Showing papers on "Smoothed finite element method published in 2006"

Finite element characterization of the size-dependent mechanical behaviour in nanosystems

Abstract: Mechanical behaviour analysis plays an important role in the design of micro/nano-electromechanical system (MEMS/NEMS) devices for reliability. In this paper, the size-dependent mechanical properties of nanostructures are numerically studied with the finite element method (FEM) by developing a kind of surface element to take into account the surface elastic effect. This method is then applied to the investigation of the interaction between two pressurized nanovoids and the effective moduli of two-dimensional nanoporous material. The numerical results indicate that surface elasticity can significantly alter the nature of interaction forms and the effective moduli by inducing a strong size dependence in conventional results.

Dynamics of Flexible Multibody Systems: Rigid Finite Element Method

Abstract: Homogenous Transformations.- The Rigid Finite Element Method.- Modification of the Rigid Finite Element Method.- Calculations for a Cantilever Beam and Methods of Integrating the Equations of Motion.- Verification of the Method.- Applications.

A Numerical Approach for Arbitrary Cracks in a Fluid-Saturated Medium

Abstract: A finite element method is proposed that can capture arbitrary discontinuities in a two-phase medium. The discontinuity is described in an exact manner by exploiting the partition-of-unity property of finite element shape functions. The fluid flow away from the discontinuity is modelled in a standard fashion using Darcy’s relation, while at the discontinuity a discrete analogon of Darcy’s relation is proposed. The results of this finite element model are independent of the original discretisation, as is demonstrated by an example of shear banding in a biaxial, plane-strain specimen.

Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes

Abstract: We consider the lowest-order Raviart-Thomas mixed finite element method for second- order elliptic problems on simplicial meshes in two and three space dimensions. This method produces saddle-point problems for scalar and flux unknowns. We show how to easily and locally eliminate the flux unknowns, which implies the equivalence between this method and a particular multi-point finite volume scheme, without any approximate numerical integration. The matrix of the final linear system is sparse, positive definite for a large class of problems, but in general nonsymmetric. We next show that these ideas also apply to mixed and upwind-mixed finite element discretizations of nonlinear parabolic convection-diffusion-reaction problems. Besides the theoretical relationship between the two methods, the results allow for important computational savings in the mixed finite element method, which we finally illustrate on a set of numerical experiments.

Meshfree simulations of thermo-mechanical ductile fracture

Abstract: In this work, a meshfree method is used to simulate thermo-mechanical ductile fracture under finite deformation. A Galerkin meshfree formulation incorporating the Johnson-Cook damage model is implemented in numerical computations. We are interested in the simulation of thermo-mechanical effects on ductile fracture under large scale yielding. A rate form adiabatic split is proposed in the constitutive update. Meshfree techniques, such as the visibility criterion, are used to modify the particle connectivity based on evolving crack surface morphology. The numerical results have shown that the proposed meshfree algorithm works well, the meshfree crack adaptivity and re-interpolation procedure is versatile in numerical simulations, and it enables us to predict thermo-mechanical effects on ductile fracture.

A simple finite element model for vibration analyses induced by moving vehicles

Abstract: This study developed a simple finite element method combining the moving wheel element, spring-damper element, lumped mass and rigid link effect to simulate complicated vehicles. The advantages of this vehicle model are (1) the dynamic matrix equation is symmetric, (2) the theory and formulations are very simple and can be added to a standard dynamic finite element codes easily and (3) very complicated vehicle models can be assembled using the proposed elements as simple as the traditional finite element method. The Fryba's solution of a simply supported beam subjected to a moving two-axle system was analysed to validate this finite element model. For a number of numerical simulations, the two solutions are almost identical, which means that the proposed finite element model of moving vehicles is considerably accurate. Field measurements were also used to validate this vehicle model through a very complicated finite element analysis, which indicates that the current moving vehicle model can be used to simulate complex problem with acceptable accuracy.

On the control volume finite element methods and their applications to multiphase flow

Abstract: In this paper we systematically review the control volume finite element (CVFE) methods for numerical solutions of second-order partial differential equations. Their relationships to the finite difference and standard (Galerkin) finite element methods are considered. Through their relationship to the finite differences, upstream weighted CVFE methods and the conditions on positive transmissibilities (positive flux linkages) are studied. Through their relationship to the standard finite elements, error estimates for the CVFE are obtained. These estimates are comparable to those for the standard finite element methods using piecewise linear elements. Finally, an application to multiphase flows in porous media is presented.

Finite element based reduction methods for static and dynamic analysis of thin-walled structures

Abstract: Nonlinear Finite Element (FE) analysis receives growing attention in industrial and research applications. Modern computer facilities together with state of the art commercial finite element programs allow large and complicated analysis to be per­formed. The nonlinearities of the structural behavior are more and more often taken into account. However, the repeated solution in time of large nonlinear systems of equations stemming from a FE discretization to reproduce the static and dynamic behavior of a general structure is still a computationally intensive task. In the present thesis methods are presented that reduce the number degrees of freedom so that the computational cost is significantly reduced, while a sufficient accuracy of the analysis result is retained. Slender and thin­walled structures constitute main structural components in various engineering areas since they feature a high strength­to­weight and stiffness­to­weight ratio. These structures are prone to function at high displacement levels when subjected to operational loads, while staying in the material linear elastic range. The subject of this thesis is therefore confined to slender and thin­walled structures subjected to static and dynamic loads that trigger geometrical nonlinearities only.

Two-scale composite finite element method for Dirichlet problems on complicated domains

Abstract: In this paper, we define a new class of finite elements for the discretization of problems with Dirichlet boundary conditions. In contrast to standard finite elements, the minimal dimension of the approximation space is independent of the domain geometry and this is especially advantageous for problems on domains with complicated micro-structures. For the proposed finite element method we prove the optimal-order approximation (up to logarithmic terms) and convergence estimates valid also in the cases when the exact solution has a reduced regularity due to re-entering corners of the domain boundary. Numerical experiments confirm the theoretical results and show the potential of our proposed method.

Structural reliability analysis using deterministic finite element programs

Abstract: THE PAPER SHOWS HOW STRUCTURAL RELIABILITY ALGORITHMS CAN BE INCORPORATED INTO DETERMINISTIC (COMMERCIAL) FINITE ELEMENT CODES AND USED TO PERFORM NUMERICAL STRUCTURAL RELIABILITY ANALYSIS BASED ON FINITE ELEMENT MODELS OF A STRUCTURE. A STRUCTURAL RELIABILITY MODULE IS DEVELOPED AND LINKED TO THE ANSYS FINITE ELEMENT PROGRAM, CREATING A CUSTOMIZED VERSION OF THE PROGRAM. STRUCTURAL RELIABILITY ANALYSIS CAN BE PERFORMED IN THE ANSYS ENVIRONMENT, AND INVOLVES CONSTRUCTION OF A PARAMETRIC ¯NITE ELEMENT MODEL, DEFINITION OF RANDOM PARAMETER DISTRIBUTIONS, DE¯NITION OF A LIMIT STATE FUNCTION BASED ON FINITE ELEMENT RESULTS, AND SOLUTION FOR THE FAILURE PROBABILITY. NUMERICAL EXAMPLES INVOLVING TRUSS AND FRAME STRUCTURES ARE STUDIED. AN APPLICATION EXAMPLE - STRUCTURAL RELIABILITY ANALYSIS OF AN EYE-BAR USPENSION BRIDGE - IS ALSO PRESENTED.

Advection approaches for single- and multi-material arbitrary Lagrangian-Eulerian finite element procedures

Abstract: The essential feature in arbitrary Lagrangian–Eulerian (ALE) based finite element approaches is the additional requirement to consider flow effects of the materials and the solution variables through the computational domain. These flow effects are commonly known as advective effects. The present paper examines different advection strategies for the application of the ALE finite element method in a finite deformation solid mechanics framework, where especially micromechanical problems are referred to. The global solution algorithm is based on the well-known fractional step method that provides an operator splitting approach for the solution of the coupled ALE equations. Distinguishing the so-called single-material and the multi-material ALE method, different advection schemes based on volume- and material-associated advection procedures are required. For the latter case, the material interfaces are not resolved explicitly by the finite element mesh. Instead a volume-of-fluid interface tracking approach in terms of the volume fractions of the different material phases is applied.

An Algebraic Multigrid Method for Higher-order Finite Element Discretizations

Abstract: In this paper, we will design and analyze a class of new algebraic multigrid methods for algebraic systems arising from the discretization of second order elliptic boundary value problems by high-order finite element methods. For a given sparse stiffness matrix from a quadratic or cubic Lagrangian finite element discretization, an algebraic approach is carefully designed to recover the stiffness matrix associated with the linear finite element disretization on the same underlying (but nevertheless unknown to the user) finite element grid. With any given classical algebraic multigrid solver for linear finite element stiffness matrix, a corresponding algebraic multigrid method can then be designed for the quadratic or higher order finite element stiffness matrix by combining with a standard smoother for the original system. This method is designed under the assumption that the sparse matrix to be solved is associated with a specific higher order, quadratic for example, finite element discretization on a finite element grid but the geometric data for the underlying grid is unknown. The resulting new algebraic multigrid method is shown, by numerical experiments, to be much more efficient than the classical algebraic multigrid method which is directly applied to the high-order finite element matrix. Some theoretical analysis is also provided for the convergence of the new method.

Further observations and review of numerical simulations of sheet metal punching

Abstract: In this report, a numerical study into the punching process is presented. During the simulations, the Gurson/Tvergaard damage model is applied in order to model void nucleation and growth. Particular attention is given in this paper to some of the inherent assumptions of both the damage mechanics model and its implementation in the finite element code, including the simulation of the process of void nucleation and growth and the role of hydrostatic pressure in the clearance zone. In spite of the fundamental nature of the assumptions, the numerical simulations compare favourably against experimental results. In order to aid further developments in damage modelling and its application in finite element simulations of punching, a number of suggestions for further investigations are presented.

An element by element spectral element method for elastic wave modeling

Abstract: The spectral element method which combines the advantages of spectral method with those of finite element method, provides an efficient tool in simulating elastic waves equation in complex medium. Based on weak from the elastodynamic equations, mathematical formulations for Legendre spectral element method are presented. The wave field on an element is discretized using high-order Lagrange interpolation, and integration over the element is accomplished based upon the Gauss-Lobotto-Legendre integration rule. This results in a diagonal mass matrix which leads to a greatly simplified algorithm. In addition, the element by element examples are resented to in our method to reduce the memory sizes and improve the computation efficiency. Finally, some numerical examples are resented to demonstrate the spectral accuracy and the efficiency. Because of combinations of the finite element scheme and a spectral algorithms, the method can be used for complex models, including free surface boundaries and strong...

A domain decomposition algorithm with finite element-boundary element coupling

Abstract: A domain decomposition algorithm coupling the finite element and the boundary element was presented. It essentially involves subdivision of the analyzed domain into sub-regions being independently modeled by two methods, i.e., the finite element method (FEM) and the boundary element method (BEM). The original problem was restored with continuity and equilibrium conditions being satisfied on the interface of the two sub-regions using an iterative algorithm. To speed up the convergence rate of the iterative algorithm, a dynamically changing relaxation parameter during iteration was introduced. An advantage of the proposed algorithm is that the locations of the nodes on the interface of the two sub-domains can be inconsistent. The validity of the algorithm is demonstrated by the consistence of the results of a numerical example obtained by the proposed method and those by the FEM, the BEM and a present finite element-boundary element (FE-BE) coupling method.

An atomistic simulation method combining molecular dynamics with finite element technique

Abstract: A numerical method that combines molecular dynamics simulation and finite element analysis to simulate the mechanical behaviors of materials and structures at nano-scale is proposed. In this combined method, the initial atomistic model is transformed to continuum model, and an approximate solution is first obtained with the finite element method for the system under the specified boundary conditions and external loadings. Then the deformed continuum model is transformed back to form a new atomistic model, and molecular dynamics simulation is performed to quickly reach the final stable equilibrium state. An example is presented to demonstrate that the combination procedure is valid and efficient. This method can take advantages of both the efficiency of continuum mechanics method and the accuracy of atomistic simulation method.