VEMLab: a MATLAB library for the virtual element method
Release of VEMLab v2.2.1
>> From VEMLab v2.2 to VEMLab v2.2.1:
- Add option to explicitly switch off all MATLAB figures in function "plot_and_output_options.m".
- Facilitate compatibility to run VEMLab in Octave.
- Update manual with a guide to running VEMLab in Octave.
VEMLab: a MATLAB library for the virtual element method
Release of VEMLab v2.2
>> From VEMLab v2.1 to VEMLab v2.2:
- Fix disp() in plot_and_ouput_options.m: disp(“Hello”) seems to work only in newer versions of MATLAB. So, it is changed to the standard MATLAB format disp(‘Hello’).
- Results that are postprocessed in the graphical user interface of GiD are now ordered in folders.
- Add option to plot deformed domain in MATLAB figures when using the LinearElastostatics module (see function “plot_and_ouput_options.m” located in the folder “config”).
- Add a function to read a meshfile having the domain type declared as “Custom”, which is useful for defining the meshfile manually or using an external mesh generator or using a customized version of the mesh generators available in VEMLab. (See example “Creating and using a custom meshfile” in the VEMLab Primer or details.)
- Add more details to the VEMLab Primer.
VEMLab: a MATLAB library for the virtual element method
Release of VEMLab v2.1
>> From VEMLab v2.0.2 to VEMLab v2.1:
- Add customized wrench domain (for PolyMesher mesh generator only).
- Add customized plate with a hole domain (for PolyMesher mesh generator only).
- Add the following test: “square_plate_with_source2_poisson2d.m” in test folder.
- Add the following test: “plate_with_hole_linelast2d.m” in test folder.
- Add the following test: “wrench_linelast2d.m” in test folder.Fix iteration counter in PolyMesher function.
- Fix iteration counter in PolyMesher function.
http://camlab.cl/research/software/vemlab/
Free and open source MATLAB library for the virtual element method.
- Two-dimensional linear elastostatics (plane strain and plane stress).
- Solution methods: VEM (polygonal elements), FEM (3-node triangles, 4-node quadrilaterals).
- Boundary conditions: Dirichlet, Neumann on boundary edges; can be a constant or a function.
- Meshers: PolyMesher, distmesh2d, quad4mesh; customized for rectangular domains only (requires adjustments for other domain types).
- Meshes need to be generated separately and stored inside folder ‘mesh_files’ located in the folder ‘test.’
- Meshes must be generated with the functions ‘create_’ located in the folder ‘mesher.’
- Solutions can be plotted to MATLAB figures, text files and GiD files.
Click here to get and browse the source code
This paper summarizes the development of an object-oriented C++ library for the virtual element method (VEM) named Veamy, whose modular design is focused on its extensibility. The two-dimensional linear elastostatic problem has been chosen as the starting stage for the development of this library. In contrast to the standard finite element method, the VEM in two dimensions uses polygonal finite element meshes. The theory of the VEM in which Veamy is based upon is presented using a notation and a terminology that is commonly found in the finite element literature, thereby allowing potential users that are familiar with finite elements to understand and implement the virtual element method under the object-oriented paradigm. A complete sample usage of Veamy is provided for a cantilever beam subjected to a parabolic end load. A displacement patch test is also solved using Veamy. A third example features the interaction between Veamy and the polygonal mesh generator PolyMesher. Step-by-step guidelines for the implementation of a problem that is currently not available in Veamy (the two-dimensional Poisson problem) are also provided. The source code is made freely available so that interested users can make free use of it, and possibly, extend Veamy to a wider class of problems.
Veamy: an extensible object-oriented C++ library for the virtual element method.
Available from: https://www.researchgate.net/publication/319057392_Veamy_an_extensible_object-oriented_C_library_for_the_virtual_element_method
Click here to get and browse the source code
-A.
Paper Accepted for Publication in International Journal for Numerical Methods in Engineering
Consistent and stable meshfree Galerkin methods using the virtual element decomposition
A. Ortiz-Bernardin, A. Russo, N. Sukumar
Abstract
Over the past two decades, meshfree methods have undergone significant development as a numerical tool to solve partial differential equations (PDEs). In contrast to finite elements, the basis functions in meshfree methods are smooth (nonpolynomial functions), and they do not rely on an underlying mesh structure for their construction. These features render meshfree methods to be particularly appealing for higher-order PDEs and for large deformation simulations of solid continua. However, a deficiency that still persists in meshfree Galerkin methods is the inaccuracies in numerical integration, which affects the consistency and stability of the method. Several previous contributions have tackled the issue of integration errors with an eye on consistency, but without explicitly ensuring stability. In this paper, we draw on the recently proposed virtual element method, to present a formulation that guarantees both the consistency and stability of the approximate bilinear form. We adopt maximum-entropy meshfree basis functions, but other meshfree basis functions can also be used within this framework. Numerical results for several two- and three-dimensional elliptic (Poisson and linear elastostatic) boundary-value problems that demonstrate the effectiveness of the proposed formulation are presented.
Keywords: meshfree Galerkin methods, maximum-entropy approximants, numerical integration, virtual element method, patch test, stability.
http://hdl.handle.net/10993/17316
We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element method (VEM). Based on the VEM, we propose a new stabilization approach to the SFEM when applied to arbitrary polygons and polyhedrons. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Later, the SFEMis combined with the scaled boundary finite element method to problems involving singularity within the framework of the linear elastic fracture mechanics in 2D.
http://hdl.handle.net/10993/17993
We present a promising approach to reduce the difficulties associated with meshing complex curved domain boundaries for higher-order finite elements. In this work, higher-order XFEM analyses for strong discontinuity in the case of linear elasticity problems are presented. Curved implicit boundaries are approximated inside an unstructured coarse mesh by using parametric information extracted from the parametric representation (the most common in Computer Aided Design CAD). This approximation provides local graded sub-mesh (GSM) inside boundary elements (i.e. an element split by the curved boundary) which will be used for integration purpose. Sample geometries and numerical experiments illustrate the accuracy and robustness of the proposed approach.