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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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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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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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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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A computer aided design system for the analysis of transferred potentials in earthing systems

A computer aided design system for the analysis of transferr...

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Proceedings of the Third International Conference on engineering Computational Technology

作者： Colominas, I. Mosqueira, G. Gómez-Calviño, J. Navarrina, F. Casteleiro, M. Group of Numerical Methods in Eng. GMNI Civil Engineering School Universidad de La Coruña La Coruña Spain

ISBN: (纸本)0948749857

A CAD system based on the boundary element method (BEM) numerical formulation for the analysis of a common problem in electrical engineering practice is presented. However, the transfer of potentials between the grounding area to outside points by buried conductors may produce serious safety problems. This paper summarizes the BE numerical approach and gives a new approach for the transferred potential analysis.

关键词： Computer aided design

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Fluid flow simulation by lagrangian particle methods

Fluid flow simulation by lagrangian particle methods

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

作者： Cueto-Felgueroso, L. Colominas, I. Mosqueira, G. Navarrina, F. Casteleiro, M. Group of Numerical Methods in Engineering GMNI Dept. of Applied Mathematics Universidad de La Coruña 15192 La Coruña Spain

In this paper we present 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.

关键词： Computational fluid dynamics

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Improvement of the computer methods for grounding analysis in layered soils by using high-efficient convergence acceleration techniques

Improvement of the computer methods for grounding analysis i...

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作者： Colominas, I. París, J. Navarrina, F. Casteleiro, M. GMNI - Group of Numerical Methods in Engineering Department of Applied Mathematics Universidad de A Coruña 15192 A Coruña Spain

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. © 2011 Civil-Comp Ltd and Elsevier Ltd. All rights reserved.

关键词： Electric grounding

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Statistical assessment of the financial performance of shale-gas wells coupling stochastic and numerical simulation

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Petroleum Science 2024年第6期21卷 4497-4511页

作者： Andres Soage Luis Ramirez Ruben Juanes Luis Cueto-Felgueroso Ignasi Colominas Group of Numerical Methods in Engineering-GMNI Center for TechnologicalInnovation in Construction and Civil Engineering-CITEEC.Civil Engineering SchoolUniversity of a CorunaCampus of ElvinaA Coruna15008GaliciaSpain Department of Civil Engineering:Hydraulics Energy and Environment.Polytechnic University of MadridMadrid2006Spain Department of Civil and Environmental Engineering Massachusetts Institute of TechnologyCambridge02139MAUA Department of Earth Atmospheric and Planetary SciencesMassachusetts Institute of TechnologyCambridge239MAUSA

We present a new methodology to statistically determine the net present value(NPV)and internal rate of return(IRR)as financial estimators of shale gas *** method allows us to forecast,in a fully probabilistic setting,financial performance risk and to understand the importance of the different factors that impact *** methodology developed in this study combines,through Monte Carlo simulation,the computational modeling of gas production from shale gas wells with a stochastic simulation of gas price as a geometric Brownian motion(GMB).To illustrate the methodology's validity,we apply it to an analysis of investments in shale gas *** results show that gas price volatility is a key variable in the performance of an investment of this type,in such a way that at high volatilities,the potential return on an investment in shale gas increases significantly,but so do the risks of economic *** finding is consistent with the history of shale gas operations in which huge investment successes coexist with unexpected investment failures.

关键词： Gas volatility Shale gas Net presentvalue Internal ratereturn Stochastic model Financial estimator MonteCarlosimulation Kernel densityfunction

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A higher-order finite volume method using multiresolution reproducing kernels

A higher-order finite volume method using multiresolution re...

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4th International Workshop on Meshfree methods for Partial Differential Equations

作者： Nogueira, Xesús Cueto-Felgueroso, Luis Colominas, Ignasi Navarrina, Fermín Casteleiro, Manuel Group of Numerical Methods in Engineering GMNI Dept. of Applied Mathematics Civil Engineering School University of A Coruña Campus de Elviña 15071 A Coruña Spain Department of Aeronautics and Astronautics Massachusetts Institute of Technology 77 Massachusetts Ave 37-451 Cambridge MA 02139 United States

ISBN: (纸本)9783540799931

In this contribution we describe a numerical method based on the application of a meshfree interpolation technique (Moving Least Squares (MLS)), for the development of a higher-order finite volume discretization useful on structured and unstructured grids. With this procedure it is possible to build a higher-order scheme in which the computation of the derivatives is performed in a truly threedimensional way. We use a MLS approach to compute the successive derivatives needed for the approximation of variables at element interfaces using Taylor series. Due to the use of cubic (or higher) reconstructions with the MLS technique, viscous fluxes are also approximated with higher-order accuracy and can be directly computed at edges. The higher-order accuracy achieved by this method makes it suitable for aeroacoustics problems and DNS and LES of turbulent flows. One of the advantages of the use of the meshfree method on a finite volume framework is that it is possible to exploit all the shock capturing techniques developed for finite volume methods, allowing the computation of compressible flows. Moreover, we also present the application of this interpolation technique to shock detection. We make use of its connection with wavelets, and develop a technique we believe superior to traditional shock capturing methods. This application could be included in a very natural way in the computations with the method presented herein.

关键词： Compressible flow

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