Implicit Boundary Method Research Articles

Application of structural rapid simulation technology in railway wagon equipment

In the traditional finite element simulation analysis, the designer spend a lot of time and energy to establish a reasonable finite element model. This approach is not suitable for rapid iterative updates and optimizations of products.Therefore, for the needs of rapid simulation of structure,this article introduced the basic principle of implicit boundary method and the characteristics of different analytical methods.The author explored and practiced the application of structural rapid simulation technology based on meshless method.Through the comparative study of simulation examples, The results of meshless analysis and finite element analysis are consistent. But the meshless method increase analysis efficiency by 92.5%.The research results have certain practical guiding significance for the application of structural rapid simulation in the engineering field.

Survey of Immersed Boundary Approaches for Finite Element Analysis

AbstractMesh generation for traditional finite element analysis has proven to be very difficult to fully automate especially using hexahedral elements for complex 3D geometry. Several modifications to the finite element method (FEM), such as the meshless methods, have been proposed for avoiding mesh generation. An alternative approach has recently gained popularity where the geometry, created as a solid model in cad software, is embedded or immersed in a nonconforming background mesh for analysis. In this approach, referred to here as the immersed boundary approach, a background mesh that is independent of the geometry is used for piecewise interpolation or approximation of the solution. Therefore, a uniform mesh with regular-shaped or undistorted elements can be used, and such a mesh is easy to generate automatically. When the geometry is immersed in the background mesh, the boundary elements are often only partly inside the geometry and the nodes of the mesh may not be on the boundaries. Many new methods have been developed to integrate over partial elements and to apply boundary and interface conditions when the boundaries of the geometries do not conform to the background mesh. These methods are reviewed in this article with particular emphasis on the implicit boundary method and step boundary method for applying boundary conditions. In addition, B-spline elements and several applications of the immersed boundary approach are surveyed including composite microstructures and structural elements for plates and shells.

An implicit boundary finite element method with extension to frictional sliding boundary conditions and elasto-plastic analyses

Implicit boundary methods, which enrich the interpolation structure with implicit weight functions, are straightforward methods for the enforcement of Dirichlet boundary conditions. In this article, we follow the implicit boundary method that uses approximate step functions (the step boundary method) developed by Kumar et al. and provide modifications that have several advantages. Roller boundary conditions have wide practical applications in engineering, however, the step boundary method for roller boundary conditions with inclinations has yet to be fully formulated through to the final linear system of equations. Thus we provide a complete derivation that leads to simplified stiffness matrices compared to the original approach, which can be implemented directly in fictitious domain finite element analysis. The approach is then extended, we believe for the first time, to the nonlinear cases of frictional boundary conditions and elasto-plastic material behaviour. The proposed formulation and procedures are validated on a number of example problems that test different aspects of the method.

Weak impositions of Dirichlet boundary conditions in solid mechanics: A critique of current approaches and extension to partially prescribed boundaries

In this article we first review various approaches developed to date for the weak imposition of Dirichlet boundary conditions in fictitious domain analysis for elasticity problems. The Hellinger–Reissner (H–R) principle, the linked Lagrange multiplier (LLM) method, the implicit boundary method and the fat boundary method are discussed along with the well-known Lagrange multiplier, penalty and Nitsche’s methods. We state these approaches in a common form starting with energy functionals and weak forms, and discretise using the fictitious domain finite element method. Previous formulations of these methods were in general developed for full prescription along the Dirichlet boundary, which generally implies no local effect of boundary inclination. However, partially prescribed conditions (such as the structural roller boundary condition) with inclination have wide practical applications in engineering. Here we provide techniques of imposing such boundary conditions in these methods in detail. For those methods that contain algorithmic parameters, such as the penalty and Nitsche’s methods, extra computation or empirical estimation is necessary to decide values of the parameters, and hence we discuss parametric and convergence behaviours through numerical examples to provide guidance on the choice of parameters.

B-spline based boundary conditions in the material point method

The material point method is an increasingly popular method for tackling solid mechanics problems involving large deformations. However, there are issues associated with applying boundary conditions in the method and, to date, no general approach for imposing both Neumann and Dirichlet boundary conditions has been proposed. In this paper, a new B-spline based boundary method is developed as a complete methodology for boundary representation, boundary tracking and boundary condition imposition in the standard material point method. The B-spline interpolation technique is employed to form continuous boundaries which are independent of the background mesh. Dirichlet boundary conditions are enforced by combining the B-spline boundaries with an implicit boundary method. Neumann boundary conditions are included by direct integration of surface tractions along the B-spline boundary. This general boundary method not only widens the problems that can be analysed by all variants of the material point method, when implemented using an implicit solver, but is also applicable to other embedded and non-matching mesh approaches. Although the Dirichlet boundary conditions are restricted to implicit methods, boundary representation, tracking and Neumann boundary condition enforcement can be applied to explicit and implicit methods.

Method for imposing boundary conditions on Reissner–Mindlin plates for analysis using structured background mesh

Elements in a conforming mesh are often distorted to fit the geometry which can cause numerical errors. If a background mesh is used for analysis, the elements can be regular shaped. The geometry must be represented independently using equations and implicit boundary method can be used to enforce essential boundary conditions. In this paper, this approach is extended to traditional Reissner–Mindlin plate elements that use mixed interpolation to avoid shear locking. The convergence of plate elements that use implicit boundary approach and a background mesh is studied in this paper using several benchmark problems to test their validity and robustness.

Mesh independent analysis of shell-like structures

Mesh independent analysis is motivated by the desire to use accurate geometric models represented as equations rather than approximated by a mesh. The trial and test functions are approximated or interpolated on a background mesh that is independent of the geometry. This background mesh is easy to generate because it does not have to conform to the geometry. Essential boundary conditions can be applied using the implicit boundary method where the trial and test functions are constructed utilizing approximate step functions such that the boundary conditions are guaranteed to be satisfied. This approach has been demonstrated for two-dimensional (2D) and three-dimensional (3D) structural analysis and is extended in this paper to model shell-like structures. The background mesh consists of 3D elements that use uniform B-spline approximations, and the shell geometry is assumed to be defined as parametric surfaces to allow arbitrarily complex shell-like structures to be modeled. Several benchmark problems are used to study the validity of these 3D B-spline shell elements. Copyright © 2012 John Wiley & Sons, Ltd.

2D modeling of moving particles with phase-change effect

The main aim of this work is to study the behavior of particulate flows taking into account the interfacial heat transfer on the particle surface including the phase change phenomena. Two flow configurations of increasing complexity are studied with the aim of unraveling fundamental properties of heat transfer in two-phase flows. The first configuration corresponds to the fluid flow past a single cylindrical ice particle melted in the water. The focus is on the influence of the Reynolds number on the melting time of a single particle and comparison of numerical data against Nu-based models. The second configuration refers to ice particles moving up in the water due to the gravity force in a two-dimensional channel. Here, the focus is on the study of particle dynamics in the presence of neighboring particles, including the influence of the viscous torque on the particle trajectories and finally on the melting time compared to the case of a single particle. An implicit fictitious boundary method (FBM) over a fixed Cartesian grid is extended to model the heat transfer and the phase change in particulate flows in two dimensions. The hydrodynamic forces acting on the particles are calculated directly through the surface integrals without the use of any semi-empirical correlations. The particle collisions are modeled directly using the hard sphere approach, taking into account the inelastic collisions. The interface velocity of the melting (solid–liquid) was calculated by means of the Stefan condition for each particle. To illustrate the impact of particle rotation caused by the viscous torques on the particle trajectory, a set of simulations was performed with and without viscous torque effect. A comparative analysis of the results showed that when the viscous moment is taken into account, the particle melting time is reduced significantly. Additionally, based on an analysis of the time history of the volume-averaged velocity in the entire domain, three regimes were found. In particular, the first regime is characterized by the acceleration of particles due to the gravity force, the second is the transitional regime and the last is the passive regime, where the melted particles follow the flow induced by particles in the past. During the last regime the particles do not have any influence on the fluid flow. The influence of the initial configuration of particles on the flow pattern and regimes is discussed.

Three-Dimensional Magnetostatic Analysis Using Structured Mesh and Nodal Elements

A structured mesh consisting of uniform, undistorted or regular shaped elements is easy to generate because it does not conform to the geometry. In order to use such a mesh for analysis, the geometry has to be represented independently of the mesh. To apply essential boundary conditions when nodes are not present on the boundary, the implicit boundary method was developed which uses solution structures constructed using approximate step functions. In this paper, this method is extended to solve 3-D magnetostatics and magnetic force computation problems that typically involve an assembly of parts made of several different materials. Traditional nodal elements are used, with specially constructed solution structures, to represent test and trial functions such that both boundary and interface conditions are enforced. Several magnetostatic problems with known solutions are modeled to validate the method.

Implicit boundary method for determination of effective properties of composite microstructures

A method that uses a structured grid to perform micromechanical analysis for determining effective properties of a composite microstructure is presented. This approach eliminates the need for constructing a mesh that has nodes along the interfaces between constituent materials of the composite. Implicit boundary method is used to ensure that interface conditions are satisfied at the material boundaries. In this method, solution structures for test and trial functions are constructed using approximate step functions such that the interface conditions are satisfied, even if there are no nodes on the material interface boundary. Since a structured grid does not conform to the geometry of the analysis domain, the geometry of the microstructure is defined independently using equations of the interface boundary curves/surfaces. Structured grids that overlap the geometry are easy to generate, and the elements in the grid are regular shaped and undistorted. A numerical example is presented to demonstrate that the proposed solution structure accurately models the solution across material interface, and convergence analysis is performed to show that the method converges as the grid density is increased. Fiber reinforced microstructures are analyzed to compute the effective elastic properties using both 2D and 3D models to show that the results match closely with the ones available in the literature.

Implicit boundary method for analysis using uniform B‐spline basis and structured grid

AbstractSeveral analysis techniques such as extended finite element method (X‐FEM) have been developed recently, which use structured grid for the analysis. Implicit boundary method uses implicit equations of the boundary to apply boundary conditions in X‐FEM framework using structured grids. Solution structures for test and trial functions are constructed using implicit equations such that the boundary conditions are satisfied even if there are no nodes on the boundary. In this paper, this method is applied for analysis using uniform B‐spline basis defined over a structured grid. Solution structures that are C1 or C2 continuous throughout the analysis domain can be constructed using B‐spline basis functions. As a structured grid does not conform to the geometry of the analysis domain, the boundaries of the analysis domain are defined independently using equations of the boundary curves/surfaces. Compared with conforming mesh, it is easier to generate structured grids that overlap the geometry and the elements in the grid are regular shaped and undistorted. Numerical examples are presented to demonstrate the performance of these B‐spline elements. The results are compared with analytical solutions as well as with traditional finite element solutions. Convergence studies for several examples show that B‐spline elements provide accurate solutions with fewer elements and nodes compared with traditional FEM. They also provide continuous stress and strain in the analysis domain, thus eliminating the need for smoothing stress/strain results. Copyright © 2008 John Wiley & Sons, Ltd.