Artículos

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https://hdl.handle.net/10784/25958

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A comparative computational study of blood flow pattern in exemplary textile vascular grafts
(Taylor and Francis Ltd., 2018-01-01) Valencia, R.A.; García, M.J.; Bustamante, J.; Mecánica Aplicada
Textile vascular grafts are biomedical devices and play an important role serving as a solution for the partial replacement of damaged arterial vessels. It is believed that the success of a textile vascular graft, in the healing process after implantation, is due to the porous micro-structure of the wall. Although the transport of fluids through textiles is of great technical interest in biomedical applications, little is known about predicting the micro-flow pattern and cellular transport through the wall. The aim of this work is to investigate how the type of fabric, permeability and porosity affect both the local fluid dynamics at several scales and the fluid-particle interaction between platelets in textile grafts, related with the graft occlusion. This study involves both experimental and computational tests. Experimental tests are performed to characterize the permeability and porosity according to the ISO 7198 standard. The numerical process is based on a multi-scale approach where the fluid flow is solved with the Finite Element Method and the discrete particles are solved with the Molecular Dynamic Method. The results have shown that the type of fabric in textile vascular grafts and the degree of porosity and permeability affect both the local fluid dynamics and the level of penetration of platelets through the wall, thus indicating their importance as design parameters. © 2017 Informa UK Limited, trading as Taylor & Francis Group.
A stiffness derivative local hypercomplex-variable finite element method for computing the energy release rate
(Elsevier BV, 2019-01-01) Aguirre-Mesa A.M.; Ramirez-Tamayo D.; Garcia M.J.; Montoya A.; Millwater H.; Mecánica Aplicada
A “local” hypercomplex-variable finite element method, L-ZFEM, is proposed for the computation of the energy release rate (ERR) using the stiffness derivative equation. This approach is analogous to the stiffness derivative method proposed by Parks and Hellen but has superior numerical accuracy. In addition, this method is significantly more efficient than the previously published “global” hypercomplex-variable finite element method, ZFEM, in that the global hypercomplex system of FE equations is not assembled nor solved. Instead, the displacement field is computed using a traditional, real-valued finite element method, and the numerical derivative of the stiffness matrix at the element level is only computed for a group of local, surrounding elements to the crack tip by using a Taylor series expansion based on complex numbers or dual numbers. The ERR is then determined as a sum of the element contributions. Derivatives of the ERR with respect to an arbitrary model parameter such as a crack extension, material property, or geometric feature are also available using a combination of the global and local methods, GL-ZFEM. Both L-ZFEM and GL-ZFEM were implemented into the commercial finite element software Abaqus through user defined element subroutines. Numerical results show that the ERR obtained by L-ZFEM has the same accuracy as that estimated through the global ZFEM or the J-integral methods but exhibits superior computational efficiency. © 2019 Elsevier Ltd
Closed-form solution of Timoshenko frames on elastic Winkler foundation using the Green’s function stiffness method
(Elsevier, 2024-10-01) Posso, Cristian; Molina-Villegas, Juan Camilo; Ballesteros Ortega, Jorge Eliecer; Universidad EAFIT; University of Central Florida; Mecánica Aplicada
This paper presents a method to obtain the exact closed-form solution for the static analysis of Timoshenko beams and frames on elastic Winkler foundation, subjected to arbitrary external loads and bending moments. The solution is derived using the Green’s Functions Stiffness Method (GFSM), a novel mesh reduction method that combines the strengths of the Stiffness Method (SM) and Green’s Functions (GFs). By incorporating the core concepts of the SM, the GFSM exhibits similarities to the Finite Element Method (FEM), including the use of shape functions, stiffness matrices, and fixed-end forces. The application of GFs facilitates the derivation of analytical expressions for displacement and internal force fields for arbitrary external loads and bending moments. Three examples are presented: a single-span beam, a two-span beam, and a one-bay, one-story plane frame on elastic Winkler foundations; which demonstrate applicability and efficacy of the method.
Closed-form solutions for axially non-uniform Timoshenko beams and frames under static loading
(Elsevier, 2024-03-23) Molina-Villegas, Juan Camilo; Ballesteros Ortega, Jorge Eliecer; Benítez Soto, Simón; Universidad EAFIT; University of Central Florida; Mecánica Aplicada
This paper presents the Green’s Functions Stiffness Method (GFSM) for solving linear elastic static problems in arbitrary axially non-uniform Timoshenko beams and frames subjected to general external loads and bending moments. The GFSM is a mesh reduction method that seamlessly integrates elements from the Stiffness Method (SM), Finite Element Method (FEM), and Green’s Functions (GFs), resulting in a highly versatile methodology for structural analysis. It incorporates fundamental concepts such as stiffness matrices, shape functions, and fixed-end forces, in line with SM and FEM frameworks. Leveraging the capabilities of GFs, the method facilitates the derivation of closed-form solutions, addressing a gap in existing methods for analyzing non-uniform reticular structures which are typically limited to simple cases like single-span beams with specific axial variations and loading scenarios. The effectiveness of the GFSM is demonstrated through three practical examples, showcasing its applicability in analyzing non-uniform beams and plane frames, thereby broadening the scope of closed-form solutions for axially non-uniform Timoshenko structures.
A comparative computational study of blood flow pattern in exemplary textile vascular grafts
(Taylor and Francis Ltd., 2018-01-01) R. VALENCIA; M. GARCÍA; J. BUSTAMANTE; R. VALENCIA; M. GARCÍA; J. BUSTAMANTE; Universidad EAFIT. Departamento de Humanidades; Centro de Estudios Urbanos y Ambientales (URBAM)
Textile vascular grafts are biomedical devices and play an important role serving as a solution for the partial replacement of damaged arterial vessels. It is believed that the success of a textile vascular graft, in the healing process after implantation, is due to the porous micro-structure of the wall. Although the transport of fluids through textiles is of great technical interest in biomedical applications, little is known about predicting the micro-flow pattern and cellular transport through the wall. The aim of this work is to investigate how the type of fabric, permeability and porosity affect both the local fluid dynamics at several scales and the fluid-particle interaction between platelets in textile grafts, related with the graft occlusion. This study involves both experimental and computational tests. Experimental tests are performed to characterize the permeability and porosity according to the ISO 7198 standard. The numerical process is based on a multi-scale approach where the fluid flow is solved with the Finite Element Method and the discrete particles are solved with the Molecular Dynamic Method. The results have shown that the type of fabric in textile vascular grafts and the degree of porosity and permeability affect both the local fluid dynamics and the level of penetration of platelets through the wall, thus indicating their importance as design parameters. © 2017 Informa UK Limited, trading as Taylor & Francis Group.
Finite element modeling of micropolar-based phononic crystals
(Elsevier BV, 2019-11-11) Guarín-Zapata N.; Gomez J.; Valencia C.; Dargush G.F.; Hadjesfandiari A.R.; Mecánica Aplicada
The performance of a Cosserat/micropolar solid as a numerical vehicle to represent dispersive media is explored. The study is conducted using the finite element method with emphasis on Hermiticity, positive definiteness, principle of virtual work and Bloch–Floquet boundary conditions. The periodic boundary conditions are given for both translational and rotational degrees of freedom and for the associated force- and couple-traction vectors. Results in terms of band structures for different material cells and mechanical parameters are provided. © 2019 Elsevier B.V.
Fluid-structure coupling using lattice-Boltzmann and fixed-grid FEM
(ELSEVIER SCIENCE BV, 2011-08-01) Garcia, Manuel; Gutierrez, Jorge; Rueda, Nestor; Mecánica Aplicada
This paper presents a method for the fluid-structure interaction by a hybrid approach that uses lattice-Boltzmann method (LBM) for the fluid dynamics analysis and fixed-grid FEM (FGFEM) for the structural analysis. The method is implemented in a high performance platform using GPUs to provide a high level of interactivity with the simulation. The solution uses the same Cartesian grid for both solvers. The coupling between both methods is accomplished by mapping the macroscopic pressure, velocity or momentum values from the LBM simulation into the corresponding nodes of the FGFEM structural problem. In spite of being based on a Cartesian grid, both solvers take into account the effect of curve boundaries. Also the effect of a moving boundary is considered in the fluid simulations. The examples presented in this paper show that the accuracy of the solution is as the same level of the finite volume method of the finite element method. On the other hand, the performance of the parallel implementation of the proposed method is of the order that allows real-time visualisation of the computing values for two-dimensional problems. © 2011 Elsevier B.V. All rights reserved.
Modeling added spatial variability due to soil improvement: Coupling FEM with binary random fields for seismic risk analysis
(Elsevier Ltd, 2018-01-01) Montoya-Noguera, Silvana; Lopez-Caballero, Fernando; Mecánica Aplicada
A binary mixture homogenization model is proposed for predicting the effects on liquefaction-induced settlement after soil improvement based on the consideration of the added spatial variability between the natural and the treated soil. A 2D finite element model of an inelastic structure founded on a shallow foundation was coupled with a binary random field. Nonlinear soil behavior is used and the model is tested for different mesh size, model parameters and input motions. Historical evidence as well as physical and numerical modeling indicate that improved sites present less liquefaction and ground deformation. In most cases this improvement is modeled as homogeneous; however, in-situ measurements evidence the high level of heterogeneity in the deposit. Inherent spatial variability in the soil and the application of some soil improvement techniques such as biogrouting and Bentonite permeations will necessary introduce heterogeneity in the soil deposit shown as clusters of the treated material in the natural soil. Hence, in this study, improvement zones are regarded as a two-phase mixture that will present a nonlinear relation due to the level of complexity of seismic liquefaction and the consequent settlement in a structure. This relation is greatly affected by the mechanical behavior of the soils used and the input motion. The effect on the latter can be efficiently related to the equivalent wave period as the proposed homogenization model depends on the stiffness demand of the input motion. © 2017 Elsevier Ltd
Shape optimisation of continuum structures via evolution strategies and fixed grid finite element analysis
(SPRINGER, 2004-01-01) Garcia, MJ; Gonzalez, CA; Mecánica Aplicada
Evolution strategies (ES) are very robust and general techniques for finding global optima in optimisation problems. As with all evolutionary algorithms, ES apply evolutionary operators and select the most fit from a set of possible solutions. Unlike genetic algorithms, ES do not use binary coding of individuals, working instead with real variables. Many recent studies have applied evolutionary algorithms to structural problems, particularly the optimisation of trusses. This paper focuses on shape optimisation of continuum structures via ES. Stress analysis is accomplished by using the fixed grid finite element method, which reduces the computing time while keeping track of the boundary representation of the structure. This boundary is represented by b-spline functions, circles, and polylines, whose control points constitute the parameters that govern the shape of the structure. Evolutionary operations are applied to each set of variables until a global optimum is reached. Several numerical examples are presented to illustrate the performance of the method. Finally, structures with multiple load cases are considered along with examples illustrating the results obtained.
Variational principles and finite element Bloch analysis in couple stress elastodynamics
(Elsevier, 2021-06-16) Guarín-Zapata, Nicolás; Gomez, Juan; Hadjesfandiari, Ali Reza; Dargush, Gary F.; Universidad EAFIT; Central Connecticut State University; University at Buffalo; Mecánica Aplicada
We address the numerical simulation of periodic solids (phononic crystals) within the framework of couple stress elasticity. The additional terms in the elastic potential energy lead to dispersive behavior in shear waves, even in the absence of material periodicity. To study the bulk waves in these materials, we establish an action principle in the frequency domain and present a finite element formulation for the wave propagation problem related to couple stress theory subject to an extended set of Bloch-periodic boundary conditions. A major difference from the traditional finite element formulation for phononic crystals is the appearance of higher-order derivatives. We solve this problem with the use of a Lagrange-multiplier approach. After presenting the variational principle and general finite element treatment, we particularize it to the problem of finding dispersion relations in elastic bodies with periodic material properties. The resulting implementation is used to determine the dispersion curves for homogeneous and porous couple stress solids, in which the latter is found to exhibit an interesting bandgap structure

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