Finite Element Method Formulation Research Articles

Numerical Analysis of Blood Flow Behaviour in a Constricted Porous Bifurcated Artery under the Influence of Magnetic Field

A numerical investigation concerning the effect of arterial constriction on the flow behaviour of blood in a porous bifurcated artery under the influence of a transverse magnetic field has been carried out. The equations of motion governing the flow are derived in the Cartesian coordinate system by treating the fluid as an electrically conducting, Newtonian, incompressible and fully developed blood flow. The blood is considered to flow through a constricted bifurcated artery with overlapping stenosis located at the mother artery. This developed model is consistent with the principles of magnetohydrodynamics. A stabilized form of finite element method, known as the Galerkin least-squares method is employed in solving the governing equation with suitably prescribed boundary conditions. Then, the non-linear systems resulting from the developed model are linearized by an iterative technique called the Newton-Raphson method. The effects of various parameters particularly the severity of stenosis, magnetohydrodynamics constant and permeability parameter on blood flow characteristics are analysed graphically for the velocity profile and streamline pattern. The findings obtained show that the presence of a magnetic field caused a significant alteration in the blood flow behaviour. Slight changes occurred in the flow pattern with the porous medium consideration. The application of a magnetic field could be utilized in controlling the hemodynamic flow of blood by decelerating the flow velocity and reducing the vortex sizes with rising in Hartmann number. While the pathological state of arterial disease as a porous structure reveals that a more porous fluid medium could have slightly promoted the growth in vortex size.

A Preprogrammable Continuum Robot Inspired by Elephant Trunk for Dexterous Manipulation.

Cable-driven continuum robots with hyper-redundant deformable backbones show great promise in applications, such as inspection in unstructured environments, where traditional rigid robots with discrete links and joints fail to operate. However, the motion of existing continuum robots is still constrained by their homogeneous backbones, and limited to environments with modest geometrical complexity. In this study, inspired by highly deformable elephant trunks, we presented a modular tensegrity structure with preprogrammable stiffness for continuum robots. Then we derived a mechanical model based on a positional formulation finite element method for predicting the configuration of the structure in different deformation scenarios. Theoretical predictions revealed that the curvature of each segment could be regulated by preprogramming their spring stiffness. Hence, our customizable design could offer an effective route for efficient robotic interactions. We further fabricated a continuum robot consisting of 12 modules, and showcased its deformation patterns under multiple scenarios. By regulating the distribution of spring stiffness, our robot could move through channels with varying curvatures, exhibiting its potential for applications where varying curvature, and conformal and efficient interactions are needed. Leveraging the inherent intelligence, this robotic system could simplify the complexity of the required actuation and control systems.

Improved friction model applied to plane sliding connections by a large deformation FEM formulation

Friction is an important source of dissipation in dynamical systems. Properly considering it in the numerical model is fundamental to obtain stable and representative responses in structures and mechanisms. This is especially significant for the well-known Coulomb model due to discontinuity in force when stick-slip transition occurs. In this work an improved friction force model is proposed to smooth the force transition at null velocity, with an additional parameter obtained from the own system state. The improved model is employed in sliding connections of plane frames finite elements. A total Lagrangian Finite Element Method (FEM) formulation based on a positional description of the motion is employed. Using a variational principle, frictional dissipation is added to the total mechanical energy to develop the equations of motion. The resulting nonlinear equations are solved by the Newton-Raphson method accounting for the friction force update in the iterative process. Examples are presented to show the formulation effectiveness and possibilities in simulating dynamical systems that present the stick-slip effect.

Computational Analysis of Dynamic Responses in Composite 2D Plane Structures Utilizing Extended Finite Element Method and State Space formulation

Computational Analysis of Dynamic Responses in Composite 2D Plane Structures Utilizing Extended Finite Element Method and State Space formulation

Estimation of thermophysic properties of a bimaterial by temperature field measurement and finite element model updating

The aim of this study is to identify simultaneously the thermal conductivity tensor and the heat capacity per unit volume of a bimaterial, whose heat conduction obeys Fourier’s law. This approach is validated by numerical simulation. The simulated temperature fields are obtained by the direct resolution of the heat conduction equation solved numerically with the help of finite element method formulation. To identify the parameters, an inverse method is developed by using the finite element model updating (FEMU) based on the Levenberg-Marquardt algorithm. This inverse finite element method approach allowed us to estimate the thermophysical parameters sought. We validated the numerical procedure by using noiseless temperature fields at different time and space steps and two types of material: an homogeneous and a bimaterial one. To be close to real conditions, the influence of the noise on the temperature fields is also studied and shows the efficiency of the inverse method. The results of this procedure show that the identified parameters are very less sensitive to the number of infra-red images varying from 40 to 80 and the number of elements ranging from 20 to 50 for a specimen size equals to 36.6 × 36.6 mm2.

Static analysis of box-girder bridge under the influence of Indian railway vehicle loading using ANSYS finite element model

The box-girder bridge has recently gained a lot of popularity because of its serviceability, stability, and structural efficiency. The box-girder bridge also has a lower structural weight than any other type of bridge. However, the analysis of such a bridge is too complex and challenging for the designers. This paper offers a modelling process for the study of a box- girder bridge with a ballastless sub-track system using the finite element method and evaluates the different static response characteristics of the bridge when it is loaded according to Indian Railway standards. The modelling and the evaluation of the 3D model of the bridge have been done using non-closed form finite element method (FEM) based ANSYS software and loadings have been applied symmetrically and un- symmetrically. Static analysis is carried out. The model has been simulated, and the resultants of deflection and stresses have been determined, taking into account the effect of different combinations of loading from the Indian Railways. The present modelling process is applied to analyze the box-girder bridge for 5 spans of 32 m each. For analysis of any box-girder bridge, though, researchers can use the modelling process described above.

Physics-Informed Neural Networks for shell structures

The numerical modeling of thin shell structures is a challenge, which has been met by a variety of finite element method (FEM) and other formulations—many of which give rise to new challenges, from complex implementations to artificial locking. As a potential alternative, we use machine learning and present a Physics-Informed Neural Network (PINN) to predict the small-strain response of arbitrarily curved shells. To this end, the shell midsurface is described by a chart, from which the mechanical fields are derived in a curvilinear coordinate frame by adopting Naghdi’s shell theory. Unlike in typical PINN applications, the corresponding strong or weak form must therefore be solved in a non-Euclidean domain. We investigate the performance of the proposed PINN in three distinct scenarios, including the well-known Scordelis–Lo roof setting widely used to test FEM shell elements against locking. Results show that the PINN can accurately identify the solution field in all three benchmarks if the equations are presented in their weak form, while it may fail to do so when using the strong form. In the small-thickness limit, where classical methods are susceptible to locking, training time notably increases as the differences in scaling of the membrane, shear, and bending energies lead to adverse numerical stiffness in the gradient flow dynamics. Nevertheless, the PINN can accurately match the ground truth and performs well in the Scordelis–Lo roof benchmark, highlighting its potential for a drastically simplified alternative to designing locking-free shell FEM formulations.

Rigorous Modal Characterization of First- and Second-Order Symmetric Waveguides Using Specular Periodic Boundary Conditions in 2D-FEM

Symmetries are widely exploited in the electromagnetic characterization of millimeter-wave devices and antennas, as they usually bring an improvement in resource usage and accuracy in full-wave simulations. Given the rising relevance of higher order symmetric devices, a challenge of integrating many different symmetries into compact formulations appears, with the objective of finding synergies and combining the strengths each one separately brings. In this work, we present a 2-D finite element method (FEM) formulation that fulfills this task for arbitrary waveguide cross sections presenting at the same time specular first-order and rotational second-order symmetries. It is based on newly introduced specular periodic boundary conditions (SPBCs), which effectively exploit the best case simulation domain for this problem. Furthermore, they avoid the need of using a mesh matching or projection procedure for periodic boundaries, while also bringing an improvement to mode classification.

A thermodynamically consistent phase-field regularized cohesive fracture model with strain gradient elasticity and surface stresses

Microstructure and surface stresses play a vital role in the micro- and nano-scale. In this paper, a thermodynamically consistent phase-field regularized cohesive fracture model (PF-CZM) is initially proposed to analyze crack propagation in the micro- and nano-scale, where strain gradient elasticity is introduced by higher-order elastic energy, and surface stresses are obtained using geometrical nonlinearity. After that, the higher-order theory is implemented through a mixed-type formulation finite element method. The specimen size effect of Mode I crack propagation is investigated. It is found that both strain gradient elasticity and surface stresses increase the critical load of crack nucleation, which becomes more pronounced as the size of the specimen decreases. The strain gradient elasticity increases the fracture toughness due to the reduction in stress singularity, while the maximum value of stress is still equal to the fracture strength during crack propagation. The surface stresses improve the local-fracture strength at the crack tip. Finally, the strain gradient elasticity further enhances the effect of surface stresses by changing the damage distribution at the crack tip when surface stresses are taken into account along with strain gradient elasticity. The presented framework has shown great potential for modeling crack propagation in the micro- and nano-scale.

Heat Transfer Study in Cylindrical Cavity with Heat Absorption or Generation

Lattice Boltzmann mesoscopic (LBM) is applied to solve energy equation of a transient conduction radiation heat transfer problem in a two-dimensional cylindrical participating (absorbing, emitting and scattering) medium in the presence of heat generation/absorption coefficient. Control volume finite element method (CVFEM) formulation is used to obtain the radiative information. To study the effectiveness of the LBM-CVFEM combination on unsteady conduction-radiation problems in cylindrical media, the energy equation of the problem is also solved using the finite difference method (FDM) in which the CVFEM is used to compute radiative information. The effects of heat generation/absorption coefficient on temperature distributions in the medium are studied. Results of the present work are benchmarked against those available in the literature. The hybrid numerical model’s results are also compared with those obtained by the FDM-CVFEM combination. All the results presented in this work show that the present method is accurate and valuable for the analysis of cylindrically axisymmetric radiative heat transfer problems .

Novel Design of a Cable-Driven Continuum Robot With Multiple Motion Patterns

Cable-driven continuum robots exhibit accessing and manipulation capabilities in constrained and cluttered environments that are unachievable for traditional robots composing of discrete links and joints. However, the existing continuum robots structured by non-scalable backbones are monofunctional, merely capable of providing bending degree of freedom, not allowing regional elongation that is necessary for dexterous manipulation. In this paper, we present a particular tensegrity topology for the continuum robotic design with an additional stretching degree of freedom, by which the robot can achieve high flexibility in both bending and contraction motion patterns for more configurable operations. To quantify kinematics of the robot under various motion patterns, we build a mechanical model following a positional formulation finite element method. Guided by the theoretical results, a triple-segmented continuum robot is designed and fabricated. To reduce the control complexity, we regulate the individual stiffness of each segment, by which the motion coupling among the segments can be eliminated. Moreover, we also demonstrate the potential applications of this robotic design in tasks of traveling through holes and avoiding obstacles.

Adaptive Quasi-Monte Carlo Finite Element Methods for Parametric Elliptic PDEs

We introduce novel adaptive methods to approximate moments of solutions of partial differential Equations (PDEs) with uncertain parametric inputs. A typical problem in Uncertainty Quantification is the approximation of the expected values of quantities of interest of the solution, which requires the efficient numerical approximation of high-dimensional integrals. We perform this task by a class of deterministic quasi-Monte Carlo integration rules derived from Polynomial lattices, that allows to control a-posteriori the integration error without querying the governing PDE and does not incur the curse of dimensionality. Based on an abstract formulation of adaptive finite element methods (AFEM) for deterministic problems, we infer convergence of the combined adaptive algorithms in the parameter and physical space. We propose a selection of examples of PDEs admissible for these algorithms. Finally, we present numerical evidence of convergence for a model diffusion PDE.

The solution of the anomalous diffusion equation by a finite element method formulation based on the Caputo derivative

The solution of the anomalous diffusion equation by a finite element method formulation based on the Caputo derivative

Study on physical behaviors according to element formulations of ballistic impact simulation models

During modeling ballistic impact, physical behaviors were investigated according to element formulations. In order to conduct the investigation, a simple ballistic impact simulation model was used. Several case studies consisting of FEM (Finite Element Method) and SPH (Smoothed Particle Hydrodynamics) models were conducted using the LS-DYNA research/commercial code. As a result, these case studies suggest that the SPH formulation is effective to simulate interactions among particles after failures so that the penetration phenomenon of the projectile were well described. In addition, some parameters relating to the SPH formulation such as particle spacing and smoothing length constant were investigated. Finally, for the verification, 20 mm fragment simulating projectile tests to verify the protection performance of K9 Thunder grill louver were compared with the simulations applying the FEM and SPH formulations.

Numerical simulation of wave propagation through interfaces using the extended finite element method for magnetic resonance elastography.

Magnetic resonance elastography (MRE) is an elasticity imaging technique for quantitatively assessing the stiffness of human tissues. In MRE, finite element method (FEM) is widely used for modeling wave propagation and stiffness reconstruction. However, in front of inclusions with complex interfaces, FEM can become burdensome in terms of the model partition and computationally expensive. In this work, we implement a formulation of FEM, known as the eXtended finite element method (XFEM), which is a method used for modeling discontinuity like crack and heterogeneity. Using a level-set method, it makes the interface independent of the mesh, thus relieving the meshing efforts. We investigate this method in two studies: wave propagation across an oblique linear interface and stiffness reconstruction of a random-shape inclusion. In the first study, numerical results by XFEM and FEM models revealing the wave conversion rules at linear interface are presented and successfully compared to the theoretical predictions. The second study, investigated in a pseudo-practical application, demonstrates further the applicability of XFEM in MRE and the convenience, accuracy, and speed of XFEM with respect to FEM. XFEM can be regarded as a promising alternative to FEM for inclusion modeling in MRE.

Well-conditioned and optimally convergent second-order Generalized/eXtended FEM formulations for linear elastic fracture mechanics

The Generalized/eXtended Finite Element Method (G/XFEM) has been established as an approach to provide optimally convergent solutions for classes of problems that are challenging for the standard version of the Finite Element Method (FEM). For problems with non-smooth solutions, as those within the Linear Elastic Fracture Mechanics (LEFM) context, the FEM convergence rates are often not optimal and are bounded by the strength of the singularity in the analytical solution. This can be overcome by G/XFEM and many researches have focused on delivering first-order convergent solutions for LEFM problems. The difficulty in obtaining higher-order accurate approximations, however, relies mainly on also controlling the growth rate of the stiffness matrix condition number. In this paper, well-conditioned and optimally convergent second-order G/XFEMs are proposed for LEFM simulations by augmenting second-order Lagrangian FEM approximation spaces. More specifically, two strategies are proposed in order to accurately represent second-order discontinuous functions along a crack. Also, a third strategy that essentially improves the use of linear Heaviside functions in the sense that these enrichments no longer cause linear dependencies among the set of G/XFEM shape functions is proposed. The numerical experiments show the robustness of the formulations presented herein for a set of crack topologies.

Geometric nonlinear analysis of large rotation behavior of a curved SWCNT

ABSTRACT Nanotubes form clusters and are found in curved bundles in nanotube films and nanocomposites. Separation phenomenon is suspected to occur in these curved bundles. In this study, the deformation of a single-wall carbon nanotube (SWCNT) interacting with curved bundle nanotubes is analyzed. It is assumed that the bundle is rigid and only van der Waals force acts between the nanotube and the bundle of nanotubes. A new method of modeling geometric nonlinear behavior of the nanotube due to finite rotation and the corresponding van der Waals force is developed using co-rotational finite element method (CFEM) formulation, combined with small deformation beam theory, with the inclusion of axial force. Current developed CFEM method overcomes the limitation of linear Finite Element Method (FEM) formulation regarding large rotations and deformations of carbon nanotubes. This study provides a numerical tool to identify the critical curvature influence on the interaction of carbon nanotubes due to van der Waals forces and can provide more insight into studying irregularities in the electronic transport properties of adsorbed nanotubes in nanocomposites.

A Novel Rigid Finite Element Formulation for Dynamic Analysis of Flexible Plates

This paper introduces a new rigid finite element method (RFEM) formulation for dynamic analysis of plates. In RFEM, a flexible body is divided into several rigid elements which are interconnected by spring and damping elements. Mainly, RFEM has been used to model systems with beam-like slender components, such as ropes and cables, and few RFEM formulations were developed to model plates and shells. In this study however, by means of the Timoshenko beam theory and cuboid rigid elements, a novel RFEM formulation is developed to model flexible flat plates with generic geometries of the surface, considering large deformation. For this purpose, an RFEM formulation is presented for straight beams with rectangular cross-section by means of the Timoshenko beam theory. Next, this formulation is expanded to model flexible rectangular plates with uniform thickness and then, it is elaborated on how to model non-rectangular plates with uniform thickness using only cuboid elements and consequently, the development of the proposed RFEM formulation is completed. After investigating various case studies, the competence of the proposed formulation is evaluated thoroughly. The results of RFEM came on a proper agreement with the FEM results in a way that the maximum difference between these results in dynamic analysis was about 3%.

An isogeometric FE-BE method to investigate fluid–structure interaction effects for an elastic cylindrical shell vibrating near a free surface

In this study, an isogeometric finite element-boundary element (FE-BE) framework is proposed to investigate frequency-dependent hydrodynamic characteristics of elastic structures vibrating at free surface or in the vicinity of free surface. The overall numerical framework consists of two parts. In the first part, in vacuo dynamic characteristics are obtained by an isogeometric finite element method (IGAFEM) formulation. Then, in the second part, frequency-dependent generalized added mass and generalized hydrodynamic damping coefficients are obtained by an isogeometric boundary element method (IGABEM) formulation, assuming that the surrounding fluid is ideal, i.e., inviscid, incompressible and its motion is irrotational. To include free surface effects, the free surface boundary conditions are satisfied with an appropriate Green’s function in the mathematical formulation. To show the applicability of the presented framework, an elastic cylindrical shell which was studied previously in the literature is investigated considering that the structure is partially or fully submerged into fluid of infinite depth. It is shown that the results obtained in this study compare very well with the results available in literature.

Inverse Method for Estimation of Thermophysics Properties of a Bimaterials

The aim of this study is to identify simultaneously the thermal conductivity tensor and the volume heat coefficient of a bimaterial (checkerboard) whose heat conduction obeys Fourier's law. This approach is validated by numerical simulation. The simulated temperature fields are obtained by the direct resolution heat conduction solved numerically by the finite element method formulation. To identify parameters, an inverse method is developed by using the finite element temperature approach (FEU-T) model fitting method based on the Levemberg-Marquardt algorithm. We validated the numerical procedure by using noiseless temperature fields at different time and space steps. The influence of the noise on the temperature fields is also studied and shows the efficiency of the inverse method. The results show that this procedure is not very sensitive to the number of elements (or space steps) and the number of time steps.