Computational Mechanics最新文献

The NURBS Surface-to-Volume Guided Mesh Generation (NSVGMG) is a general-purpose mesh generation method, introduced to increase the scope of isogeometric analysis in computing complex-geometry problems. In the NSVGMG, NURBS patch surface meshes serve as guides in generating the patch volume meshes. The interior control points are determined independent of each other, with only a small subset of the surface control points playing a role in determining each interior point. In the updated version of the NSVGMG we are introducing in this article, in the process of determining the location of an interior point in a parametric direction, more weight is given to the closer guides, with the closeness measured along the guides in the other parametric directions. Tests with 2D and 3D shapes show the effectiveness of the NSVGMG in generating good quality meshes, and the robustness of the updated NSVGMG even in mesh generation for complex shapes with distorted boundaries.

The primary objective of this work is to determine the effective permeability of porous media consisting of an isotropic permeable solid matrix containing pores of arbitrary shapes. Fluid flow through the matrix phase is modeled by Darcy’s law, while the flow inside the pores follows the Stokes equations. The interfaces between the matrix phase and inclusions are defined by the general form of the Beavers-Joseph-Saffman conditions. To achieve this objective, the Boundary Element Method (BEM) is first developed to solve the coupled Darcy and Stokes problem related to fluid flow through an infinite solid phase containing an arbitrarily shaped pore under a uniform prescribed pressure gradient at infinity. In contrast to the classical BEM where integration equations are often singular, our method, incorporating both finite difference and analytical integration schemes, overcomes this inconvenience. Additionally, compared to the commonly used numerical method based on the finite element method, our approach, which only requires discretization of the solid/fluid interface, significantly enhances computational speed and efficiency. Subsequently, each pore is substituted with an equivalent permeable inclusion, and its permeability is determined. Finally, employing classical micromechanical schemes, the macroscopic permeabilities of the porous material under consideration are estimated. These macroscopic permeability estimates are then compared with the relevant data available in the literature, as well as several numerical results provided by the finite element method.

This study investigates guided-wave reflection and transmission at a water pipe joint. The system comprises a linearly elastic pipe filled with water with a joint that is modeled as a discontinuity of the solid region. Wave reflection and transmission are solved using the finite element method (FEM) with radiation conditions for reflected and transmitted guided waves into infinite waveguides. For the radiation conditions, the reflected and transmitted waves are expressed by modal expansion using the semi-analytical finite-element (SAFE) dispersion analysis method. This study extends the hybrid SAFE-FEM to the coupled fluid–solid axisymmetric problem. Numerical results demonstrate that the hybrid SAFE-FEM provides sufficiently accurate solutions. The propagation modes, similar to the modes in a solid pipe, are strongly or perfectly reflected by the joint. However, the modes are transmitted through the joint with little scattering after they converge to the modes in a water bar. The crossing of dispersion curves with those for modes in a solid pipe causes mode conversion and induces scattering attenuation.

In this work, we present a first-order stabilization-free virtual element method (SFVEM) for three-dimensional hyperelastic problems. Different from the conventional virtual element method, which necessitates additional stabilization terms in the bilinear formulation, the method developed in this work operates without the need for any stabilization. Consequently, it proves highly suitable for the computation of nonlinear problems. The stabilization-free virtual element method has been applied in two-dimensional hyperelasticity and three-dimensional elasticity problems. In this work, the format will be applied to three-dimensional hyperelasticity problems for the first time. Similar to the techniques used in the two-dimensional stabilization-free virtual element method, the new virtual element space is modified to allow the computation of the higher-order (L_2) projection of the gradient. This paper reviews the calculation process of the traditional (mathcal {H}_1) projection operator; and describes in detail how to calculate the high-order (L_2) projection operator for three-dimensional problems. Based on this high-order (L_2) projection operator, this paper extends the method to more complex three-dimensional nonlinear problems. Some benchmark problems illustrate the capability of the stabilization-free VEM for three-dimensional hyperelastic problems.

Nonlinear multi-point constraints are essential in modeling various engineering problems, for example in the context of (a) linking individual degrees of freedom of multiple nodes to model nonlinear joints, (b) coupling different element types in finite element analysis, (c) enforcing various types of rigidity in parts of the mesh and (d) considering deformation-dependent Dirichlet boundary conditions. One method for addressing constraints is the master–slave elimination, which offers the benefit of reducing the problem dimension as opposed to Lagrange multipliers and the penalty method. However, the existing master–slave elimination method is limited to linear constraints. In this paper, we introduce a new master–slave elimination method for handling arbitrary smooth nonlinear multi-point constraints in the system of equations of the discretized system. We present a rigorous mathematical derivation of the method. Within this method, new constraints can be easily considered as an item of a “constraint library”; i.e. no case-by-case-programming is required. In addition to the theoretical aspects, we also provide helpful remarks on the efficient implementation. Among others, we show that the new method results in a reduced computational complexity compared to the existing methods. The study also places emphasis on comparing the new approach with existing methods via numerical examples. We have developed innovative benchmarks which encompass all relevant computational properties, and provide analytical and reference solutions. Our findings demonstrate that our new method is as accurate, robust and flexible as the Lagrange multipliers, and more efficient due to the reduction of the total number of degrees of freedom, which is particularly advantageous when a large number of constraints have to be considered.

The present work is a comparative study of different data transfer techniques in the context of the finite cell method (FCM) in combination with remeshing for hyperelastic problems undergoing large deformations. The FCM is an immersed-boundary method that uses Cartesian grids for the discretization so as to avoid the generation of boundary conforming meshes. To overcome problems with heavily distorted meshes at large deformation states, we apply a remeshing procedure. During the remeshing, the data containing the deformation history has to be transferred between the meshes. In the present study, different methods are considered and compared: radial basis functions without and with polynomial extension, inverse distance weighting, and (textit{L}_text {2})-projection applying the shape functions used in the FCM for the trial and test functions.

We consider the aeroelastic simulation of flexible mechanical structures submerged in subsonic fluid flows at low Mach numbers. The nonlinear kinematics of flexible bodies are described in the total Lagrangian formulation and discretized by finite elements. The aerodynamic loads are computed using the unsteady vortex-lattice method wherein a free wake is tracked over time. Each implicit time step in the dynamic simulation then requires solving a nonlinear equation system in the structural variables with additional aerodynamic load terms. Our focus here is on the efficient numerical solution of this system by accelerating the Newton algorithm. The particular structure of the aeroelastic nonlinear system suggests the structural derivative as an approximation to the full derivative in the linear Newton system. We investigate and compare two promising algorithms based on this approximation, a quasi-Newton type algorithm and a novel inexact Newton algorithm. Numerical experiments are performed on a flexible plate and on a wind turbine. Our computational results show that the approximation can indeed accelerate the Newton algorithm substantially. Surprisingly, the theoretically preferable inexact Newton algorithm is much slower than the quasi-Newton algorithm, which motivates further research to speed up derivative evaluations.

This study addresses the fundamental challenge of extending the deep material network (DMN) to accommodate multiple microstructures. DMN has gained significant attention due to its ability to be used for fast and accurate nonlinear multiscale modeling while being only trained on linear elastic data. Due to its limitation to a single microstructure, various works sought to generalize it based on the macroscopic description of microstructures. In this work, we utilize a mechanistic machine learning approach grounded instead in microstructural informatics, which can potentially be used for any family of microstructures. This is achieved by learning from the graph representation of microstructures through graph neural networks. Such an approach is a first in works related to DMN. We propose a mixed graph neural network (GNN)-DMN model that can single-handedly treat multiple microstructures and derive their DMN representations. Two examples are designed to demonstrate the validity and reliability of the approach, even when it comes to the prediction of nonlinear responses for microstructures unseen during training. Furthermore, the model trained on microstructures with complex topology accurately makes inferences on microstructures created under different and simpler assumptions. Our work opens the door for the possibility of unifying the multiscale modeling of many families of microstructures under a single model, as well as new possibilities in material design.

A framework to solve fast dynamic problems involving a non-smooth interface behavior with contact and decohesion is under concern. In previous works, unilateral contact and impact have been studied in explicit dynamics but no damage nor cohesion were involved. Combining a contact problem and a thermodynamically motivated damage model within the so-called CD-Lagrange explicit dynamics scheme is the aim of this work. To do so, RCCM macroscopic model of adhesion with damage of the interface is studied. The thermodynamic motivation of the model and the use of a symplectic explicit scheme creates a framework based on good energy balance. In this work, illustrations and feasibility are shown for small displacement problems.

Detection of biomarkers is exploited in lab-on-a-chip devices by means of Love type Surface Acoustic Waves (SAW). Finger type arrangement of electrodes, used for InterDigital-Transducers (IDT), perform well to create and detect SAW by using electro-mechanical coupling. Efficiency of such a transceiver depends on design parameters such as chosen material orientation, thickness, placement of electrodes. An optimized design reduces production costs, hence, we need a digital twin of the device with multiphysics simulations that compute deformation and electric field. In this study, we develop a framework with the open-source package called FEniCS for modal and transient analyses of IDTs by using the Finite Element Method (FEM). Specifically, we discuss all possible sensor design parameters and propose a computational design guideline that determines the “best” thickness parameter by maximizing mass sensitivity, thus, efficiency for a Love surface acoustic wave sensor.