Optimization of least-weight grillages by finite element method

A numerical method is presented for the minimization of the volume of grillages with a stress constraint. The material distribution in the design domain is optimized by a fully-stressed criterion using a finite element method. The densities and orientations of the beams at nodes in grillages are taken as design variables, which vary in the design domain continuously. As intermediate densities are not suppressed in the optimization procedure, numerical instabilities are completely avoided. As a result, the optimal distribution fields of moments, deformation and material are obtained simultaneously. Subsequently the discrete structures are determined from the optimal distribution fields. The optimization procedure is accomplished by the computer program automatically. The capability of the proposed procedure is demonstrated on several classical benchmark problems.     

Tuning the Schur complement computations for finite element partitions

The domain decomposition method (DDM) is an efficient algorithmic tool for the parallelization of finite element computer codes. A variant of the DDM with direct solution algorithm is based on computation of Schur complement matrices for finite element partitions. This paper describes a simple technique that considerably improves execution rate of computationally intensive routines of the Schur complement computations. The technique uses ‘block of columns’ matrix operations and loop unrolling to reduce load instructions from cache memory and to increase instruction-level parallelism. For superscalar RISC processors, experimental results show that it is possible to improve performance of the DDM solution procedure by several times.     

A splitting-based finite element method for the Biot poroelasticity system

In this work, we propose a finite element method for solving the linear poroelasticity equations. Both displacement and pressure are approximated by continuous piecewise polynomials. The proposed method is sequential, leading to decoupled smaller linear systems compared to the systems resulting from a fully implicit finite element approach. A priori error estimates are derived. Numerical results validate the theoretical convergence rates.     

An analysis of natural convection using the thermal finite element discrete Boltzmann equation

The lattice Boltzmann method (LBM) is the simple numerical simulator for fluids because it consists of linear equations. Excluding the higher differential term, the LBM for a temperature field is also achieved as an easy numerical simulation method. However, the LBM is hardly applied to body fitted coordinates for its formulation. It is then difficult to calculate complex lattices using the LBM. In this paper, the finite element discrete Boltzmann equation (FEDBE) is introduced to deal with this weakness of the LBM. The finite element method is applied to the discrete Boltzmann equation (DBE) of the basic equation of the LBM. For FEDBE, the simulation using complex lattices is achieved, and it will be applicable for the development in engineering fields. The natural convection in a square cavity and the Rayleigh–Bernard convection are chosen as the test problem. Each simulation model is accurate enough for the flow patterns, the temperature distribution and the Nusselt number. This method is now considered good for the flow and temperature field, and is expected to be introduced for complex lattices using the DBE.     

基于有限元法的发动机罩猛关失效分析

用有限元法分析并解决某车型发动机罩猛关失效问题.通过试验确定涵盖多数客户样本的发动机罩关闭速度,发现该车型发动机罩关闭过程中前端与格栅发生干涉,并通过有限元法再现此问题.改进缓冲块安装方案并进行有限元分析和实车验证,有效解决该车型发动机罩猛关失效问题.     

Development of a methodology for a simplified finite element model and optimum design

As computer power is increased, refined finite element models are employed for structural analysis and design. However, it is still difficult and expensive to make and use refined finite element models in the design stage. The refined models usually cause problems in the preliminary design where the design is frequently changed. Therefore, the development of a simplified finite element model is desirable for use in the preliminary design stage. This paper describes the methodology for the simplified model and its optimum design. A Goal programming algorithm is used for system identification to make the simplified model. The developed methodology consists of three phases such as simplification, design, and inverse process. The simplified finite element model is used for the design change and the changed design is recovered onto the original design. The presented methodology is verified through a few examples.     

A computer algebra based finite element development environment

A finite element development environment based on the technical computing program Mathematica is described. The environment is used to automatically program standard element formulations and develop new elements with novel features. Source code can also be exported in a format compatible with commercial finite element program user-element facilities. The development environment is demonstrated for three mixed Petrov–Galerkin plane stress elements: a standard formulation, an advanced formulation incorporating rotational degrees of freedom and a standard formulation in which the stiffness matrix is integrated analytically, before being exported as ANSYS user elements. The results presented illustrate the accuracy of the standard mixed formulation element and the enhancement of performance when rotational degrees of freedom are added. Further, the analytically integrated element shows that computational requirements can be greatly reduced when analytical integration schemes are used in the formation.     

Comparison of finite element and pendulum models for simulation of sloshing

The pendulum model is a cost effective tool for the simulation of sloshing. However, the accuracy and applicability of the model has not been well established. In this article, we compare the simulation results obtained from the pendulum model and a more complicated finite element model for sloshing of liquids in tanker trucks. In the pendulum model, we assume that the liquid in the tanker is a point mass oscillating like a frictionless pendulum subjected to an external acceleration. In the finite element model, we solve the full Navier-Stokes equations written for two fluids to obtain the location and motion of the free surface. Stabilized finite element formulations are used in these complex 3D simulations. These finite element formulations are implemented in parallel using the message-passing interface libraries. The numerical example includes the simulation of sloshing in tanker trucks during turning.     

Vectorizable preconditioners for mixed finite element solution of second-order elliptic problems

We compare the performance of the CG (conjugate gradient) method, the point-wise incomplete factorization preconditioned CG method, and the block-incomplete factorization preconditioned CG method for solving problems arising in mixed finite element discretization of second order elliptic differential equations. The robustness and vectorizable properties of these methods are illustrated by a large set of numerical tests.     

Fully discrete potential-based finite element methods for a transient eddy current problem

Fully discrete potential-based finite element methods called methods are used to solve a transient eddy current problem in a three-dimensional convex bounded polyhedron. Using methods, fully discrete coupled and decoupled numerical schemes are developed. The existence and uniqueness of solutions for these schemes together with the energy-norm error estimates are provided. To verify the validity of both schemes, some computer simulations are performed for the model from TEAM Workshop Problem 7. This work was supported by Postech BSRI Research Fund-2009, National Basic Research Program of China (2008CB425701), NSFC under the grant 10671025 and the Key Project of Chinese Ministry of Education (No. 107018).     

A Galerkin finite element method for time-fractional stochastic heat equation

In this study, a Galerkin finite element method is presented for time-fractional stochastic heat equation driven by multiplicative noise, which arises from the consideration of heat transport in porous media with thermal memory with random effects. The spatial and temporal regularity properties of mild solution to the given problem under certain sufficient conditions are obtained. Numerical techniques are developed by the standard Galerkin finite element method in spatial direction, and Gorenflo–Mainardi–Moretti–Paradisi scheme is applied in temporal direction. The convergence error estimates for both semi-discrete and fully discrete schemes are established. Finally, numerical example is provided to verify the theoretical results.     

Biomechanical study of lumbar spine with dynamic stabilization device using finite element method

A finite element model of the human lumbar spine was developed for the parametric study of the stiffness of a dynamic stabilization device. Spinal segments (L2-L5) were used to investigate the effect of dynamic stabilization and the influence on the mobility of adjacent intervertebral segments. Three spines were analysed and compared: (1) a lumbar spine with intact discs, used as a reference; (2) a fused spine with a fixation device after the the facetectomy and the total laminectomy; and (3) a spine stabilized with a dynamic stabilization device after the facetectomy and the total laminectomy.The Range of Motion (ROM) and the intervertebral disc pressure of L3-L4 and the ROM and disc pressure of the adjacent segments were examined to determine the influence of the implant on the adjacent segments.In the case of the dynamically stabilized spine, the total ROM was greater than that of the fused spine but similar to that of the intact spine. Furthermore, the disc pressure on the adjacent segments in the fused spine was greater than that of the intact spine, but the disc pressure of the dynamically stabilized spine was similar to the intact spine. In particular, the dynamic stabilization device having a stiffness of 10-15 N/mm made the destabilized spine more similar to the intact spine.Results indicated that the use of dynamic stabilization devices restored functionality closer to that of the intact spine as compared to the fused spine. The stiffness value utilized in the device was determined to be an important design parameter in manufacturing the dynamic stabilization device.     

Using three-dimensional finite element analysis in time domain to model railway-induced ground vibrations

For the prediction of ground vibrations generated by railway traffic, finite element analysis (FEA) appears as a competitive alternative to simulation tools based on the boundary element method: it is largely used in industry and does not suffer any limitation regarding soil geometry or material properties. However, boundary conditions must be properly defined along the domain border so as to mimic the effect of infinity for ground wave propagation. This paper presents a full three-dimensional FEA for the prediction of railway ground-borne vibrations. Non-reflecting boundaries are compared to fixed and free boundary conditions, especially concerning their ability to model the soil wave propagation and reflection. Investigations with commercial FEA software ABAQUS are presented also, with the development of an external meshing tool, so as to automatically define the infinite elements at the model boundary. Considering that ground wave propagation is a transient problem, the problem is formulated in the time domain. The influence of the domain dimension and of the element size is analysed and rules are established to optimise accuracy and computational burden. As an example, the structural response of a building is simulated, considering homogeneous or layered soil, during the passage of a tram at constant speed.     

Solving Wick-stochastic water waves using a Galerkin finite element method

A Galerkin finite element approximation of Wick-stochastic water waves is developed and numerically investigated. The problems under study consist of a class of shallow water equations driven by white noise. Random effects may appear in the water free surface or in the bottom topography among others. To perform a rigorous study of stochastic effects in the shallow water equations we employ techniques from Wick calculus. The differentiation respect to time and space along with the product operations are performed in a distribution sense. Using the Wiener-Itô chaos expansion for treating the randomness, the governing equations are transformed into a sequence of deterministic shallow water equations to be solved for each chaos coefficient by standard methods from computational fluid dynamics. In our study, we formulate a finite element method for spatial discretization and a backward Euler scheme for time integration. Once the chaos coefficients are obtained, statistical moments for the stochastic solution are carried out. Numerical results are presented for stochastic water waves in the Strait of Gibraltar.     

The elastic problem for fractal media: basic theory and finite element formulation

In a previous paper [Comput. Methods Appl. Mech. Eng. 190 (2001) 6053], the framework for the mechanics of solids, deformable over fractal subsets, was outlined. Anomalous mechanical quantities with fractal dimensions were introduced, i.e., the fractal stress [σ∗], the fractal strain [ε∗] and the fractal work of deformation W∗. By means of the local fractional operators, the static and kinematic equations were obtained, and the Principle of Virtual Work for fractal media was demonstrated. In this paper, the constitutive equations of fractal elasticity are put forward. From the definition of the fractal elastic potential φ∗, the linear elastic constitutive relation is derived. The physical dimensions of the second derivatives of the elastic potential depend on the fractal dimensions of both stress and strain. Thereby, the elastic constants undergo positive or negative scaling, depending on the topological character of deformation patterns and stress flux. The direct formulation of elastic equilibrium is derived in terms of the fractional Lamé operators and of the equivalence equations at the boundary. The variational form of the elastic problem is also obtained, through minimization of the total potential energy. Finally, discretization of the fractal medium is proposed, in the spirit of the Ritz-Galerkin approach, and a finite element formulation is obtained by means of devil’s staircase interpolating splines.     

On numerical stabilization in the solution of Saint-Venant equations using the finite element method

Solving the Saint-Venant equations by using numerical schemes like finite difference and finite element methods leads to some unwanted oscillations in the water surface elevation. The reason for these oscillations lies in the method used for the approximation of the nonlinear terms. One of the ways of smoothing these oscillations is by adding artificial viscosity into the scheme. In this paper, by using a suitable discretization, we first solve the one-dimensional Saint-Venant equations by a finite element method and eliminate the unwanted oscillations without using an artificial viscosity. Second, our main discussion is concentrated on numerical stabilization of the solution in detail. In fact, we first convert the systems resulting from the discretization to systems relating to just water surface elevation. Then, by using M-matrix properties, the stability of the solution is shown. Finally, two numerical examples of critical and subcritical flows are given to support our results.     

Feature based object decomposition for finite element meshing

Performing a finite element analysis requires overlaying an object with a mesh of varying density based on the expected stress levels within the part. Attempts have been made in the past to automat the finite element meshing procedure. The method presented here is intelligent in the sense that it examines the complete part for potential stress gradients and decomposes the part into hexahedral regions according to the geometry gradients in the part. High geometry gradients are regions of high curvature, especially edges. The algorithm segregates high gradient features into isolation volumes. It then continues to decompose each isolation volume dependent on the particular geometry contained in the feature. The result is a set of hexahedral bricks suitable for passing to an automatic meshing routine.     

Three dimensional thermal finite element simulation of electro-discharge diamond surface grinding

The key to achieve good surface integrity in the workpiece due to Electro-Discharge Diamond Grinding (EDDG) process, which is hybrid of grinding and EDM, is by preventing the excessive temperature and thermal stress generated during the process. EDDG in surface grinding mode called Electro-Discharge Diamond Surface Grinding (EDDSG), used for finishing operation, is a complex machining process where several disciplines of science and engineering are involved in its theory. The complexity of the process includes the random occurrence of spark during EDM process and nonlinear behavior of workpiece material includes temperature dependent thermal properties. The present work involves the development of a simulation model to simulate the complex EDDSG process which consists of simulation of each constituent process namely EDM and surface grinding for temperature and thermal stress distribution. In order to simulate the realistic complex conditions, the three dimensional FEM is used in the process of development of the model accounting the random occurrence of the spark during EDM. The effect of different dielectric fluid, duty factor and energy partition during EDM on the temperature distribution and MRR study related to EDM contribution are reported. It is observed that the spark contributes primarily to the temperature. The predicted results can be used to determine the surface integrity of the machined surface.