The present paper describes a Fortran library FLIPP constituting arun‐time environment that is linked to scientific applications software(such as finite‐element analysis programs…
Abstract
The present paper describes a Fortran library FLIPP constituting a run‐time environment that is linked to scientific applications software (such as finite‐element analysis programs) to support programming of interactive program control and use of persistent user‐defined dynamic data structures. The system consists of control and data definition and manipulation subsystems. The FLIPP routines are fully‐portable standard Fortran 77 procedures and the use of FLIPP leads the programmer to information hiding, e.g. as in object‐oriented systems. Program design and maintenance are facilitated to a considerable degree, while at the same time the performance of the programs using the FLIPP system remains fairly good as demonstrated by the examples.
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This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics…
Abstract
This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.
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Peter Wriggers and Wilhelm T. Rust
This paper aims to describe the application of the virtual element method (VEM) to contact problems between elastic bodies.
Abstract
Purpose
This paper aims to describe the application of the virtual element method (VEM) to contact problems between elastic bodies.
Design/methodology/approach
Polygonal elements with arbitrary shape allow a stable node-to-node contact enforcement. By adaptively adjusting the polygonal mesh, this methodology is extended to problems undergoing large frictional sliding.
Findings
The virtual element is well suited for large deformation contact problems. The issue of element stability for this specific application is discussed, and the capability of the method is demonstrated by means of numerical examples.
Originality/value
This work is completely new as this is the first time, as per the authors’ knowledge, the VEM is applied to large deformation contact.
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The aim of this paper is to extend the Element Free Galerkin method (EFGM) in order to perform the elasto‐plastic analysis of isotropic plates.
Abstract
Purpose
The aim of this paper is to extend the Element Free Galerkin method (EFGM) in order to perform the elasto‐plastic analysis of isotropic plates.
Design/methodology/approach
The EFGM shape‐function construction is briefly presented. The Newton‐Raphson method and the elasto‐plastic algorithm adapted to the EFGM, are described. Several plate bending non‐linear material problems are solved and the obtained solutions are compared with available finite element method (FEM) solutions.
Findings
The paper finds that the developed EFGM approach is a good alternative to the FEM for the solution of non‐linear problems, once the obtained results with the EFGM show a high similarity with the obtained FEM results.
Research limitations/implications
Comparing the FEM and the EFGM there are some drawbacks for the EFGM. The computational cost of the EFGM is higher, the imposition of the essential boundary conditions is more complex and there is a high sensitivity of the method in what concerns the choice of the influence domain and the choice of the weight function.
Practical implications
The knowledge that the EFGM formulation can be treated almost as the FEM formulation once the EFGM parameters are calibrated and optimized.
Originality/value
The extension of the EFGM to the elasto‐plastic analysis of isotropic plates.
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Wenan Wu and Hong Zheng
This study aims to introduce the hybrid finite element (FE) – meshfree method and multiscale variational principle into the traditional mixed FE formulation, leading to a stable…
Abstract
Purpose
This study aims to introduce the hybrid finite element (FE) – meshfree method and multiscale variational principle into the traditional mixed FE formulation, leading to a stable mixed formulation for incompressible linear elasticity which circumvents the need to satisfy inf-sup condition.
Design/methodology/approach
Using the hybrid FE–meshfree method, the displacement and pressure are interpolated conveniently with the same order so that a continuous pressure field can be obtained with low-order elements. The multiscale variational principle is then introduced into the Galerkin form to obtain stable and convergent results.
Findings
The present method is capable of overcoming volume locking and does not exhibit unphysical oscillations near the incompressible limit. Moreover, there are no extra unknowns introduced in the present method because the fine-scale unknowns are eliminated using the static condensation technique, and there is no need to evaluate any user-defined stability parameter as the classical stabilization methods do. The shape functions constructed in the present model possess continuous derivatives at nodes, which gives a continuous and more precise stress field with no need of an additional smooth process. The shape functions in the present model also possess the Kronecker delta property, so that it is convenient to impose essential boundary conditions.
Originality/value
The proposed model can be implemented easily. Its convergence rates and accuracy in displacement, energy and pressure are even comparable to those of second-order mixed elements.
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A 3D surface mesh generation scheme is suggested for the triangulation of general bi‐variate surfaces. The target surface to be meshed is represented as a union of bi‐variate…
Abstract
A 3D surface mesh generation scheme is suggested for the triangulation of general bi‐variate surfaces. The target surface to be meshed is represented as a union of bi‐variate sub‐surfaces and hence a wide range of surfaces can be modelled. Different useful features such as repeated curves, crack lines and surface branches are included in the geometrical and topological models to increase the flexibility of the mesh generation scheme. The surface metric tensor specification is employed to define and control the element characteristics in the mesh generation procedure. A robust metric triangulation kernel is used for parametric space mesh generation. The shape qualities of the sub‐surface meshes generated are then improved by using some ad hoc mesh quality enhancement schemes before they are combined together to form the final mesh. Numerical examples indicate that high quality surface meshes with rapid varying element size and stretching characteristics can be generated within a reasonable time limit in a few mesh adaptive iterations.
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Gleber Nelson Marques, José Márcio Machado, Sérgio Luis Lopes Verardi, Stephan Stephany and Airam Jonatas Preto
This paper proposes an interpolating approach of the element‐free Galerkin method (EFGM) coupled with a modified truncation scheme for solving Poisson's boundary value problems in…
Abstract
Purpose
This paper proposes an interpolating approach of the element‐free Galerkin method (EFGM) coupled with a modified truncation scheme for solving Poisson's boundary value problems in domains involving material non‐homogeneities. The suitability and efficiency of the proposed implementation are evaluated for a given set of test cases of electrostatic field in domains involving different material interfaces.
Design/methodology/approach
The authors combined an interpolating approximation with a modified domain truncation scheme, which avoids additional techniques for enforcing the Dirichlet boundary conditions and for dealing with material interfaces usually employed in meshfree formulations.
Findings
The local electric potential and field distributions were correctly described as well as the global quantities like the total potency and resistance. Since, the treatment of the material interfaces becomes practically the same for both the finite element method (FEM) and the proposed EFGM, FEM‐oriented programs can, thus, be easily extended to provide EFGM approximations.
Research limitations/implications
The robustness of the proposed formulation became evident from the error analyses of the local and global variables, including in the case of high‐material discontinuity.
Practical implications
The proposed approach has shown to be as robust as linear FEM. Thus, it becomes an attractive alternative, also because it avoids the use of additional techniques to deal with boundary/interface conditions commonly employed in meshfree formulations.
Originality/value
This paper reintroduces the domain truncation in the EFGM context, but by using a set of interpolating shape functions the authors avoided the use of Lagrange multipliers as well as of a penalty strategy. The resulting formulation provided accurate results including in the case of high‐material discontinuity.
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Suvranu De and Klaus‐Jürgen Bathe
Computational efficiency and reliability are clearly the most important requirements for the success of a meshless numerical technique. While the basic ideas of meshless…
Abstract
Computational efficiency and reliability are clearly the most important requirements for the success of a meshless numerical technique. While the basic ideas of meshless techniques are simple and well understood, an effective meshless method is very difficult to develop. The efficiency depends on the proper choice of the interpolation scheme, numerical integration procedures and techniques of imposing the boundary conditions. These issues in the context of the method of finite spheres are discussed.
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Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the…
Abstract
Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.
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S. D'Heedene, K. Amaratunga and J. Castrillón‐Candás
This paper presents a novel framework for solving elliptic partial differential equations (PDEs) over irregularly spaced meshes on bounded domains.
Abstract
Purpose
This paper presents a novel framework for solving elliptic partial differential equations (PDEs) over irregularly spaced meshes on bounded domains.
Design/methodology/approach
Second‐generation wavelet construction gives rise to a powerful generalization of the traditional hierarchical basis (HB) finite element method (FEM). A framework based on piecewise polynomial Lagrangian multiwavelets is used to generate customized multiresolution bases that have not only HB properties but also additional qualities.
Findings
For the 1D Poisson problem, we propose – for any given order of approximation – a compact closed‐form wavelet basis that block‐diagonalizes the stiffness matrix. With this wavelet choice, all coupling between the coarse scale and detail scales in the matrix is eliminated. In contrast, traditional higher‐order (n>1) HB do not exhibit this property. We also achieve full scale‐decoupling for the 2D Poisson problem on an irregular mesh. No traditional HB has this quality in 2D.
Research limitations/implications
Similar techniques may be applied to scale‐decouple the multiresolution finite element (FE) matrices associated with more general elliptic PDEs.
Practical implications
By decoupling scales in the FE matrix, the wavelet formulation lends itself particularly well to adaptive refinement schemes.
Originality/value
The paper explains second‐generation wavelet construction in a Lagrangian FE context. For 1D higher‐order and 2D first‐order bases, we propose a particular choice of wavelet, customized to the Poisson problem. The approach generalizes to other elliptic PDE problems.