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Journal articles on the topic 'Monolithic finite element formulation'

Author: Grafiati

Published: 6 September 2023

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1

Gupta, Adhip, and C. S. Jog. "A Monolithic Finite Element Formulation for Magnetohydrodynamics Involving a Compressible Fluid." Fluids 7, no. 1 (January 7, 2022): 27. http://dx.doi.org/10.3390/fluids7010027.

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This work develops a new monolithic finite-element-based strategy for magnetohydrodynamics (MHD) involving a compressible fluid based on a continuous velocity–pressure formulation. The entire formulation is within a nodal finite element framework, and is directly in terms of physical variables. The exact linearization of the variational formulation ensures a quadratic rate of convergence in the vicinity of the solution. Both steady-state and transient formulations are presented for two- and three-dimensional flows. Several benchmark problems are presented, and comparisons are carried out against analytical solutions, experimental data, or against other numerical schemes for MHD. We show a good coarse-mesh accuracy and robustness of the proposed strategy, even at high Hartmann numbers.

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2

Antunes, A. R. E., P. R. M. Lyra, R. B. Willmersdorf, and S. M. A. Bastos. "An implicit monolithic formulation based on finite element formulation for incompressible Navier–Stokes equations." Journal of the Brazilian Society of Mechanical Sciences and Engineering 37, no. 1 (March 18, 2014): 199–210. http://dx.doi.org/10.1007/s40430-014-0155-x.

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3

Sun, WaiChing. "A stabilized finite element formulation for monolithic thermo-hydro-mechanical simulations at finite strain." International Journal for Numerical Methods in Engineering 103, no. 11 (April 30, 2015): 798–839. http://dx.doi.org/10.1002/nme.4910.

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4

Kutlu, Akif. "Mixed finite element formulation for bending of laminated beams using the refined zigzag theory." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 235, no. 7 (July 2021): 1712–22. http://dx.doi.org/10.1177/14644207211018839.

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This study presents a mixed finite element formulation for the stress analysis of laminated composite beams based on the refined zigzag theory. The Hellinger–Reissner variational principle is employed to obtain the first variation of the functional that is expressed in terms of displacements and stress resultants. Due to C0 continuity requirements of the formulation, linear shape functions are adopted to discretize the straight beam domain with two-noded finite elements. The proposed formulation is shear locking free from nature since it introduces displacement and stress resultant terms as independent field variables. A monolithic solution of the global finite element equations is preferred, hence the stress resultants are directly obtained from the solution of these equations. The in-plane strain measures of the beam are obtained directly at the nodes over the compliance matrix and stress resultants by avoiding error-prone spatial derivatives. Following, transverse shear stresses are calculated from the equilibrium equations at the post-processing level. This simple but effective finite element formulation is first verified and tested for convergence behavior. The robustness of the approach is shown through some examples and its accuracy in predicting the displacement and stress components is revealed.

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5

Панасюк, Леонид, Leonid Panasyuk, Галина Кравченко, Galina Kravchenko, Елена Труфанова, Elena Trufanova, Инал Тарба, Inal Tarba, Лаша Цвейба, and Lasha Cveyba. "FINITE ELEMENT MODELLING OF INTERACTION BUILDING FRAME AND SLAB-PILE FOUNDATION." Construction and Architecture 7, no. 1 (April 19, 2019): 34–38. http://dx.doi.org/10.29039/article_5c646f16bffb38.56532696.

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The article deals with the simulation of joint work of slab grillage and monolithic frame of the building by finite element method. The finite-element model is developed in the spatial formulation according to the complex scheme "upper structure-base plate-pile Foundation". The pile field was modeled by pliable rods with stiffness corresponding to the average draft of the pile field. Static and dynamic calculations are performed in the ING+software package. The results of the stress-strain state of the building frame elements demonstrate the correctness of this approach to take into account the compliance of the base.

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6

Lozovskiy, Alexander, Maxim A. Olshanskii, and Yuri V. Vassilevski. "A finite element scheme for the numerical solution of the Navier–Stokes/Biot coupled problem." Russian Journal of Numerical Analysis and Mathematical Modelling 37, no. 3 (June 1, 2022): 159–74. http://dx.doi.org/10.1515/rnam-2022-0014.

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Abstract A finite element method for a monolithic quasi-Lagrangian formulation of a fluid–porous structure interaction problem with a corrected balance of stresses on the fluid–structure interface is considered. Deformations of the elastic medium are not necessarily small and are modelled using Saint Venant–Kirchhoff (SVK) constitutive relation. The stability of the method is proved in a form of energy bound for the finite element solution.

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7

Chen, Xiangxiang, Xudong Chen, Andrew Chan, Yingyao Cheng, and Hongfan Wang. "A FDEM Parametric Investigation on the Impact Fracture of Monolithic Glass." Buildings 12, no. 3 (February 25, 2022): 271. http://dx.doi.org/10.3390/buildings12030271.

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Due to the brittleness, monolithic glass may fracture under impact, resulting in catastrophic sequences. The combined finite-discrete element method, i.e., FDEM, is employed to investigate both the oblique and the perpendicular impact failures of monolithic glass parametrically, particularly the soda-lime glass. Using FDEM, glass is discretised into discrete elements where a finite element formulation is incorporated, leading to accurate evaluation of the contact forces and structural deformation. Following the basic theories of the FDEM, a cohesive Mode I fracture model of glass is briefly introduced. Numerical examples are given for the verification of the employed fracture model and the applicability of the FDEM, and comparisons have been made against the computational and experimental results in the literature. The investigated parameters include the impact velocity, the impact angle, the material properties of glass, etc. The obtained results not only revealed the impact fracture mechanism of soda-lime glass but also provided guidance for its design and manufacturing.

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8

Grabmaier, Sebastian, Matthias Jüttner, and Wolfgang Rucker. "Coupling of finite element method and integral formulation for vector Helmholtz equation." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 37, no. 4 (July 2, 2018): 1405–17. http://dx.doi.org/10.1108/compel-08-2017-0346.

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Purpose Considering the vector Helmholtz equation in three dimensions, this paper aims to present a novel approach for coupling the finite element method and a boundary integral formulation. It is demonstrated that the method is well-suited for many realistic three-dimensional problems in high-frequency engineering. Design/methodology/approach The formulation is based on partial solutions fulfilling the global boundary conditions and the iterative interaction between them. In comparison to other coupling formulation, this approach avoids the typical singularity in the integral kernels. The approach applies ideas from domain decomposition techniques and is implemented for a parallel calculation. Findings Using confirming elements for the trace space and default techniques to realize the infinite domain, no additional loss in accuracy is introduced compared to a monolithic finite element method approach. Furthermore, the degree of coupling between the finite element method and the integral formulation is reduced. The accuracy and convergence rate are demonstrated on a three-dimensional antenna model. Research limitations/implications This approach introduces additional degrees of freedom compared to the classical coupling approach. The benefit is a noticeable reduction in the number of iterations when the arising linear equation systems are solved separately. Practical implications This paper focuses on multiple heterogeneous objects surrounded by a homogeneous medium. Hence, the method is suited for a wide range of applications. Originality/value The novelty of the paper is the proposed formulation for the coupling of both methods.

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9

Zoalkfl, Danial, Anton Chepurnenko, Batyr Yazyev, Aleksandr Ishchenko, and Stepan Litvinov. "Determination of temperature fields and stresses during the construction of a massive monolithic foundation slab of a wind turbine tower." E3S Web of Conferences 402 (2023): 12002. http://dx.doi.org/10.1051/e3sconf/202340212002.

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The article proposes a method for determining temperature fields and stresses during the construction of massive monolithic structures in a two-dimensional axisymmetric formulation. The solution is performed using the finite element method. The calculation takes into account the shrinkage of concrete, as well as the change in its physical and mechanical characteristics over time. The problem of calculating a massive monolithic foundation of a wind turbine is presented. Recommendations are given to reduce the risk of early cracking.

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10

Liu, Chun Jie, Xi Wang, and De’an Wan. "Study on Angular Stiffness of Monolithic Flexible Joint." Advanced Materials Research 189-193 (February 2011): 1816–21. http://dx.doi.org/10.4028/www.scientific.net/amr.189-193.1816.

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The monolithic flexible joint is introduced as a novel component of inertial guidance instrument. The angular stiffness of the joint is investigated by employing theory of flexure hinges considering the key part of the joint is a variation of the common circular flexure hinge. Closed-form equation is formulated to unify the typical angular stiffness equations developed by other authors in terms of the circular hinge, and the main variables of the formulation are also discussed. Finite element models of the monolithic joint are built to confirm the analytical model predictions. A measuring system controlled by computer is also developed to evaluate the angular stiffness of the monolithic flexible joint. Checked against finite element analysis and experimental measurement data, the analytical model predictions are within 7% error margins. The study results indicate that the angular stiffness is more sensitive to the minimal thickness of hinge and less sensitive to the notch angle and the oblique angle of hinge.

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11

Agrawal, Manish, and C. S. Jog. "Monolithic formulation of electromechanical systems within the context of hybrid finite elements." Computational Mechanics 59, no. 3 (November 28, 2016): 443–57. http://dx.doi.org/10.1007/s00466-016-1356-1.

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12

Stanford, B., P. Beran, and M. Kurdi. "Model reduction strategies for nonlinear beams subjected to large rotary actuations." Aeronautical Journal 113, no. 1150 (December 2009): 751–62. http://dx.doi.org/10.1017/s0001924000003419.

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Abstract The solution to nonlinear structural dynamics problems with time marching schemes can be very expensive, particularly if the desired time-periodic response takes many cycles to form. Two cost reduction methods, which need not be considered separately, are formulated in this work. The first projects the nonlinear system of equations onto a reduced basis defined by a set of modes computed with proper orthogonal decomposition. The second utilises a monolithic time spectral element method, whereby the system of ordinary differential equations is converted into a single algebraic system of equations. The spectral element method can be formulated such that only the time-periodic response is computed. These techniques are implemented for a planar elastic beam, actuated at its base to emulate a flapping motion. Nonlinear elastic terms are computed with a corotational finite element method, while inertial terms are computed with a standard multibody dynamics formulation. For a variety of actuation frequencies and kinematic motions, results are given in terms of POD modes, reduced order model accuracy, and computational cost, for both the time marching and the monolithic time schemes.

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13

ZHANG, L. X., and Y. GUO. "SIMULATION OF TURBULENT FLOW IN A COMPLEX PASSAGE WITH A VIBRATING STRUCTURE BY FINITE ELEMENT FORMULATIONS." Modern Physics Letters B 23, no. 03 (January 30, 2009): 257–60. http://dx.doi.org/10.1142/s021798490901814x.

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A modeling of the turbulent flow in a complex passage with dynamical fluid-structure interaction (FSI) is established on the generalized variational principle. A monolithic coupling method on the finite element formulations (FEM) is used to realize numerical computation of the flow with dynamical FSI. The comparisons with LES show that the results on the FEM formulations suggested in this paper are favorable, and the computing effort is economical.

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14

Baaran, J., L. Kärger, and A. Wetzel. "Efficient prediction of damage resistance and tolerance of composite aerospace structures." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 222, no. 2 (February 1, 2008): 179–88. http://dx.doi.org/10.1243/09544100jaero278.

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The present work introduces efficient methodologies based on the finite-element method for a quick evaluation of damage resistance and damage tolerance of composite aerospace structures. Monolithic, stringer-stiffened structures, and sandwich structures are considered. The presented methodologies cover the simulation of the dynamic response of a structure during a low velocity impact event including the prediction of the internal non-visible or barely visible damage that develops during the impact. Additionally, methods for the prediction of the compression-after-impact strength are presented. In order to permit an accurate and efficient calculation of deformations and stresses in sandwich structures, special finite-element formulations have been developed. A comparison of simulation results with experimental data is presented for a two-stringer monolithic panel and for a honeycomb sandwich plate. The examples demonstrate that the presented methodologies can be used to quickly assess the damage tolerance of composite structures.

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15

Hajano, Nazim Hussain, Muhammad Sabeel Khan, and Lisheng Liu. "Increasing Micro-Rotational Viscosity Results in Large Micro-Rotations: A Study Based on Monolithic Eulerian Cosserat Fluid–Structure Interaction Formulation." Mathematics 10, no. 22 (November 9, 2022): 4188. http://dx.doi.org/10.3390/math10224188.

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In classical continuum mechanics, a monolithic Eulerian formulation is used for numerically solving fluid–structure interaction (FSI) problems in the frame of a physically deformed configuration. This numerical approach is well adapted to large-displacement fluid–structure configurations where velocities of solids and fluids are computed all at once in a single variational equation. In the recent past, a monolithic Eulerian formulation for solving FSI problems of finite deformation to study the different physical features of fluid flow has been employed. Almost all the current studies use a classical framework in their approach. Despite producing decent results, such methods still need to be appropriately configured to generate exceptional results. Recently, a number of researchers have used a non-classical framework in their approach to analyze several physical problems. Therefore, in this paper, a monolithic Eulerian formulation is employed for solving FSI problems in a non-classical framework to study the micro-structural characteristics of fluid flow by validating the results with classical benchmark solutions present in the literature. In this respect, the Cosserat theory of continuum is considered where a continuum of oriented rigid particles has, in addition to the three translational degrees of freedom of classical continuum, three micro-rotational degrees of freedom. The mathematical formulation of model equations is derived from the general laws of continuum mechanics. Based on the variational formulation of the FSI system, we propose the finite element method and semi-implicit scheme for discretizing space and time domains. The results are obtained by computing a well-known classical FSI benchmark test problem FLUSTRUK-FSI-3* with FreeFem++. The results of the study indicate that the increase in micro-rotational viscosity μr leads to significantly large micro-rotations in fluid flow at the micro-structural level. Further, it is found that the amplitude of oscillations is related inversely to the material parameters c1 and μr while the increase in c1 stabilizes the amplitude of oscillations relatively more quickly than increasing μr The color snapshots of the numerical results at different times during the computer simulations and general conclusions drawn from the results are presented.

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16

Vescovini, Riccardo, and Lorenzo Dozio. "Analysis of Monolithic and Sandwich Panels Subjected To Non-Uniform Thickness-Wise Boundary Conditions." Curved and Layered Structures 5, no. 1 (August 1, 2016): 232–49. http://dx.doi.org/10.1515/cls-2018-0017.

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Abstract The analysis of monolithic and sandwich plates is illustrated for those cases where the boundary conditions are not uniform along the thickness direction, and run at a given position along the thickness direction. For instance, a sandwich plate constrained at the bottom or top face can be considered. The approach relies upon a sublaminate formulation,which is applied here in the context of a Ritz-based approach. Due to the possibility of dividing the structure into smaller portions, viz. the sublaminates, the constraints can be applied at any given location, providing a high degree of flexibility in modeling the boundary conditions. Penalty functions and Lagrange multipliers are introduced for this scope. Results are presented for free-vibration and bending problems. The close matching with highly refined finite element analyses reveals the accuracy of the proposed formulation in determining the vibration frequencies, as well as the internal stress distribution. Reference results are provided for future benchmarking purposes.

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17

Matseevich, Tatiana. "Finite Element Analysis of the Bearing Capacity of Beamless Floor Slabs under Punching, Taking into Account the Design Parameters of the Contacting Elements." Buildings 13, no. 5 (May 5, 2023): 1221. http://dx.doi.org/10.3390/buildings13051221.

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Static calculations of experimental models in an elastic formulation were carried out, and the regularities connecting the dependences of forces in the calculated cross-section of punching out from the main structural parameters of contacting elements (reinforced concrete slabs and pylons) and from the used concrete class were revealed. This article concerns the safety issues of reinforced concrete slabs under punching with different ratios and combinations of pylon and slab thickness parameters, as well as concrete strength. The objectives of the research are consideration of the fracture pattern of reinforced concrete monolithic slabs due to punching shear; comparative analysis of modern normative calculation methods and flat reinforced concrete slabs due to static punching shear; finite element modelling and analysis of the punching shear calculation results for reinforced concrete floor slabs; and the force distribution over the area of the contacting elements-saw and floor slab. The practical significance of the results lies in the use of the obtained forces in the contacting elements for the calculation and design of reliable structures of beamless floor slabs.

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18

Aissa, Nesrine, Louis Douteau, Emmanuelle Abisset-Chavanne, Hugues Digonnet, Patrice Laure, and Luisa Silva. "Octree Optimized Micrometric Fibrous Microstructure Generation for Domain Reconstruction and Flow Simulation." Entropy 23, no. 9 (September 2, 2021): 1156. http://dx.doi.org/10.3390/e23091156.

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Over recent decades, tremendous advances in the field of scalable numerical tools and mesh immersion techniques have been achieved to improve numerical efficiency while preserving a good quality of the obtained results. In this context, an octree-optimized microstructure generation and domain reconstruction with adaptative meshing is presented and illustrated through a flow simulation example applied to permeability computation of micrometric fibrous materials. Thanks to the octree implementation, the numerous distance calculations in these processes are decreased, thus the computational complexity is reduced. Using the parallel environment of the ICI-tech library as a mesher and a solver, a large scale case study is performed. The study is applied to the computation of the full permeability tensor of a three-dimensional microstructure containing 10,000 fibers. The considered flow is a Stokes flow and it is solved with a stabilized finite element formulation and a monolithic approach.

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19

Frost, Miroslav, and Jan Valdman. "Vectorized MATLAB Implementation of the Incremental Minimization Principle for Rate-Independent Dissipative Solids Using FEM: A Constitutive Model of Shape Memory Alloys." Mathematics 10, no. 23 (November 23, 2022): 4412. http://dx.doi.org/10.3390/math10234412.

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The incremental energy minimization principle provides a compact variational formulation for evolutionary boundary problems based on constitutive models of rate-independent dissipative solids. In this work, we develop and implement a versatile computational tool for the resolution of these problems via the finite element method (FEM). The implementation is coded in the MATLAB programming language and benefits from vector operations, allowing all local energy contributions to be evaluated over all degrees of freedom at once. The monolithic solution scheme combined with gradient-based optimization methods is applied to the inherently nonlinear, non-smooth convex minimization problem. An advanced constitutive model for shape memory alloys, which features a strongly coupled rate-independent dissipation function and several constraints on internal variables, is implemented as a benchmark example. Numerical simulations demonstrate the capabilities of the computational tool, which is suited for the rapid development and testing of advanced constitutive laws of rate-independent dissipative solids.

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20

Ha, Truong Sang. "A NUMERICAL INVESTIGATION OF BLOOD FLOW THROUGH THE AORTIC VALVE." Journal of Science and Technique 17, no. 5 (November 29, 2022): 16–27. http://dx.doi.org/10.56651/lqdtu.jst.v17.n05.527.

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This article aims to present a numerical analysis of blood flow in the aortic valve using fluid-structure interaction simulation. The finite element method is employed both for fluid and solid domains, and the monolithic scheme is used for the strong fluid-structure interaction coupling to solve well the two challenges: add-mass and large deformation problems. The Navier-Stokes equations are solved using the integrated method based on the unstructured grid on Arbitrary Lagrangian-Eulerian (ALE) framework with the total Lagrangian formulation is used for the non-linear behavior of the aortic valve. A smoothing technique based on the Laplace equation is employed to improve the mesh quality for both 2D and 3D geometries. The fluid characteristics, such as the velocity and pressure in the valve, are evaluated and analyzed in detail. The results show that velocity and pressure reach their maximum values when the valve is at its maximum opening. On the other hand, more vortices appear behind the valve during the closing phases. The simulation results can be used to help fully to predict and treat cardiovascular diseases.

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21

Phan, Thanh Vu, and Huy-Tuan Pham. "Design and Optimization of a Large-Stroke Compliant Constant-Torque Mechanism." Journal of Technical Education Science, no. 68 (February 28, 2022): 93–100. http://dx.doi.org/10.54644/jte.68.2022.1098.

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Compliant constant-torque mechanism (CTM) can produce an output torque that does not change within a prescribed input rotation range. This stability is maintained regardless of complicated sensorized control systems. Owing to the monolithic nature of the compliant mechanism, the device is more compact, lightweight, and portable, which is favorable to human joint rehabilitative devices or mobility-assisting devices. However, before approaching the stable range, the mechanism has to undergo a pre-loading range which usually accounts for one-third of the entire operational journey. In addition, the deformation of flexible segments is restricted due to the yield strength of the materials. This limited working range hampers other potential applications of compliant CTMs. This paper presents a novel design of a compliant 2-stage CTM with long-stroke by using serially connected curved beams that deform sequentially. The design process is implemented via a shape optimization scheme using genetic algorithm. Finite element analysis is used to characterize the constant-torque behavior of the CTM under static loading. A general design formulation is also proposed to synthesize this special kind of compliant mechanism. The results show that this CTM gets the stable torque range from 300 to 1100 over two stages with the deviation less than 4.3%.

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22

Jadaan, O. M., L. M. Powers, and J. P. Gyekenyesi. "Multixial Creep Life Prediction of Ceramic Structures Using Continuum Damage Mechanics and the Finite Element Method." Journal of Engineering for Gas Turbines and Power 121, no. 4 (October 1, 1999): 577–85. http://dx.doi.org/10.1115/1.2818511.

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High temperature and long duration applications of monolithic ceramics can place their failure mode in the creep rupture regime. A previous model advanced by the authors described a methodology by which the creep rupture life of a loaded component can be predicted. That model was based on the life fraction damage accumulation rule in association with the modified Monkman-Grant creep rupture criterion. However, that model did not take into account the deteriorating state of the material due to creep damage (e.g., cavitation) as time elapsed. In addition, the material creep parameters used in that life prediction methodology, were based on uniaxial creep curves displaying primary and secondary creep behavior, with no tertiary regime. The objective of this paper is to present a creep life prediction methodology based on a modified form of the Kachanov-Rabotnov continuum damage mechanics (CDM) theory. In this theory, the uniaxial creep rate is described in terms of stress, temperature, time, and the current state of material damage. This scalar damage state parameter is basically an abstract measure of the current state of material damage due to creep deformation. The damage rate is assumed to vary with stress, temperature, time, and the current state of damage itself. Multiaxial creep and creep rupture formulations of the CDM approach are presented in this paper. Parameter estimation methodologies based on nonlinear regression analysis are also described for both, isothermal constant stress states and anisothermal variable stress conditions. This creep life prediction methodology was preliminarily added to the integrated design code named Ceramics Analysis and Reliability Evaluation of Structures/Creep (CARES/Creep), which is a postprocessor program to commercially available finite element analysis (FEA) packages. Two examples, showing comparisons between experimental and predicted creep lives of ceramic specimens, are used to demonstrate the viability of this methodology and the CARES/Creep program.

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23

Kos, Zeljko, Yevhenii Klymenko, Irina Karpiuk, and Iryna Grynyova. "Bearing Capacity near Support Areas of Continuous Reinforced Concrete Beams and High Grillages." Applied Sciences 12, no. 2 (January 11, 2022): 685. http://dx.doi.org/10.3390/app12020685.

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This work presents a proposed engineering method for calculating the bearing capacity of the supporting sections of continuous monolithic reinforced concrete tape beams, which combine pressed or driven reinforced concrete piles into a single foundation design. According to the mechanics of reinforced concrete, it is recommended to consider the grillage to be a continuous reinforced concrete beam, which, as a rule, collapses according to the punching scheme above the middle support (pile caps), with the possible formation of a plastic hinge above it. The justification for the proposed method included the results of experimental studies, comparisons of the experimental tensile shear force with the results of calculations according to the design standards of developed countries, and modeling of the stress-strain state of the continuous beam grillage in the extreme span and above the middle support-pile adverse transverse load in the form of concentrated forces. The work is important, as it reveals the physical essence of the phenomenon and significantly clarifies the physical model of the operation of inclined sections over the middle support. The authors assessed the influence of design factors in continuous research elements, and on the basis of this, the work of the investigated elements under a transverse load was simulated in the Lira-Sapr PC to clarify the stress-strain state and confirm the scheme of their destruction adopted in the physical model by the finite element method in nonlinear formulation. Based on the analysis and comparison of the experimental and simulation results, a design model was proposed for bearing capacity near the supporting sections of continuous reinforced concrete beams and high grillages that is capable of adequately determining their strength.

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Меретин, А. С. "A software package for the mathematical simulation of fracture in a thermo-poroelastic medium." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 2 (March 19, 2020): 138–51. http://dx.doi.org/10.26089/nummet.v21r212.

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Приведено описание программного комплекса для математического моделирования эволюции термопороупругой среды с учетом ее разрушения. Используемая математическая модель является модификацией модели Био для случая термопороупругих сред и позволяет моделировать изменение напряженно-деформированного состояния среды, фильтрацию флюида, неизотермические эффекты, а также разрушение среды. Разрушение среды описывается с использованием подхода континуальной механики разрушения путем введения дополнительной переменной, называемой параметром повреждаемости. Этот параметр характеризует степень разрушения среды, а его эволюция определяется заданным кинетическим уравнением. Вычислительный алгоритм основан на методе конечных элементов. Дискретизация уравнений по времени производится по неявной схеме для перемещений, давления и температуры и по явной для параметра повреждаемости. В качестве конечных элементов выбраны элементы Тейлора-Худа, имеющие второй порядок аппроксимации по перемещениям и первый по давлению и температуре. Система уравнений решается в рамках монолитной постановки без итерационного связывания между группами уравнений. Рассмотрены результаты расчетов с использованием программного модуля на примере задачи термического воздействия на нефтяной пласт. A software package for the mathematical simulation of thermo-poroelastic medium evolution with damage is considered. The employed model is a modification of the Biot model for thermo-poroelastic media and allows one to simulate the changes in the stress-strain state of the medium, the fluid flows, the nonisothermic effects, and the medium fracture. The medium damage is simulated using the continuum damage mechanics approaches by introducing a special variable called the damage parameter. This parameter characterizes the degree of medium fracture and its evolution is described by a given kinetic equation. The numerical algorithm is based on a finite element method. The time discretization is performed using an implicit scheme for displacements, pressure, and temperature and an explicit scheme for the damage parameter. The Taylor-Hood finite elements of second-order approximation in displacements and first-order approximation in pressure and temperature are chosen. The system of equations is solved in the framework of the monolithic formulation without the iterative coupling between groups of equations. The numerical results of solving the problem on the rock damage evolution due to thermal action are discussed.

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Kim, Cheol, and Dong Yeub Lee. "Design Optimization of a Curved Actuator with Piezoelectric Fibers." International Journal of Modern Physics B 17, no. 08n09 (April 10, 2003): 1971–75. http://dx.doi.org/10.1142/s0217979203019964.

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Piezoelectric Fiber Composite with Interdigitated Electrodes (PFCIDE) was previously introduced as an alternative to monolithic wafers with conventional electrodes for applications of structural actuation. This paper is an investigation into the performance improvement of piezoelectric fiber composite actuators by optimizing the stacking sequence and changing the matrix material. This paper presents the numerical optimization of a piezoelectric fiber/piezoelectric matrix composite actuator with IDE (PFPMIDE). Various concepts from different backgrounds, including three-dimensional linear elastic and dielectric theories, have been incorporated into the present linear piezoelectric model. To see the structural responses of the actuator integrated with the PFPMIDE, three dimensional finite element formulations were derived. Numerical analyses show larger center displacement of the curved actuator with the PFPMIDE due to optimization of the piezoelectric fiber angles. This paper presents the concept of a curved actuator that occurs naturally via thermal residual stress during the curing process, as well as the optimization of the maximum curved actuator displacement, which is accomplished using the Davidon-Fletcher-Powell (DFP) method.

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Hachem, E., H. Digonnet, E. Massoni, and T. Coupez. "Immersed volume method for solving natural convection, conduction and radiation of a hat‐shaped disk inside a 3D enclosure." International Journal of Numerical Methods for Heat & Fluid Flow 22, no. 6 (August 3, 2012): 718–41. http://dx.doi.org/10.1108/09615531211244871.

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PurposeThe purpose of this paper is to present an immersed volume method that accounts for solid conductive bodies (hat‐shaped disk) in calculation of time‐dependent, three‐dimensional, conjugate heat transfer and fluid flow.Design/methodology/approachThe incompressible Navier‐Stokes equations and the heat transfer equations are discretized using a stabilized finite element method. The interface of the immersed disk is defined and rendered by the zero isovalues of a level set function. This signed distance function allows turning different thermal properties of each component into homogeneous parameters and it is coupled to a direct anisotropic mesh adaptation process enhancing the interface representation. A monolithic approach is used to solve a single set of equations for both fluid and solid with different thermal properties.FindingsIn the proposed immersion technique, only a single grid for both air and solid is considered, thus, only one equation with different thermal properties is solved. The sharp discontinuity of the material properties was captured by an anisotropic refined solid‐fluid interface. The robustness of the method to compute the flow and heat transfer with large materials properties differences is demonstrated using stabilized finite element formulations. Results are assessed by comparing the predictions with the experimental data.Originality/valueThe proposed method demonstrates the capability of the model to simulate an unsteady three‐dimensional heat transfer flow of natural convection, conduction and radiation in a cubic enclosure with the presence of a conduction body. A previous knowledge of the heat transfer coefficients between the disk and the fluid is no longer required. The heat exchange at the interface is solved and dealt with naturally.

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Islam, Mohammad, Nicolas Huerta, and Robert Dilmore. "Effect of Computational Schemes on Coupled Flow and Geo-Mechanical Modeling of CO2 Leakage through a Compromised Well." Computation 8, no. 4 (November 13, 2020): 98. http://dx.doi.org/10.3390/computation8040098.

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Carbon capture, utilization, and storage (CCUS) describes a set of technically viable processes to separate carbon dioxide (CO2) from industrial byproduct streams and inject it into deep geologic formations for long-term storage. Legacy wells located within the spatial domain of new injection and production activities represent potential pathways for fluids (i.e., CO2 and aqueous phase) to leak through compromised components (e.g., through fractures or micro-annulus pathways). The finite element (FE) method is a well-established numerical approach to simulate the coupling between multi-phase fluid flow and solid phase deformation interactions that occur in a compromised well system. We assumed the spatial domain consists of a three-phases system: a solid, liquid, and gas phase. For flow in the two fluids phases, we considered two sets of primary variables: the first considering capillary pressure and gas pressure (PP) scheme, and the second considering liquid pressure and gas saturation (PS) scheme. Fluid phases were coupled with the solid phase using the full coupling (i.e., monolithic coupling) and iterative coupling (i.e., sequential coupling) approaches. The challenge of achieving numerical stability in the coupled formulation in heterogeneous media was addressed using the mass lumping and the upwinding techniques. Numerical results were compared with three benchmark problems to assess the performance of coupled FE solutions: 1D Terzaghi’s consolidation, Liakopoulos experiments, and the Kueper and Frind experiments. We found good agreement between our results and the three benchmark problems. For the Kueper and Frind test, the PP scheme successfully captured the observed experimental response of the non-aqueous phase infiltration, in contrast to the PS scheme. These exercises demonstrate the importance of fluid phase primary variable selection for heterogeneous porous media. We then applied the developed model to the hypothetical case of leakage along a compromised well representing a heterogeneous media. Considering the mass lumping and the upwinding techniques, both the monotonic and the sequential coupling provided identical results, but mass lumping was needed to avoid numerical instabilities in the sequential coupling. Additionally, in the monolithic coupling, the magnitude of primary variables in the coupled solution without mass lumping and the upwinding is higher, which is essential for the risk-based analyses.

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Bedon, Chiara, and Maria Vittoria Santi. "Simplified Procedure for Capacity Check of Historic Monolithic Glass Windows under Soft-Body Collision/Bird-Strike." Symmetry 14, no. 10 (October 19, 2022): 2198. http://dx.doi.org/10.3390/sym14102198.

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Differing from present structural design procedures, most of the existing glass windows and even historic components in traditional/old buildings are not specifically designed to resist possible accidental loads. Rather thin monolithic ordinary annealed glass panels can be found in vertical non-structural envelopes, where they are often arranged to cover large surfaces. As such, an accidental glass fracture could originate even from rather common and moderate impact events and result in severe risk for people, due to propagation of dangerous shards from these vulnerable and fragile building components. To assess potential risks and support possible mitigation strategies, the present study is focused on the bird-strike analysis of existing/historic linearly restrained non-structural glass windows, based on a parametric Smoothed-Particle Hydrodynamics (SPH)–Finite Element (FE) model. Starting from a 1 m–wide and 1.5 m–high configuration, the attention is first given to various influencing parameters, such as impactor features (mass, 0.35–1.81 kg; impact speed, 0–40 m/s; and, thus, impact energy) and the target window (glass thickness, 4–6 mm; impact point; and, thus, glass stiffness). Local and global effects due to parametric localized bird-strikes are discussed based on non-linear dynamic numerical analyses and in terms of expected deflections, tensile stress peaks, and damage extension/severity (i.e., D1 to D3 damage levels). Scale effects are also examined for a case-study historic envelope (≈7 m in total size, 5 mm in thickness), and one of its 2.58 m × 3.3 m large glass components. Furthermore, a simplified empirical approach based on analytical formulations and normalized charts is proposed for a preliminary vulnerability assessment of historic monolithic glass envelopes, including parameters to account for impactor features and glass panel size/thickness, based on vibration-frequency considerations.

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Gandhi, M. V., B. S. Thompson, S. B. Choi, and S. Shakir. "Electro-Rheological-Fluid-Based Articulating Robotic Systems." Journal of Mechanisms, Transmissions, and Automation in Design 111, no. 3 (September 1, 1989): 328–36. http://dx.doi.org/10.1115/1.3259003.

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The limitations of the current generation of robotic systems has triggered a new research thrust for predicting the elastodynamic response of assemblages of articulating flexible-bodied systems. This research thrust is extended herein by proposing the fabrication of robotic systems in either monolithic or ultra-advanced composite laminated high-strength, high-stiffness materials in which are incorporated electro-rheological fluids. These multiphase fluid systems, which change their rheological behavior instantaneously when subjected to an externally applied electrical field, provide a potential for tailoring the vibrational characteristics of these hybrid materials from which the structural members of the proposed robotic systems are fabricated. This paper is focused on developing the necessary design tools for predicting the vibrational response of flexible multibodied articulating systems fabricated with this new class of advanced materials. A variational theorem is developed herein as a basis for finite element formulations which can be employed to predict the elastodynamic response of these systems. A coherent combination of experimental and theoretical work on cantilevered beams is presented to demonstrate the viability of the proposed design methodology. In addition, computer simulation results are presented to demonstrate the potential payoffs in terms of superior performance characteristics of a new generation of robotic systems capitalizing on this innovative and revolutionary design philosophy.

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Kožar, Ivica, and Adnan Ibrahimbegović. "Finite element formulation of the finite rotation solid element." Finite Elements in Analysis and Design 20, no. 2 (June 1995): 101–26. http://dx.doi.org/10.1016/0168-874x(95)00014-k.

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Kemal Öztorun, Namik. "A rectangular finite element formulation." Finite Elements in Analysis and Design 42, no. 12 (August 2006): 1031–52. http://dx.doi.org/10.1016/j.finel.2006.03.004.

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Agrawal, Om Prakash. "A GENERAL FRACTIONAL FINITE ELEMENT FORMULATION." IFAC Proceedings Volumes 39, no. 11 (January 2006): 141. http://dx.doi.org/10.3182/20060719-3-pt-4902.00024.

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Hayata, K., K. Miura, and M. Koshiba. "Finite element formulation for lossy waveguides." IEEE Transactions on Microwave Theory and Techniques 36, no. 2 (1988): 268–76. http://dx.doi.org/10.1109/22.3515.

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Kang, Yeon June, Bryce K. Gardner, and J. Stuart Bolton. "An axisymmetric poroelastic finite element formulation." Journal of the Acoustical Society of America 106, no. 2 (August 1999): 565–74. http://dx.doi.org/10.1121/1.428041.

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Le van, Anh, and Christian Wielgosz. "Finite element formulation for inflatable beams." Thin-Walled Structures 45, no. 2 (February 2007): 221–36. http://dx.doi.org/10.1016/j.tws.2007.01.015.

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Demir, Çiğdem, and Ömer Civalek. "Nonlocal Finite Element Formulation for Vibration." International Journal Of Engineering & Applied Sciences 8, no. 2 (August 19, 2016): 109. http://dx.doi.org/10.24107/ijeas.252149.

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Irudayaraj, Joseph, and Kamyar Haghighi. "I. THEORY AND FINITE ELEMENT FORMULATION." Drying Technology 11, no. 5 (January 1993): 900–927. http://dx.doi.org/10.1080/07373939308916876.

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Izamshah R.A., R., John Mo, and Song Lin Ding. "Finite Element Analysis of Machining Thin-Wall Parts." Key Engineering Materials 458 (December 2010): 283–88. http://dx.doi.org/10.4028/www.scientific.net/kem.458.283.

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In an attempt to decrease weight, new commercial and military aircraft are designs with unitised monolithic metal structural components which contains of thinner ribs (i.e., walls) and webs (i.e., floors). Most of the unitised monolithic metal structural components are machined from solid plate or forgings with the start-to-finish weight ratio of 20:1. The resulting thin-walled structure often suffers a deformation which causes a dimensional surface error due to the action of the cutting force generated during the machining process. To alleviate the resulting surface errors, current practices rely on machining through repetitive feeding several times and manual calibration which resulting in long cycle times, low productivity and high operating cost. A finite element analysis (FEA) machining model is developed in this project to specifically predict the distortion or deflection of the part during end milling process. The model aims to provide an input for downstream decision making on error compensation strategy when machining a thin-wall unitised monolithic metal structural components. A set of machining tests have been done in order to validate the accuracy of the model and the results between simulation and experiment are found in a good agreement.

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Balah, Mohamed, and Hamdan N. Al-Ghamedy. "Finite element formulation of a third order laminated finite rotation shell element." Computers & Structures 80, no. 26 (October 2002): 1975–90. http://dx.doi.org/10.1016/s0045-7949(02)00222-5.

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Ramesh, Binoj, and Antoinette M. Maniatty. "Stabilized finite element formulation for elastic–plastic finite deformations." Computer Methods in Applied Mechanics and Engineering 194, no. 6-8 (February 2005): 775–800. http://dx.doi.org/10.1016/j.cma.2004.06.025.

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Koch, S., H. De Gersem, and T. Weiland. "Magnetostatic Formulation With Hybrid Finite-Element, Spectral-Element Discretizations." IEEE Transactions on Magnetics 45, no. 3 (March 2009): 1136–39. http://dx.doi.org/10.1109/tmag.2009.2012654.

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Yang, Yong, Chang He Li, and Fa Zhan Yang. "Mechanics Model and Machining Distortion Analysis for High Speed Milling of Titanium Alloy Aircraft Monolithic Component." Applied Mechanics and Materials 29-32 (August 2010): 354–59. http://dx.doi.org/10.4028/www.scientific.net/amm.29-32.354.

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A physics-based material processing simulation is approached to research the machining distortion for high speed milling of titanium alloy aircraft monolithic component by the finite element method (FEM). Several mechanics models, such as material constitutive model, material removal model, and cutting loads application model, have been implemented to improve the accuracy of finite element simulation. The distortion result of aircraft monolithic component resulting from FEM show a good agreement with the experiment result. The research result shows that the distortion law of titanium alloy aircraft monolithic component is bending distortion and protruding upward, and the maximum distortion dimension lies in the middle of monolithic component.

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Bonghwan Kim, Lee, Chi-Woo, and 안국찬. "Finite element simulations of ballistic impact on monolithic glass." Journal of the Korean Society of Mechanical Technology 16, no. 3 (June 2014): 1477–82. http://dx.doi.org/10.17958/ksmt.16.3.201406.1477.

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Jog, C. S., and G. S. J. Gautam. "A monolithic hybrid finite element strategy for nonlinear thermoelasticity." International Journal for Numerical Methods in Engineering 112, no. 1 (February 10, 2017): 26–57. http://dx.doi.org/10.1002/nme.5500.

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Marinkovic, Dragan, and Manfred Zehn. "Finite Element Formulation for Active Composite Laminates." American Journal of Engineering and Applied Sciences 8, no. 3 (March 1, 2015): 328–35. http://dx.doi.org/10.3844/ajeassp.2015.328.335.

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Cihan, Mertcan, BlaŽ Hudobivnik, Fadi Aldakheel, and Peter Wriggers. "Virtual Element Formulation for Finite Strain Elastodynamics." Computer Modeling in Engineering & Sciences 129, no. 3 (2021): 1151–80. http://dx.doi.org/10.32604/cmes.2021.016851.

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Zhao, MingHao, XiaoYing Yan, BingBing Wang, and QiaoYun Zhang. "Finite element formulation for piezoelectric semiconductor plates." Materials Today Communications 30 (March 2022): 103098. http://dx.doi.org/10.1016/j.mtcomm.2021.103098.

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Spacone, E., V. Ciampi, and F. C. Filippou. "Mixed formulation of nonlinear beam finite element." Computers & Structures 58, no. 1 (January 1996): 71–83. http://dx.doi.org/10.1016/0045-7949(95)00103-n.

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Clough, Ray W. "Original formulation of the finite element method." Finite Elements in Analysis and Design 7, no. 2 (November 1990): 89–101. http://dx.doi.org/10.1016/0168-874x(90)90001-u.

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Barrenechea, Gabriel R., and Petr Knobloch. "Analysis of a group finite element formulation." Applied Numerical Mathematics 118 (August 2017): 238–48. http://dx.doi.org/10.1016/j.apnum.2017.03.008.

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