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Meshing
Phase2 incorporates a state-of-the-art 2 dimensional automatic finite element mesh generator, which can generate meshes based on either triangular or quadrilateral finite elements. The advanced meshing algorithm used in Phase2 enormously simplifies the task of mesh generation for the user - a high quality mesh can be generated with just one mouse click!! The mesh can easily be customized if required.
One-click automatic mesh generation
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Mesh: Mesh Setup
The main configuration parameters for the mesh are specified in the Mesh Setup dialog. This allows you to choose the Mesh Type (Graded, Uniform or Radial) and Element Type (3-noded or 6-noded Triangles, or 4-noded or 8-noded Quadrilaterals).
Mesh Setup dialog
Various discretization and gradation parameters can also be specified, including the Advanced Discretization option, which allows the user to customize the discretization of boundaries.
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Mesh: Mesh Type
In the Mesh Setup dialog you can choose one of 3 different mesh types: Graded, Uniform or Radial. Graded meshing is applicable for underground excavations which use Excavation boundaries. Uniform meshing is suitable for models without explicitly defined excavation boundaries (e.g. surface excavations, groundwater models, slope stability models). Radial meshing is a specialized option which can be used for circular or near-circular excavations.
Mesh Type: Graded
Mesh Type: Uniform
Mesh Type: Radial
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Mesh: Element Type
In the Mesh Setup dialog, you may choose one of the following solid element types:
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3-noded triangle
6-noded triangle
4-noded quadrilateral
8-noded quadrilateral
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3-noded triangle, 4-noded quadrilateral
6-noded triangle, 8-noded quadrilateral
In general, elements with mid-side nodes (i.e. 6-noded triangles or 8-noded quadrilaterals) will improve the accuracy of results, however computation times and file sizes will increase accordingly. All mesh customization options are available regardless of which element type you choose.
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Mesh: Customization
In many cases the default mesh generated by Phase2 will not require further input by the user. However, should it be necessary to customize the discretization of the boundaries or the element density at any location, Phase2 provides several methods of mesh customization. This includes:
Custom Discretization allows the user to select any boundary line segments, and specify the number of discretizations per segment, or a multiplication factor.
Custom Discretization dialog
Advanced Discretization is located within the Mesh Setup dialog. This option allows you to select boundaries or regions, and specify the approximate number of nodes or element length on all boundaries in the selected region.
Advanced Discretization option
The Increase Discretization Density option allows you to double the discretization density on boundaries within a selected region. The Increase Element Density option allows you to increase the mesh density within boundaries, without affecting the mesh density on the boundaries.
Increase Element Density option (selecting area to refine mesh)
Mesh is automatically refined in selected area (note: boundary discretization is not changed).
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Mesh: Mapped Meshing
Mapped meshing (also known as "structured meshing"), allows you to create a mesh with a regular pattern of elements. In Phase2, a mapped mesh may be created within triangular (3-sided) or quadrilateral (4-sided) regions of the model, using the Mapped Mesh option. Mapped meshing can use either triangular or quadrilateral finite elements.
A mapped mesh can be generated with one mouse-click, after you have defined the appropriate boundary discretization. In the following example, material boundaries have been used to divide a dam model into quadrilateral and triangular regions, and a mapped mesh of triangular elements has been generated.
Mapped mesh using triangular elements, dam model
Mapped meshing can be used in conjunction with the automatic free meshing to create a mesh with both mapped and free zones.
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Mesh: Boundary Conditions
After the finite element mesh is generated, the default boundary condition is a pinned (i.e. zero displacement) condition for all nodes on the external boundary. Displacement boundary conditions can easily be defined by the user with a few mouse clicks. You may select line segments or individual nodes, and apply Free, Fixed X, Fixed Y or Fixed XY (pinned) conditions, as required.
In the following open pit mine model, vertical rollers (Fixed X) have been applied to the sides, horizontal rollers (Fixed Y) have been applied to the bottom, the ground surface is Free, and the bottom corners have been pinned (Fixed XY).
Boundary conditions for open pit mine model
You may also define a fixed non-zero displacement as a boundary condition with the Set Displacement option.
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Mesh: Infinite Elements
Infinite Elements are an alternative to the use of fixed boundary conditions on the External boundary. They allow the user to solve a problem with a potentially much smaller finite element mesh, and still obtain good results.
In 2-dimensions, infinite elements extend to infinity in one direction, and allow the displacement to decay gradually from the external boundary toward the infinite domain.
Display of Infinite Elements (radial arrows) on External boundary
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Mesh: Mesh Quality
In a finite element mesh, it is generally desirable to avoid elements of high aspect ratio (i.e. long "thin" elements). The presence of such elements can have adverse effects on the analysis results. Such elements can influence analysis results, and lead to misleading and inaccurate results, which are dependent on the mesh. In extreme cases, such elements may even be responsible for non-convergence of the finite element solution, and the analysis will be aborted.
In order to help the user determine the "quality" of a finite element mesh, Phase2 can automatically locate and highlight elements in a mesh which are deemed to be of "poor" quality, according to user-definable criteria.
This is done with the Show Mesh Quality and Define Mesh Quality options.
The Define Mesh Quality dialog allows the user to specify the criteria that define a "poor quality" element
The Show Mesh Quality option will locate and highlight all elements on the model that conform to the criteria of a "poor quality" element, as defined in the Define Mesh Quality dialog. Poor quality elements are filled with a red hatch pattern, and can also be highlighted with an (optional) blue rectangle so they are easier to locate in the mesh.
Show Mesh Quality option highlights poor quality elements
Phase2 can also check that all parts of the mesh are connected to each other, when you select the Contiguous Mesh Check option. This ensures that the mesh consists of a single continuous region of elements at each stage, and that there are no isolated regions or individual elements which are not connected to the rest of the mesh. Multiple mesh regions will cause problems with the analysis and must be avoided.
Invalid mesh (two separate regions of material)
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