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A Comparative Review of FEM Like Techniques Applied to the Linear Analysis of Molecular Structures

Archives of Computational methods in engineering 2025年 1-28页

作者： Fernández-San Miguel, Andrés Ramírez, Luis Couceiro, Iván Navarrina, Fermín Group of Numerical Methods in Engineering-GMNI Center for Technological Innovation in Construction and Civil Engineering-CITEEC Civil Engineering School Universidade da Coruña Campus de Elviña A Coruña15071 Spain

In this study, a historical review of the Finite Element Method (FEM) and Molecular Dynamics (MD), widely used at the macro and nanoscale respectively is presented, emphasizing the actual parallelisms between their development and applications. After this historical introduction, where certain similarities between both methods are pointed out, different FEM-like methods are analyzed and compared as for first order analysis of structures at the nanoscale. Firstly, the Structural Mechanics (SM) approach is analyzed, where it is assumed that the use of Euler Bernoulli beam elements is equivalent to working directly from the force field. On the other hand, the Molecular Element Method (MEM), which provides the stiffness matrices directly from the potentials, is analyzed. Several analytical static cases are studied for the validation and comparison of both methods. Finally, it is shown that, other branch of methods such as Elastic Network Models (ENM) can be viewed as a particular sub-case of the MEM, or as truss-type finite elements. As an example, the analysis of SARS-CoV2 spikes vibrations is included, comparing with both experimental results and continuous models. © The Author(s) 2025.

关键词： Stiffness matrix

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Computational examples of reaction-convection-diffusion equations solution under the influence of fluid flow: First example

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APPLIED MATHEMATICAL MODELLING 2012年第10期36卷 5029-5045页

作者： Garzon-Alvarado, Diego A. Galeano, C. H. Mantilla, J. M. Group of Modeling and Numerical Methods in Engineering (GNUM) Department of Mechanical and Mechatronic Engineering National University of Colombia Colombia

This paper presents several numerical tests on reaction-diffusion equations in the Turing space, affected by convective fields present in incompressible flows under the Schnakenberg reaction mechanism. The tests are performed in 2D on square unit, to which we impose an advective field from the solution of the problem of the flow in a cavity. The model developed consists of a decoupled system of equations of reaction-advection-diffusion, along with the Navier-Stokes equations of incompressible flow, which is solved simultaneously using the finite element method. The results show that the pattern generated by the concentrations of the reacting system varies both in time and space due to the effect exerted by the advective field. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Reaction-convection-diffusion Turing instabilities Navier-Stokes Problem of the cavity

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On the intrinsic instability of the advection-diffusion equation

On the intrinsic instability of the advection-diffusion equa...

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European Congress on Computational methods in Applied Sciences and engineering, ECCOMAS 2004

作者： Gomez, H. Colominas, I. Navarrina, F. Casteleiro, M. Department of Mathematical Methods Group of Numerical Methods in Engineering University of A Coruña Spain

A new theory for the advective-diffusive phenomenon is described in this study and the causes for the failure of the conventional numerical methods for this problem are investigated. It is shown that Fick's law - the constitutive equation of the transport problem - is the cause of the appearance of oscillations in the numerical solutions of predominantly advective problems. Fick's law leads to the unreasonable result that mass can propagate at an infinite speed. We propose a new formulation for the advective-diffusive problem by using a constitutive equation derived by M. Carlo Cattaneo in 1958 for thermodynamic and pure-diffusion problems. This new approach overcomes the problem of mass propagation at an infinite speed. It is also shown that the advective-diffusive problem is a wave-like problem. Hence, a pollutant diffuses like a wave in a fluid. A detailed analysis of the new equations shows an important conclusion: a critical fluid velocity exists for each advective-diffusive problem. When fluid velocity is greater or equal than this critical speed the steady state problem is not anymore a well-posed problem and the transient problem is as well ill-posed if it is stated as a bounduary value problem. In this case we should formulate the advective-diffusive problem as an initial value problem. Furthermore, we propose stability conditions for the steady state advective-diffusive problem. Several problems have been solved to check the good behaviour of the numerical solution of the new equations and the proposed stability conditions.

关键词： Constitutive equations

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High performance parallel computing in structural topology optimization

High performance parallel computing in structural topology o...

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12th International Conference on Civil, Structural and Environmental engineering Computing, CC 2009

作者： Colominas, I. París, J. Navarrina, F. Casteleiro, M. GMNI-Group of Numerical Methods in Engineering Civil Engineering School University of Coruña Spain

ISBN: (纸本)9781905088300

Minimum weight topology optimization of structures with stress constraints formulations have been recently proposed as an alternative to the traditional maximum stiffness statements. These minimum weight approaches offer some improvements and avoid unwanted phenomena associated to maximum stiffness approaches (mesh dependency, checkerboard layouts). In addition, minimum weight formulations address the most useful analysis from a practical point of view in engineering (to reduce the cost of the structure) and it imposes stress constraints. Thus, the feasibility of the optimal solutions obtained is guaranteed while the cost is minimized. However, these formulations also require higher computing effort than the traditional maximum stiffness statements. Thus, it is necessary to introduce numerical and computational techniques that allow to reduce the computational requirements. In this paper, we propose the use of parallelization techniques in order to reduce the computing time required to solve the topology optimization problem proposed. © Civil-Comp Press, 2009.

关键词： Computer aided engineering

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Isogeometric shape sensitivity analysis

Isogeometric shape sensitivity analysis

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12th International Conference on Optimum Design of Structures and Materials in engineering, OP12

作者： Navarrina, F. Gómez, H. París, J. Colominas, I. Nogueira, X. Casteleiro, M. GMNI - Group of Numerical Methods in Engineering Civil Engineering School University of A Coruña Spain

ISBN: (纸本)9781845645984

On a regular basis, engineering analysis requires stating and solving systems of partial differential equations (PDEs). The most powerful and widely extended techniques for solving PDEs are the so-called Weighted Residuals methods. To this group belong, among others, the Finite Element Method (FEM), the Boundary Element Method (BEM), the Finite Volume Method (FVM) and the Mesh-Free Method (MFM), as well as the many different formulations included in each of these categories. The new Isogeometric Analysis (IGA) methods were proposed by Hughes et al. in 2005, and it is our belief that they really deserve special attention. The key idea of IGA is to use a previously generated CAD model for discretizing both the geometry and the solution to the problem being analyzed. In return for some minor drawbacks, IGA offers a number of major advantages that make the technique specially attractive and promising in comparison with standard FEM, BEM, FVM and MFM formulations. In this presentation we will state a general formulation for the sensitivity analysis of Weighted Residual methods, both for linear and non-linear problems with constant or varying geometry. The effects due to variation of geometry are addressed by defining a generic procedure for integration in manifolds on the basis of the metric tensor concept. The proposed approach leads to compact and relatively simple expressions to obtain directional derivatives of arbitrarily high order. The resulting scheme can be easily applied to IGA formulations, its implementation being quite a straightforward task. Finally, one application example is presented. © 2012 WIT Press.

关键词： Boundary element method

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Convergence acceleration techniques in computer aided design systems for grounding analysis in layered soils

Convergence acceleration techniques in computer aided design...

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12th International Conference on Civil, Structural and Environmental engineering Computing, CC 2009

作者： Colominas, I. París, J. Navarrina, F. Casteleiro, M. GMNI-Group of Numerical Methods in Engineering Civil Engineering School University of Coruña Spain

ISBN: (纸本)9781905088300

In the last years the authors have developed a numerical formulation based on the Boundary Element Method for the analysis of grounding systems embedded in uniform soils. This approach has been implemented in a CAD system that currently allows to analyze real grounding grids in real-time in personal computers. The extension of this approach for the grounding analysis in layered soils is straightforward by application of the method of images. However in some practical cases the resulting series have a poor rate of convergence;consequently, the analysis of real earthing grids in multilayer soils requires an out of range computational cost. In this paper we present a CAD system based on this BEM numerical formulation for grounding analysis in multilayer soils that include an efficient technique based on the Aitken acceleration in order to improve the rate of convergence of the involved series expansions. Finally, we show some examples by using the geometry of real grounding systems. © Civil-Comp Press, 2009.

关键词： Boundary element method

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Structural optimization of high voltage transmission line towers considering continuum and discrete design variables

Structural optimization of high voltage transmission line to...

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12th International Conference on Optimum Design of Structures and Materials in engineering, OP12

作者： París, J. Martínez, S. Navarrina, F. Colominas, I. Casteleiro, M. GMNI - Group of Numerical Methods in Engineering Civil Engineering School University of A Coruña Spain

ISBN: (纸本)9781845645984

Structural optimization has been usually applied to singular projects (e.g. a dam) and/or to common designs largely repeated (e.g. automotive components), and high voltage transmission towers can be included in both groups since they are expensive and a large number of them is required. In this paper, the authors propose a general formulation for obtaining the structural optimum design of latticed high voltage towers. The formulation is devoted to obtaining the most common objective in engineering (minimum cost) considering the limitations imposed in actual norms for this kind of structure. According to this idea, real applications are studied and modeled under real conditions (e.g. loads, constraints, building process). Constructive aspects like the specific geometry, the structural elements or the building process are specifically considered. The optimization model proposed also deals with continuum design variables (global geometry variables) and discrete design variables (area, inertia and/or cross section dimensions, for example) both together. The use of both types of design variables is crucial for defining a realistic model that can be used in practical applications in engineering. The optimum design formulation proposed is general and can be easily applied to other different types of 3D latticed structures. Finally, a real application example of a high voltage tower under real conditions and requirements is analyzed. © 2012 WIT Press.

关键词： Structural optimization

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numerical simulation of free surface flows by lagrangian particle methods

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3rd International Conference on Fluid Structure Interaction and 8th International Conference on Computational Modelling and Experimental Measurements of Free and Moving Boundaries

作者： Cueto-Felgueroso, L. Colominas, I. Navarrina, F. Casteleiro, M. Group of Numerical Methods in Engineering Civil Engineering School University of La Coruña Spain

ISBN: (纸本)1845640276

This paper presents a Galerkin based SPH formulation with moving least-squares meshless approximation, applied to free surface flows. The Galerkin scheme provides a clear framework to analyze several procedures widely used in the classical SPH literature, suggesting that some of them should be reformulated in order to develop consistent algorithms. The performance of the methodology proposed is tested through various dynamic simulations, demonstrating the attractive ability of particle methods to handle severe distortions and complex phenomena. © 2005 WIT Press.

关键词： Hydrodynamics

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A continuation framework for quasi-periodic solution branches based on different torus discretization strategies 30

A continuation framework for quasi-periodic solution branche...

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30th International Conference on Noise and Vibration engineering, ISMA 2022 and 9th International Conference on Uncertainty in Structural Dynamics, USD 2022

作者： Bäuerle, S. Seifert, A. Kappauf, J. Hetzler, H. University of Kassel Institute for Mechanics Engineering Dynamics: Numerical Methods Group Mönchebergstraße 7 Kassel34121 Germany

ISBN: (纸本)9789082893151

In dynamical systems, the study of stationary solutions - such as equilibrium points or periodic orbits - is of fundamental interest. Quasi-periodic oscillations are another stationary solution type, which receives increasing attention from practitioners: as a kind of higher dimensional periodic solution, they contain at least two base frequencies that have no rational ratio. This leads to an infinite "period length". Such a quasi-periodic trajectory evolves in state space on a torus surface and fills it densely. Due to the density, it is permissible to study this finite torus surface instead of the infinite trajectory. In this contribution, we present two approximation methods - a FOURIER-GALERKIN and a quasi-periodic shooting method - for computing such finite surfaces. These methods are implemented in the software framework COSTAR in MATLAB® for continuing equilibria, periodic and quasi-periodic solution curves. We discuss results of curve continuation using the example of a quasi-periodically forced DUFFING oscillator. © 2022 Proceedings of ISMA 2022 - International Conference on Noise and Vibration engineering and USD 2022 - International Conference on Uncertainty in Structural Dynamics. All rights reserved.

关键词： MATLAB

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numerical analysis of anisotropic stiffness and strength for geomaterials

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Journal of Rock Mechanics and Geotechnical engineering 2023年第2期15卷 323-338页

作者： Fei Song Manuel A.González-Fernández Alfonso Rodriguez-Dono Leandro R.Alejano Department of Civil and Environmental Engineering Universitat Politècnica de Catalunya(UPC)Barcelona08034Spain CINTECX GESSMin GroupDepartment of Natural Resources and Environmental EngineeringUniversity of VigoVigo36310Spain International Centre for Numerical Methods in Engineering(CIMNE) Barcelona08034Spain

In numerical modelling,selection of the constitutive model is a critical factor in predicting the actual response of a *** use of oversimplified or inadequate models may not be sufficient to reproduce the actual geomaterial *** selection is especially relevant in the case of aniso-tropic rocks,and particularly for shales and slates,whose behaviour may be affected,*** stability in geothermal or oil and gas production *** this paper,an alternative anisotropic constitutive model has been implemented in the finite element method software CODE_BRIGHT,which is able to account for the anisotropy of shales and slates in terms of both deformability and *** this purpose,a transversely isotropic version of the generalised Hooke’s law is adopted to represent the stiffness anisotropy,while a nonuniform scaling of the stress tensor is introduced in the plastic model to represent the strength ***,a detailed approach has been proposed to determine the model parameters based on the stressestrain results of laboratory ***,numerical analyses are performed to model uniaxial and triaxial tests on Vaca Muerta shale,Bossier shale and slate from the northwest of Spain(NW Spain slate).The experimental data have been recovered from the literature in the case of the shale and,in the case of the slate,performed by the authors in terms of stress-strain curves and strengths.A good agreement can be generally observed between numerical and experi-mental results,hence showing the potential applicability of the approach to actual case ***,the presented constitutive model may be a promising approach for analysing the anisotropic behaviour of rocks and its impact on well stability or other relevant geomechanical problems in aniso-tropic rocks.

关键词： Rock mechanics Anisotropy numerical modelling CODE_BRIGHT Shale Slate

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