WordPress Shortcode. Next SlideShares. Download Now Download to read offline and view in fullscreen. Download Now Download Download to read offline. Engineering Technique Follow. Design Efficiency Improvement Through Collaboration. Related Books Free with a 30 day trial from Scribd. Related Audiobooks Free with a 30 day trial from Scribd. Elizabeth Howell. Views Total views. Actions Shares. No notes for slide. The basic idea of FEA is to make calculations at only limited Finite number of points and then interpolate the results for the entire domain surface or volume.
Finite Element Method reduces the degrees of freedom from infinite to finite with the help of discretization or meshing nodes and elements. You need these elements to be able to apply Finite Element since Finite Element is all about having a basis local to an Element and stitching a bunch of local solutions together to build the global one.
If you did not mesh and just assumed some basis that covered the whole domain that would be a Spectral Method. One other aspect of meshing is the accuracy of your solution. Due to these contributors to accuracy, it's important to be careful about how you implement your mesh to ensure angles within elements are larger smaller angles hurts accuracy and that you get it sufficiently refined to get the accuracy you wish. Solid Mesh 3D Element : The program creates a solid mesh with tetrahedral 3D solid elements for all solid components.
Tetrahedral elements are suitable for bulky objects. Figure 1 shows the model with solid mesh. Shell Mesh 2D Element : The program automatically creates a shell mesh for sheet- metals with uniform thicknesses except drop test study and surface geometries.
For sheet metals, the mesh is automatically created at the mid-surface. The trade-off is that the higher the accuracy, the larger the simulations become and thus solve times are extended. There is no point in spending extra hours running a simulation with a dense mesh if a coarser mesh will give you the results you need! Engineers often perform convergence studies to obtain the optimal balance between accuracy and solve time.
It is not just mesh size that matters. Another important meshing consideration is element type. Elements can be 1D, 2D, or 3D with varying aspect ratios. The list below identifies the element type and its use:. For structures that have a dimension e. For constraining parts of the structure Membrane Element For thin fabric-like surfaces Truss Element. For modeling line-like structures that support loading along the axis of the element Connector Element For applying a behavior between two nodes, e.
For unbounded domains. Meshing in OnScale is not automatic: OnScale gives users full control over the mesh, and a mesh must be created before allocating materials. Generally, this is very straightforward as most geometries can be very well represented by a fine structured mesh.
The element size, which we typically refer to as box, is one of the key components to obtaining accurate results. In order to determine the size of box , the smallest wavelength must be calculated by dividing the lowest wave velocity typically a shear wave velocity in the model by the highest frequency of interest?
It can have almost any shape in any size and is used to solve Partial Differential Equations. Each cell of the mesh represents an individual solution of the equation which, when combined for the whole network, results in a solution for the entire mesh.
Solving the entire object without dividing it into smaller pieces can be impossible because of the complexity that is within the object. Holes, corners and angles can make it extremely difficult for solvers to obtain a solution.
Small cells, on the other hand, are comparably easy to solve and therefore the preferred strategy. The history of the mesh and meshing techniques is closely related to the history of numerical methods.
Historically, rectangular and Cartesian grids are associated with the Finite Differences since it depends on the adjacent cells and nodes to approximate the behavior of the variables. The first step for numerically solving a set of partial differential equations PDEs is the discretization of the equations and the discretization of the problem domain. As mentioned earlier, solving the entire problem domain at once is impossible whereas solving multiple small pieces of the problem domain is perfectly fine.
The equations discretization process is related to methods such as the Finite Difference Method, Finite Volume Method FVM and Finite Element Method, whose purpose is to take equations in the continuous form and generate a system of algebraic difference equations. The domain discretization process generates a set of discrete cells and therefore points or nodes that cover the continuous problem domain.
A mesh is, by definition, a set of points and cells, when connected to form a network. This network can have many forms of geometry and topology, as will be discussed later. Each cell or node of the mesh will hold a local solution of the equations, depending on whether the equations were discretized over the cells or nodes. The choice of discretization is a project decision. Sometimes the point discretization can be used together with the Finite Volume Method, however, cells are going to be implicitly used around points.
When the equations to be discretized are considered in the weak form, integral form, or conservative form, it is common to solve the integrals over discrete cells. For example, when considering transport phenomena, the Finite Volume Method can be formulated as discrete cells representing small volumes.
Then, the fluxes can be balanced through those cells, while supposing that the solution is constant inside them. As discussed before, structured meshes are historically related to the Finite Differences Method. The Finite Volume and Finite Element methods allow for more general meshes. Structured meshes, also commonly called grids, are meshes whose structure and formation allow for easy identification of neighboring cells and points.
This property is derived from the fact that structured meshes are applied over analytical coordinate systems rectangular, elliptical, spherical, etc. From a programming point of view, the cells or points that form a structured mesh can be enumerated in such a way that neighboring queries can be made analytically upon the cells or points coordinates. Consider the mesh from the picture below. Its first cells are enumerated, along with the first four left and right boundary cells. This mesh is an example of a rectangular mesh.
Similarly, the top adjacency from any cell is obtained by summing nine to the cell enumeration. This allows for each mesh element to be mapped directly to an array or vector, making computations easier.
Any curvilinear grid can be mapped to such a coordinate and neighboring system. Therefore, from a programming standpoint, there is little to no difference between a curvilinear grid and a rectangular grid in terms of adjacency queries.
Structured grids might also be defined in terms of boundary fitting. For example, a cartesian grid fits the boundary of a rectangle, and the cylindrical grid fits the boundary of a cylinder. The meshing algorithm will decide how points will be distributed through those surfaces, and how opposing surfaces will be connected to each other, given how many points should be created for each curve or surface.
Unstructured meshes are more general and can arbitrarily approximate any geometry shape. In contrast with structured meshes, where the coordinates and connectivities map into the elements of a matrix, unstructured meshes require special data structures, such as an adjacency matrix or list and the node coordinates list.
Complex geometries that would be impractical to generate a structured mesh within, can be discretized using unstructured meshing techniques.
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