A simplified finite element solution for the plates on elastic foundation

The simplified Finite Element Method is used to analyze plates supported on an elastic continuum. The method assembles the stiffness matrix of the foundation into a banded, diagonal matrix and, therefore, can be solved by using the tridiagonal technique. This process reduces the computer storage dramatically. Various problems of plates on elastic continua have been solved and the results are compared with those obtained using the conventional Finite Element Methods. Good agreements are obtained.     

The role of a connectivity matrix in the assemblage process of the finite element method

Following the Finite Element Method and Procedures, by introducing a connectivity matrix, the assembling process is achieved in a general and standard way for any system with one- and two-dimensional linear elements. This allows us to set an algorithm and to program it to get the total stiffness matrix of the system. A plane truss and a heat transfer problem are presented as examples to show several properties inherent to the connectivity matrix.     

Ill-conditioned stars in the finite difference method for arbitrary meshes

The optimisation and ill-conditioning of stars in the Finite Difference Method for arbitrary irregular meshes is discussed. The criteria used to compare two stars is the condition number of the star matrix associated to the Taylor series expansion. Results are presented for stars with 13 grid nodes used in biharmonic problems, for which nodal arrangements are studied in order to avoid singularity of the star matrix and minimise the condition number.     

基于全电极模式的三维电阻抗成像有限元法的算法实现

三维电阻抗成像(3D-EIT)技术是当今生物医学工程领域一项全新的研究课题,其中有限元法在EIT中的实现是EIT成像的基础。本文把有限元法用于3D-EIT中,利用全电极模式(CEM)详细推导了单元矩阵和总体矩阵,建立了相应的三维EIT有限元网格模型,并在计算机上运用Matlab7.0软件得以全部实现。     

The Finite Patch Method: a nodal equation method based on FEM

The recently developed (Finite) Patch Method is introduced. In these equations for a patch of finite elements are rearranged to obtain a patch matrix E. This provides equations for corner, edge and interior nodes of a domain, which are then solved by relaxation. The method is similar to the classical FDM except that FEM is used to form equations and thus equations for boundary nodes are automatically included. The method is applied to potential and plane stress problems and problems including line elements and irregular boundaries.     

Iterative solution of systems of linear equations arising in the context of stochastic finite elements

The particular properties of systems of linear equations arising in the context of the Stochastic Finite Element Method (SFEM) motivate the customization of existing iterative solution algorithms. The implementation described in this paper has aimed at optimizing data management, MAT-VEC operations and preconditioning strategies. It turns out that SFEM-systems can be solved with much less effort than their size suggests. The main idea is based on the fact that the full system matrix consists of few, relatively small submatrices with identical dimensions and sparsity pattern. This makes it very efficient to perform matrix–vector multiplications at the submatrix level and to avoid the assembly of the full coefficient matrix.     

An active areas bandsolver for the resolution of moderately large systems of equations

A complete package of programs for the resolution of systems of linear equations deriving from the Finite Element Method (with the use of auxiliary direct access device), is presented and discussed. The active areas technique, used during Gaussian elimination, allows total elimination of not meaningful operations. Furthermore, considering that most of solving time is normally spent in transferring data to/from auxiliary memories, special care has been devoted to this aspect during assembling equations, imposing prescribed displacements and reducing the assembled matrix.     

应变式多维力传感器结构优化设计方法研究

多维力传感器的结构决定了其精度及静、动态性能指标,对应变式多维力传感器弹性体结构耦合误差传递的原因进行了探讨,对比分析了传感器特性矩阵的目标优化函数的选择与优化方法、有限元法以及正交设计与极差分析法在传感器结构优化设计中的运用,提出了综合优化设计的思想,结合实例分析并阐述了该方法的实用性和有效性.     

The finite cell method for nearly incompressible finite strain plasticity problems with complex geometries

In this paper, the performance of the Finite Cell Method is studied for nearly incompressible finite strain plasticity problems. The Finite Cell Method is a combination of the fictitious domain approach with the high-order Finite Element Method. It provides easy mesh generation capabilities for highly complex geometries; moreover, this method offers high convergence rates, the possibility to overcome locking and robustness against high mesh distortions. The performance of this method is numerically investigated based on computations of benchmark and applied problems. The results are also verified with the $h$- and $p$-version Finite Element Method. It is demonstrated that the Finite Cell Method is an appropriate simulation tool for large plastic deformations of structures with complex geometries and microstructured materials, such as porous and cellular metals that are made up of ductile materials obeying nearly incompressible $J_2$ theory of plasticity.     

Mathematical conditions for and physical meaning of a maximum of the determinant of K∼T in the prebuckling regime

It is shown that the determinant of the tangent stiffness matrix has a maximum in the prebuckling regime if and only if the determinant of a specific linear combination of the first and the third derivative of this matrix with respect to a dimensionless load factor vanishes. The mathematical tool for this proof is the so-called consistently linearized eigenproblem in the frame of the Finite Element Method. The physical meaning of the mentioned maximum is the one of a minimum of the percentage bending energy of the total strain energy. The paper provides mathematical and physical background knowledge on numerical results that were obtained 35 years ago.     

An object-oriented approach to the Generalized Finite Element Method

The Generalized Finite Element Method (GFEM) is a meshbased approach that can be considered as one instance of the Partition of Unity Method (PUM). The partition of unity is provided by conventional interpolations used in the Finite Element Method (FEM) which are extrinsically enriched by other functions specially chosen for the analyzed problem. The similarities and differences between GFEM and FEM are pointed out here to expand a FEM computational environment. Such environment is an object-oriented system that allows linear and non-linear, static and dynamic structural analysis and has an extense finite element library. The aiming is to enclose the GFEM formulation with a minimum impact in the code structure and meet requirements for extensibility and robustness. The implementation proposed here make it possible to combine different kinds of elements and analysis models with the GFEM enrichment strategies. Numerical examples, for linear analysis, are presented in order to demonstrate the code expansion and to illustrate some of the above mentioned combinations.     

High-Order Numerical Methods for 2D Parabolic Problems in Single and Composite Domains

In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at interfaces, considering (i) the Cut Finite Element Method; (ii) the Difference Potentials Method; and (iii) the summation-by-parts Finite Difference Method. First we give a brief introduction for each of the three methods. Next, we propose benchmark problems, and consider numerical tests—with respect to accuracy and convergence—for linear parabolic problems on a single domain, and continue with similar tests for linear parabolic problems on a composite domain (with the interface defined either explicitly or implicitly). Lastly, a comparative discussion of the methods and numerical results will be given.     

过程驱动法实现协议栈软件有限状态机的分析

文章主要分析实现有限状态机(FSM)的方法:“过程驱动法”。有限状态机的抽象构建及实现是网络通信协议栈软件设计的基本方法。以GPRS协议移动台侧的子网相关汇聚协议层(SNDCP)为例,分析了用过程驱动法实现的程序复杂度、运行效率。文章最后提出用过程驱动法实现的主要数据结构。     

Surface Representation with Closest Point Projection in the X-FEM

Mathematical Models and Computer Simulations - At present, the eXtended Finite Element Method (X-FEM) is a common generalization of the classical finite element method for solving problems of...     

Development of an RVE using a DEM–FEM scheme under modified approximate periodic boundary condition to estimate the elastic mechanical properties of open foams

Engineering with Computers - In this article, a methodology based on Discrete Element Method (DEM) and Finite Elements Method (FEM) combined with modified Approximate Periodic Boundary Condition...     

基于ANSYS的铝电解槽电场数值仿真研究

铝电解槽的电场作为形成各物理场的基础,其分布好坏直接影响电解槽的生产。采用基于ANSYS的仿真分析方法研究了铝电解槽的电场分布。采用有限元法,建立了铝电解槽电场的数学模型,并利用有限元仿真分析软件ANSYS建立电解槽三维电场有限元模型,计算了铝电解槽各导电部分的电场分布,总结了分布规律,为电解槽多物理场优化提供基础。其仿真结果与实测结果相吻合,验证了方法的正确性。     

Linear buckling analysis of thin-walled members combining the Generalised Beam Theory and the Finite Element Method

A finite element procedure to carry out linear buckling analysis of thin-walled members is developed on the basis of the existing Generalised Beam Theory (GBT) and constrained Finite Strip Method (cFSM). It allows designers to uncouple the buckling modes of a finite element model and, consequently, to calculate pure elastic buckling loads. The procedure can easily be applied to members with general boundary conditions subjected to compression or bending. The results obtained are rather accurate when compared to the values calculated via GBT and cFSM. As a consequence, it is demonstrated that linear buckling analyses can be performed with the Finite Element Method in a similar way as can be done with the existing GBT and cFSM procedures.     

An enriched finite element method for efficient solutions of transient heat diffusion problems with multiple heat sources

Engineering with Computers - We propose an efficient formulation using the framework of Generalized Finite Element Method (GFEM) for the solutions of transient heat diffusion problems having...     

A combined DEM–FEM numerical method for Shot Peening parameter optimisation

A numerical modelling approach capable of simulating Shot Peening (SP) processes of industrial interest was developed by combining the Discrete Element Method (DEM) with the Finite Element Method (FEM).In this approach, shot–shot and shot–target interactions as well as the overall shot flow were simulated efficiently using rigid body dynamics. A new algorithm to dynamically adapt the coefficient of restitution (CoR) for repeated impacts of shots on the same spot was implemented in the DEM code to take into account the effect of material hardening. Then, a parametric study was conducted using the Finite Element Method (FEM) to investigate the influence of the SP parameters on the development of residual stresses.Finally, a two-step coupling method is presented to combine the output of DEM simulation with FEM analyses to retrieve the Compressive Residual Stresses (CRS) after multiple impacts with the aim to evaluate the minimum area required to be modelled to realistically capture the field of residual stresses. A series of such coupled analyses were performed to determine the effect of peening angle and the combination of initial velocity and mass flow rate on CRS.     

Finite elements using long vectors of the DAP

The Finite Element Method for solving partial differential equations using the long vector mode of the DAP is presented. This work was developed on a 32 × 32 version of the DAP attached to a Perq scientific workstation.

First, the implementation of finite elements using the long vector mode of the DAP is given, followed by the treatment of boundary conditions and the solution of the finite element equations using a parallel conjugate gradient method. Two solution procedures for the parallel conjugate gradient method, first without global matrix assembly and second with global matrix assembly, are presented and their advantages and disadvantages are discussed. Preconditioners for the conjugate gradient method based on iteration methods are also discussed and results include a 1-step point Jacobi preconditioner, a m-step point Jacobi preconditioner and a m-step multi-colour preconditioner. Finally long vector implementations for a larger system which stores multinodes per processor using a sliced mapping technique and domain decomposition are included.