Abstract

Abstract

A reduced-order model for an efficient analysis of cardiovascular hemodynamics problems using multiscale approach is presented in this work. Starting from a patient-specific computational mesh obtained by medical imaging techniques, an analysis methodology based on a two-step automatic procedure is proposed. First a coupled 1D-3D Finite Element Simulation is performed and the results are used to adjust a reduced-order model of the 3D patient-specific area of interest. Then, this reduced-order model is coupled with the 1D model. In this way, three-dimensional effects are accounted for in the 1D model in a cost effective manner, allowing fast computation under different scenarios. The methodology proposed is validated using a patient-specific aortic coarctation model under rest and non-rest conditions.

Abstract

The paper describes the application of the simple rotation‐free basic shell triangle (BST) to the non‐linear analysis of shell structures using an explicit dynamic formulation. The derivation of the BST element involving translational degrees of freedom only using a combined finite element–finite volume formulation is briefly presented. Details of the treatment of geometrical and material non linearities for the dynamic solution using an updated Lagrangian description and an hypoelastic constitutive law are given. The efficiency of the BST element for the non linear transient analysis of shells using an explicit dynamic integration scheme is shown in a number of examples of application including problems with frictional contact situations.

Abstract

In this paper, we propose a way to weakly prescribe Dirichlet boundary conditions in embedded finite element meshes. The key feature of the method is that the algorithmic parameter of the formulation which allows to ensure stability is independent of the numerical approximation, relatively small, and can be fixed a priori. Moreover, the formulation is symmetric for symmetric problems. An additional element‐discontinuous stress field is used to enforce the boundary conditions in the Poisson problem. Additional terms are required in order to guarantee stability in the convection–diffusion equation and the Stokes problem. The proposed method is then easily extended to the transient Navier–Stokes equations.

Abstract

Abstract

Laplace formulations are weak formulations of the Navier–Stokes equations commonly used in computational fluid dynamics. In these schemes, the viscous terms are given as a function of the Laplace diffusion operator only. Despite their popularity, recently, it has been proven that they violate a fundamental principle of continuum mechanics, the principle of objectivity. It is remarkable that such flaw has not being noticed before, neither detected in numerical experiments. In this work, a series of objectivity tests have been designed with the purpose of revealing such problem in real numerical experiments. Through the tests it is shown how, for slip boundaries or free-surfaces, Laplace formulations generate non-physical solutions which widely depart from the real fluid dynamics. These tests can be easily reproduced, not requiring complex simulation tools. Furthermore, they can be used as benchmarks to check consistency of developed or commercial software. The article is closed with a discussion of the mathematical aspects involved, including the issues of boundary conditions and objectivity.

Abstract

In this work an extended class of multilayer perceptron is presented. This includes independent parameters, boundary conditions and lower and upper bounds. In some cases, such extensions contain a priori information of the problem. On some other situations they are necessary in order to define a correct representation for the solution.

The use of this augmented class of neural network is illustrated through a case study in the optimal control theory. The numerical results are compared against the analytical solution.

Abstract

In the discrete element method (DEM), the granular response is affected by the selection of boundary conditions, thereby emphasizing the importance of their careful consideration [1]. Replicating the boundary conditions employed in experiments is crucial to have a quantitative agreement between the response observed in the simulation and laboratory test [2]. In this study, a calibrated and validated DEM model was utilized to perform a series of simulations featuring regular polygons with varying numbers of corners subjected to different boundary conditions. The aim was to examine the combined effect of particle shape and boundary conditions on the mechanical response of granular assemblies. Simulations were performed under three boundary conditions: rigid frictional walls (in which the friction between the particle-wall interface is equal to that between the particle-particle interface), rigid frictionless walls, and periodic boundary conditions (PBC). Interestingly, it was observed that qualitatively, the effect of particle shape on granular response was invariant, irrespective of boundary conditions employed. However, quantitatively, the shear strength of all shapes was significantly affected by boundary settings, with the maximum and minimum strengths exhibited under rigid frictional walls and periodic boundaries, respectively. The magnitude of the decrease in shear strength due to boundary conditions was contingent upon the particle shape, with angular assemblies demonstrating a significant change in strength relative to round assemblies. Angular particles in contact with rigid wall frictional boundaries exhibited lesser rotations, thereby inducing relatively significant shear forces on the walls, particularly those parallel to the shearing direction. On the other hand, round particles in contact with walls rotated to a greater extent, resulting in little or negligible shear forces with the walls. Furthermore, boundary conditions also affected deformation patterns, including the development of shear bands.

Abstract