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Additive manufacturing processes have evolved considerably in the past years, growing into a wide range of products through the use of different materials depending on its application sectors. Nevertheless, the fused deposition modelling (FDM) technique has proven to be an economically feasible process turning additive manufacture technologies from consumer production into a mainstream manufacturing technique. Current advances in the finite element method (FEM) and the computer-aided engineering (CAE) technology are unable to study three-dimensional (3D) printed models, since the final result is highly dependent on processing and environment parameters. Because of that, an in-depth understanding of the printed geometrical mesostructure is needed to extend FEM applications. This study aims to generate a homogeneous structural element that accurately represents the behavior of FDM-processed materials, by means of a representative volume element (RVE). The homogenization summarizes the main mechanical characteristics of the actual 3D printed structure, opening new analysis and optimization procedures. Moreover, the linear RVE results can be used to further analyze the in-deep behavior of the FDM unit cell. Therefore, industries could perform a feasible engineering analysis of the final printed elements, allowing the FDM technology to become a mainstream, low-cost manufacturing process in the near future.

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19

Bringmann, P., C. Carstensen, and G. Starke. "An Adaptive Least-Squares FEM for Linear Elasticity with Optimal Convergence Rates." SIAM Journal on Numerical Analysis 56, no. 1 (January 2018): 428–47. http://dx.doi.org/10.1137/16m1083797.

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20

Zhao, Jun, Li Jun Wang, and Dan Ying Gao. "Non-Linear FEM Analysis of Steel Fiber Reinforced Concrete Shearwall." Advanced Materials Research 163-167 (December 2010): 1551–54. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.1551.

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The numerical simulation by nonfinear finite element method(FEM) was adopted to analyze the behavior and the influences of the fraction of steel fiber by volume fraction and the strength of steel fiber reinforced concrete on the bearing capacity and the ductility of reinforced concrete shearwalls. The results show that with the increase of the fraction of steel fiber by volume fraction, the bearing capacity and ductility coefficient of steel fiber reinforced concrete shearwalls increase gradually. With the increase of the strength of steel fiber reinforced concrete, the bearing capacity and ductility coefficient of steel fiber reinforced concrete shearwalls decrease. It proves the rationality of the unit type, stress-strain relation of material and failure criteria used in the finite element analysis model.

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21

Koleva, Miglena. "FINITE ELEMENT SOLUTION OF BOUNDARY VALUE PROBLEMS WITH NONLOCAL JUMP CONDITIONS." Mathematical Modelling and Analysis 13, no. 3 (September 30, 2008): 383–400. http://dx.doi.org/10.3846/1392-6292.2008.13.383-400.

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We consider stationary linear problems on non‐connected layers with distinct material properties. Well posedness and the maximum principle (MP) for the differential problems are proved. A version of the finite element method (FEM) is used for discretization of the continuous problems. Also, the MP and convergence for the discrete solutions are established. An efficient algorithm for solution of the FEM algebraic equations is proposed. Numerical experiments for linear and nonlinear problems are discussed.

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22

Perrella, Michele, Pasquale Franciosa, and Salvatore Gerbino. "FEM and BEM Stress Analysis of Mandibular Bone Surrounding a Dental Implant." Open Mechanical Engineering Journal 9, no. 1 (May 15, 2015): 282–92. http://dx.doi.org/10.2174/1874155x01509010282.

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In the present work the structural behaviour of a mandible with a dental implant, considering a unilateral occlusion, is numerically analysed by means of the Finite Element Method (FEM) and the Boundary Element Method (BEM). The mandible, whose CAD model was obtained by computer tomography scans, is considered as completely edentulous and only modelled in the zone surrounding the implant. The material behaviour of bone is assumed as isotropic linear elastic or, alternatively, as orthotropic linear elastic. With reference to the degree of osteo-integration between the implant and the mandibular bone, a partial osteo-integration is considered; consequently a nonlinear contact analysis is performed, with allowance for friction at the interface between implant and bone. A model of a commercial dental implant is digitised by means of optical 3D scanning process and fully reconstructed in all its geometrical features. Special attention is drawn to the mathematical reconstruction of the CAD model in order to facilitate the meshing process in the BEM environment and reduce the geometrical imperfections generated during the CAD to CAE translation process. The results of FEM and BEM analyses in terms of stress distribution on the mandible are compared in order to benchmark the two methodologies against accuracy and pre-processing efforts.

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23

Ming, F. R., A. M. Zhang, and S. P. Wang. "Smoothed Particle Hydrodynamics for the Linear and Nonlinear Analyses of Elastoplastic Damage and Fracture of Shell." International Journal of Applied Mechanics 07, no. 02 (April 2015): 1550032. http://dx.doi.org/10.1142/s1758825115500325.

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It is a troublesome and focused problem of solid mechanics to solve shell structures with Smoothed particle hydrodynamics (SPH), which is a fully meshfree method. In this paper, an integral model of SPH shell is proposed to more accurately capture the nonlinear strain along the thickness direction. Though the idea is similar to the "Gaussian integral point" in Finite element method (FEM), it is absent and just the first presentation in SPH. Furthermore, focusing on the metal materials, a high-efficiency iteration algorithm for plasticity is derived and the plastic damage theory of Lemaitre–Chaboche is also introduced based on the studies of Caleyron et al. (2011). As for the dynamic fracture of SPH shell, the multiple line segments algorithm is proposed to treat crack adaptively, which overcomes the mesh dependency occurring in mesh method. These algorithms and theories are successfully applied in the integral model of SPH shell of elasticity, plastic damage and dynamic fracture. Finally, the linear and nonlinear analyses of geometry and material are carried out with FEM, the global model and the integral model of SPH shell to prove the feasibility and the accuracy of the integral model.

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24

Santini, Silvia, Carlo Baggio, Valerio Sabbatini, and Claudio Sebastiani. "Seismic Assessment of Roman Concrete Groin Vaults through UAV, NDT and 3D Analyses." Heritage 5, no. 1 (January 27, 2022): 311–31. http://dx.doi.org/10.3390/heritage5010017.

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In Roman Baths, the Romans employed barrel and groin vaults of great dimensions, with maximum span more than 20 m; simple tools of structural analysis of ancient wide span vaulted halls are still lacking, due to geometrical and material complexity. In this paper, we study the collapse behavior, under horizontal static action, of a corner cross vault of the Baths of Diocletian in Rome (Hall I). Two methods of analysis are here used: non-linear incremental finite element and limit analysis. In both cases, 3D models have been developed by means of UAV inspection, NDT measures, and AVT monitoring. The construction of the overall 3D geometry has been here afforded with a specific pre-processing approach. Midas commercial software has been employed for FEM analysis, assuming a constitutive law specifically developed for Roman concrete. In limit analysis, masonry is discretized as a system of interacting rigid bodies in no-tension and frictional contact. The computational code consists in a linear approach, which makes use of a series of optimization packages via lower and upper bound techniques. Finally, a strategy based on FEM analysis including discontinuities was implemented, and the results were compared with the two previous approaches.

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25

Lua, Yuan Jie, and Robert H. Sues. "Probabilistic Finite-Element Analysis of Airfield Pavements." Transportation Research Record: Journal of the Transportation Research Board 1540, no. 1 (January 1996): 29–38. http://dx.doi.org/10.1177/0361198196154000105.

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Mechanistic pavement analysis and design based on either layered elastic analysis (LEA) or the finite element method (FEM) is increasingly being used to replace the empirical design process. The simplifying assumptions of a uniform, homogeneous layer of linear material used in LEA can render its analysis inaccurate for real pavement structures. The FEM is more attractive for structural analysis of pavements; the generality of the FEM also allows both the use of comprehensive material models and modeling of the spatial variability that exists in pavement systems. To date, spatial variability and uncertainty are ignored in pavement system finite element analyses. Ignoring spatial variability and uncertainty implies a false sense of accuracy in the results and can lead to inaccurate assessment of the pavement. The first application of the probabilistic finite element method to pavement response analysis and life prediction and the first investigation of the effects of spatial variability on pavement life prediction are presented. It is concluded that the probabilistic FEA, with spatial variability, is a more accurate representation of the true physical condition and leads to results that are less conservative than those obtained with probabilistic LEA.

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26

Nadal, E., J. J. Ródenas, J. Albelda, M. Tur, J. E. Tarancón, and F. J. Fuenmayor. "Efficient Finite Element Methodology Based on Cartesian Grids: Application to Structural Shape Optimization." Abstract and Applied Analysis 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/953786.

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This work presents an analysis methodology based on the use of the Finite Element Method (FEM) nowadays considered one of the main numerical tools for solving Boundary Value Problems (BVPs). The proposed methodology, so-called cg-FEM (Cartesian grid FEM), has been implemented for fast and accurate numerical analysis of 2D linear elasticity problems. The traditional FEM uses geometry-conforming meshes; however, in cg-FEM the analysis mesh is not conformal to the geometry. This allows for defining very efficient mesh generation techniques and using a robust integration procedure, to accurately integrate the domain’s geometry. The hierarchical data structure used in cg-FEM together with the Cartesian meshes allow for trivial data sharing between similar entities. The cg-FEM methodology uses advanced recovery techniques to obtain an improved solution of the displacement and stress fields (for which a discretization error estimator in energy norm is available) that will be the output of the analysis. All this results in a substantial increase in accuracy and computational efficiency with respect to the standard FEM. cg-FEM has been applied in structural shape optimization showing robustness and computational efficiency in comparison with FEM solutions obtained with a commercial code, despite the fact that cg-FEM has been fully implemented in MATLAB.

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27

He, Xiao Cong. "Comparisons of Linear and Nonlinear FEA of Adhesively Bonded Beams." Advanced Materials Research 1088 (February 2015): 763–68. http://dx.doi.org/10.4028/www.scientific.net/amr.1088.763.

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The effect of boundary conditions on the stress distributions in single-lap adhesively bonded cantilevered beams has been investigated using the three-dimensional linear static and non-linear quasi-static finite element method. The displacement obtained from the linear static and the non-linear quasi-static analyses are compared under the same deformation scale factor for three typical boundary conditions. The analysis results indicate that there are significant differences between the linear static and non-linear quasi-static analyses only if there are significant bending effect on the bonded section. The bigger the bending effect on the bonded section, the bigger the difference between the linear static and non-linear quasi-static analyses.

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28

Beuchler, Sven, and Martin Purrucker. "Schwarz Type Solvers for -FEM Discretizations of Mixed Problems." Computational Methods in Applied Mathematics 12, no. 4 (2012): 369–90. http://dx.doi.org/10.2478/cmam-2012-0030.

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AbstractThis paper investigates the discretization of mixed variational formulation as, e.g., the Stokes problem by means of the hp-version of the finite element method. The system of linear algebraic equations is solved by the preconditioned Bramble-Pasciak conjugate gradient method. The development of an efficient preconditioner requires three ingredients, a preconditioner related to the components of the velocity modes, a preconditioner for the Schur complement related to the components of the pressure modes and a discrezation by a stable finite element pair which satisfies the discrete inf-sup-condition. The last condition is also important in order to obtain a stable discretization scheme. The preconditioner for the velocity modes is adapted from fast $hp$-FEM preconditioners for the potential equation. Moreover, we will prove that the preconditioner for the Schur complement can be chosen as a diagonal matrix if the pressure is discretized by discontinuous finite elements. We will prove that the system of linear algebraic equations can be solved in almost optimal complexity. This yields quasioptimal hp-FEM solvers for the Stokes problems and the linear elasticity problems. The latter are robust with respect to the contraction ratio ν. The efficiency of the presented solver is shown in several numerical examples.

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29

Gong, Z. X., Y. B. Chai, and W. Li. "Coupled Analysis of Structural–Acoustic Problems Using the Cell-Based Smoothed Three-Node Mindlin Plate Element." International Journal of Computational Methods 13, no. 02 (March 2016): 1640007. http://dx.doi.org/10.1142/s0219876216400077.

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The cell-based smoothed finite element method (CS-FEM) using the original three-node Mindlin plate element (MIN3) has recently established competitive advantages for analysis of solid mechanics problems. The three-node configuration of the MIN3 is achieved from the initial, complete quadratic deflection via ‘continuous’ shear edge constraints. In this paper, the proposed CS-FEM-MIN3 is firstly combined with the face-based smoothed finite element method (FS-FEM) to extend the range of application to analyze acoustic fluid–structure interaction problems. As both the CS-FEM and FS-FEM are based on the linear equations, the coupled method is only effective for linear problems. The cell-based smoothed operations are implemented over the two-dimensional (2D) structure domain discretized by triangular elements, while the face-based operations are implemented over the three-dimensional (3D) fluid domain discretized by tetrahedral elements. The gradient smoothing technique can properly soften the stiffness which is overly stiff in the standard FEM model. As a result, the solution accuracy of the coupled system can be significantly improved. Several superior properties of the coupled CS-FEM-MIN3/FS-FEM model are illustrated through a number of numerical examples.

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30

Chen, Jie, Hai Wang, and Jie Wang. "Buckling and vibration analyses of composite laminates with weak interfaces by a coupled meshfree and finite element method." Science and Engineering of Composite Materials 23, no. 1 (January 1, 2016): 93–105. http://dx.doi.org/10.1515/secm-2014-0102.

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AbstractBuckling and free vibration analyses for composite laminates with weak interfaces were performed based on a three-dimensional hybrid semianalytical model. The model was established by coupling the radial point interpolation method and finite element method (FEM) in a Hamilton system. A direct coupling approach was developed based on the FEM background cell algorithm, and a modified Hamiltonian function for buckling analysis of rectangular laminated plates was given. The governing equations were deduced with the transfer matrix technique and a general linear spring layer model based on the modified Hellinger-Reissner variational principle. Several numerical examples are also presented to validate the efficiency and accuracy of the present method.

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31

Becker, Roland, Michael Innerberger, and Dirk Praetorius. "Adaptive FEM for Parameter-Errors in Elliptic Linear-Quadratic Parameter Estimation Problems." SIAM Journal on Numerical Analysis 60, no. 3 (June 2022): 1450–71. http://dx.doi.org/10.1137/21m1458077.

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32

Syrkin, Ilya. "Linear Synchronous Motor Model." MATEC Web of Conferences 297 (2019): 02006. http://dx.doi.org/10.1051/matecconf/201929702006.

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Liner synchronous motor (LSM) is perspective motor for milling machines and other manufacturing equipment such as 3D printers, laser cutting and engraving machines, etc. Some different construction of LSM can be found. The LSM with permanent magnets is modeled in this paper. Comsol Multiphysics is used for finite element model of LSM. Motor stator is built using rear earth magnets N52, an anchor consists of 6 teeth with 3-phase winding. Large cogging force is the problem of LSM, so there is task to reduce this force. This task can be solved by motor geometry optimization. Geometric parameter of motor is represented by variables. It allowed using optimization methods for best geometry search. FEM model with two different mesh sizes is analysed in this paper. Each mesh allows find solution but calculation time and tolerance are different. During experiments, optimal size of tooth for maximal driving force is found. Cogging force is also reduced.

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33

Novák, Josef. "FEM Analysis of Piezoelectric Resonator Polarization Process." Applied Sciences 11, no. 24 (December 17, 2021): 12045. http://dx.doi.org/10.3390/app112412045.

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The polarization of the piezoelectric resonator depends on the direction of the applied electric field. The direction of the applied electric field is determined by the shape of the resonator and the position of the electrodes. In case of resonators with electrodes incompletely covering their bases, an inhomogeneous electric field is generated, which results in an inhomogeneous polarization of the resonator. The resonator will be polarized in some places either in a direction other than the desired one or not polarized at all. The aim of this work is to analyze the polarization process on resonators with electrodes incompletely covering their bases. The physical description is given by the linear piezoelectric equations, the Gaussian equation for the description of the electric field and by Newton’s law of force. On this basis, a FEM model is developed and used to analyze the polarization process. The results of the calculation of the electric field vector distribution are presented. Finally, the areas are identified in which polarization in the desired direction is achieved in the resonator as well as the ones where no polarization occurs.

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34

XU, X., G. R. LIU, Y. T. GU, and G. Y. ZHANG. "A CONFORMING POINT INTERPOLATION METHOD (CPIM) BY SHAPE FUNCTION RECONSTRUCTION FOR ELASTICITY PROBLEMS." International Journal of Computational Methods 07, no. 03 (September 2010): 369–95. http://dx.doi.org/10.1142/s0219876210002295.

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A conforming point interpolation method (CPIM) is proposed based on the Galerkin formulation for 2D mechanics problems using triangular background cells. A technique for reconstructing the PIM shape functions is proposed to create a continuous displacement field over the whole problem domain, which guarantees the CPIM passing the standard patch test. We prove theoretically the existence and uniqueness of the CPIM solution, and conduct detailed analyses on the convergence rate; computational efficiency and band width of the stiffness matrix of CPIM. The CPIM does not introduce any additional degrees of freedoms compared to the linear FEM and original PIM; while convergence rate of quadratic CPIM is in between that of linear FEM and quadratic FEM which results in the high computational efficiency. Intensive numerical studies verify the properties of the CPIM.

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35

Meloni, Daniel, and Barbara de Nicolo. "Non Linear Fem Modelling for the Design of Openings in Masonry Walls." Key Engineering Materials 747 (July 2017): 44–51. http://dx.doi.org/10.4028/www.scientific.net/kem.747.44.

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Countries like Italy have to face the constant issue of preserving and renewing existing buildings, both for the sake of conservation of the architectural and monumental heritage and due to the need of requalification and reuse. Considering the seismic hazard of most of Italian regions, structural interventions need to be carefully evaluated since National Codes don’t allow any sort of weakening of buildings and conversely regard any structural intervention as an opportunity to improve existing building safety. Most of existing and historical buildings in Italy are masonry structures, whose functional and architectonical requalification usually consists of new openings in masonry walls, but, according to the above mentioned principles, these modifications need to be designed at least without significantly affecting the pre-existent structural behavior. Thus, steel or reinforced concrete frames are to be designed in order to restore the previous conditions of masonry integrity. In this paper FEM analyses are performed and discussed in order to achieve this goal.

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36

Hidayah, Aisyah Putri, and Siti Rahmawati. "Effect of Leadership Style on the Performance of Student Organization Management." Management Journal of Binaniaga 7, no. 2 (December 31, 2022): 105–18. http://dx.doi.org/10.33062/mjb.v7i2.3.

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The Student Executive Board of the Faculty of Economics and Management, Bogor Agricultural University (BEM FEM IPB) is a faculty-level organization that has succeeded in making achievements as a Healthy Student Organization at the IPB Appreciation Week event for two consecutive years, namely 2020 and 2021. Based on the results of research conducted by BEM FEM IPB to students of the Faculty of Economics and Management found that the performance of organizational management was not good enough and there were gaps in the results of performance assessments between departments in BEM FEM IPB. This study aims to identify leadership styles, organizational management performance, and analyze the influence of leadership style on the performance of BEM FEM IPB student organization administrators 2020/2021. The results of multiple linear regression analysis show that the leadership style that has the most dominant influence is the achievement-oriented leadership style. The performance of BEM FEM IPB management is in the good category. The results of multiple linear regression analysis show that leadership style influences the performance of BEM FEM IPB organizational management simultaneously and only achievement-oriented leadership style significantly influences the performance of organizational management.

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37

Chen, Tao, and Hua Dong He. "Finite Element Analysis of a Steel Spiral Staircase with Multiple Supports." Advanced Materials Research 255-260 (May 2011): 1964–67. http://dx.doi.org/10.4028/www.scientific.net/amr.255-260.1964.

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This paper presents finite element analyses of a steel spiral staircase with multiple supports. The complex geometries were modeled using commercial finite element method (FEM) software. Linear elastic analyses were carried out to investigate its deformation and moment distribution. Besides these, mode analysis was also performed to explore its pedestrian comfort. Finally the reliability of the structure is proved.

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38

Soares Jr, D., O. von Estorff, and W. J. Mansur. "Efficient non-linear solid-fluid interaction analysis by an iterative BEM/FEM coupling." International Journal for Numerical Methods in Engineering 64, no. 11 (2005): 1416–31. http://dx.doi.org/10.1002/nme.1408.

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39

Legrain, G., N. Moës, and E. Verron. "Robust and direct evaluation ofJ2in linear elastic fracture mechanics with the X-FEM." International Journal for Numerical Methods in Engineering 76, no. 10 (December 3, 2008): 1471–88. http://dx.doi.org/10.1002/nme.2366.

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40

Tokuda, N., T. Sakurai, and T. Teraoku. "Sloshing Analysis Method Using Existing FEM Structural Analysis Code." Journal of Pressure Vessel Technology 117, no. 3 (August 1, 1995): 268–72. http://dx.doi.org/10.1115/1.2842122.

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A fluid analysis method using an analogy relating the pressure wave equation of fluid to elasticity equations is applied to sloshing analysis, where existing FEM structural analysis codes are available. It is seen from theoretical consideration that the present method is equivalent to the classical FEM formulation of linear sloshing analysis. The numerical analyses of liquid sloshing in a rigid cubic tank and of vibration of tubulous fluid under gravitational force are performed by using the present method. The results are shown to be in excellent agreement with the theoretical values.

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41

Köster, M., and S. Turek. "The Influence of Higher Order FEM Discretisations on Multigrid Convergence." Computational Methods in Applied Mathematics 6, no. 2 (2006): 221–32. http://dx.doi.org/10.2478/cmam-2006-0011.

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AbstractQuadratic and even higher order finite elements are interesting candidates for the numerical solution of partial differential equations (PDEs) due to their improved approximation properties in comparison to linear approaches. The systems of equations that arise from the discretisation of the underlying (elliptic) PDEs are often solved by iterative solvers like preconditioned Krylow-space methods, while multigrid solvers are still rarely used – which might be caused by the high effort that is associated with the realisation of the necessary data structures as well as smoothing and intergrid transfer operators. In this note, we discuss the numerical analysis of quadratic conforming finite elements in a multigrid solver. Using the “correct” grid transfer operators in conjunction with a quadratic finite element approximation allows to formulate an improved approximation property which enhances the (asymptotic) behaviour of multigrid: If m denotes the number of smoothing steps, the convergence rates behave asymptotically like O(1/m2) in contrast to O(1/m) for linear FEM.

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42

Funken, Stefan, Dirk Praetorius, and Philipp Wissgott. "Efficient implementation of adaptive P1-FEM in Matlab." Computational Methods in Applied Mathematics 11, no. 4 (2011): 460–90. http://dx.doi.org/10.2478/cmam-2011-0026.

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Abstract We provide a MATLAB package p1afem for an adaptive P1-finite element method (AFEM). This includes functions for the assembly of the data, different error estimators, and an indicator-based adaptive meshrefining algorithm. Throughout, the focus is on an efficient realization by use of MATLAB built-in functions and vectorization. Numerical experiments underline the efficiency of the code which is observed to be of almost linear complexity with respect to the runtime. Although the scope of this paper is on AFEM, the general ideas can be understood as a guideline for writing efficient MATLAB code.

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43

Teranishi, T., and Hironobu Nisitani. "Effectiveness of Linear Notch Mechanics under the Condition of Small Scale Yielding." Key Engineering Materials 452-453 (November 2010): 21–24. http://dx.doi.org/10.4028/www.scientific.net/kem.452-453.21.

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The linear notch mechanics (LNM) was proposed by H. Nisitani in 1983. The concept of LNM can assure the occurrence of the same phenomena in a notched specimen and a real object. The effectiveness of LNM under the condition of small scale yielding has not been confirmed sufficiently. In this paper, the effectiveness of LNM under the condition of small scale yielding is discussed based on the results of FEM elastic-plastic analyses.

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44

Ma, Lv Zhou, Jian Liu, Xun Lin Diao, and Xiao Dong Jia. "Numerical Examples of Variable Cross-Section Beam Elements." Advanced Materials Research 557-559 (July 2012): 822–25. http://dx.doi.org/10.4028/www.scientific.net/amr.557-559.822.

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Based on MATLAB platform, program VCBEP (Variable Cross-section Beam Element based on Positional FEM) is compiled, and the cantilever beam with linear profile and the parabolic simple supported beam are calculated. The variable cross-section beam element is proposed to analyze rectangular beam whose beam depth changes in a linear or quadratic parabolic way and beam width is fixed and the exact solution can be obtained.

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45

LI, Y., M. LI, and G. R. LIU. "A MODIFIED TRIANGULATION ALGORITHM TAILORED FOR THE SMOOTHED FINITE ELEMENT METHOD (S-FEM)." International Journal of Computational Methods 11, no. 01 (September 2, 2013): 1350069. http://dx.doi.org/10.1142/s0219876213500692.

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Meshing is one of the key tasks in using the finite element method (FEM), the smoothed finite element method (S-FEM), finite volume method (FVM), and many other discrete numerical methods. Linear triangular (T3) mesh is one of the most widely used mesh, because it can be generated and refined automatically for discrete domains of complicated geometry, and hence save significantly the time for model creation. This paper presents a modified triangulation algorithm based on the advancing front technique to provide a comprehensive linear triangular mesh generator with six connectivity lists, including element–node (Ele–N) connectivity, element–edge (Ele–Eg) connectivity, edge–node (Eg–N) connectivity, edge–element (Eg–Ele) connectivity, node–edge (N–Eg) connectivity and node–element (N–Ele) connectivity. These six connectivity lists are generated along the way when the T3 elements are created, and hence it is done in a most efficient fashion. The connectivity is recorded in the usual counter-clockwise convention for convenient utilization in various S-FEM models for effective analyses. In addition, an algorithm is developed for renumbering the nodes in the T3 mesh to obtain a minimized bandwidth of stiffness matrices for both FEM and S-FEM models.

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46

MARASCA, C. Z. S., E. BITTENCOURT, and V. M. R. D. BESSA. "Modelling of fracture problems in quasi-brittle materials by the E-FEM." Revista IBRACON de Estruturas e Materiais 11, no. 2 (April 2018): 244–54. http://dx.doi.org/10.1590/s1983-41952018000200002.

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Abstract In this paper a numerical model with strong discontinuities is presented to address fracture problems in quasi-brittle materials. A non-symmetrical statically and kinematically consistent formulation is implemented. The strong discontinuity in the displacement field is represented using the elemental enrichment finite element method (E-FEM). In other words, the strong discontinuity is introduced into the finite element and the additional degrees of freedom are condensed at the element level, allowing the implementation into existing computational codes. Two constitutive models are used to analyze the behavior of the cracked zone, linear and exponential. The exponential model results are closer to those obtained in experimental data and representative numerical simulations than the linear model.

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47

CARDOSO, M. T. S. A., and M. C. V. LIMA. "Physical and geometrical non-linear behavior of precast beams on elastomeric supports." Revista IBRACON de Estruturas e Materiais 11, no. 1 (February 2018): 183–202. http://dx.doi.org/10.1590/s1983-41952018000100010.

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Abstract The stability of long and slender precast beams has been associated with structural collapse during the transitory phase of construction. The inevitable deviations regarding the execution between the support cross-section and midspan aggravate the instability problem, thus causing the beams to become even more susceptible to its effects. The focal point of this study is the numerical and behavioral evaluation of concrete beams that present geometric imperfections on elastomeric supports and analyze the influence exerted by the variables of: strength characteristics of concrete, physical non-linearity of the concrete and the compression stiffness of the bearing pad. The numerical analyses were developed on a computer program based on the finite element method (FEM). Among the principle conclusions drawn from the study, one finds that the increase in the characteristic strength of the concrete provides the beam with a higher degree of stability, and the consideration of the physical non-linear behavior of the material did not allow the equilibrium point on the numerical model to be found in some of the cases that were evaluated. The rotational stiffness of the pad decreases as the skew angle increases. Therefore, one needs to remember that in very critical situations, it may not be possible to find the point of equilibrium, thus leading to collapse.

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48

Romero, A., P. Galvín, and J. Domínguez. "3D non-linear time domain FEM–BEM approach to soil–structure interaction problems." Engineering Analysis with Boundary Elements 37, no. 3 (March 2013): 501–12. http://dx.doi.org/10.1016/j.enganabound.2013.01.001.

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49

Gudi, Thirupathi, and Kamana Porwal. "A Reliable Residual Based A Posteriori Error Estimator for a Quadratic Finite Element Method for the Elliptic Obstacle Problem." Computational Methods in Applied Mathematics 15, no. 2 (April 1, 2015): 145–60. http://dx.doi.org/10.1515/cmam-2015-0005.

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AbstractA residual based a posteriori error estimator is derived for a quadratic finite element method (FEM) for the elliptic obstacle problem. The error estimator involves various residuals consisting of the data of the problem, discrete solution and a Lagrange multiplier related to the obstacle constraint. The choice of the discrete Lagrange multiplier yields an error estimator that is comparable with the error estimator in the case of linear FEM. Further, an a priori error estimate is derived to show that the discrete Lagrange multiplier converges at the same rate as that of the discrete solution of the obstacle problem. The numerical experiments of adaptive FEM show optimal order convergence. This demonstrates that the quadratic FEM for obstacle problem exhibits optimal performance.

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50

Barrios, Tomás P., Edwin M. Behrens, and María González. "Low cost a posteriori error estimators for an augmented mixed FEM in linear elasticity." Applied Numerical Mathematics 84 (October 2014): 46–65. http://dx.doi.org/10.1016/j.apnum.2014.05.008.

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