Solid Elements

The Solid or 8 node brick element allows you to model structures that are too thick to be modeled by plate elements. Common applications could include dam models, extremely thick pile caps or vibrating equipment with extremely thick support slabs. Essentially, these elements should be used whenever the Mindlin – Reissner assumption of linear strain through the thickness of the element would not be appropriate.

Solid elements may be viewed / edited in a couple of ways, but can only be created by extruding existing plate elements.

Create Solids

Solid Elements are not drawn in RISA-3D. Instead, they must be extruded from a mesh of plate elements. Use the Insert menus or the Drawing Toolbar to create new solids. Once you have created these items, you can use other graphic features to load the model and set boundary conditions.

Creating solid models requires more forethought than either beam or plate elements. To create solids you must first create a plate element mesh, and then extrude that mesh into a series of solid elements. See Plate Modeling Tips and Plate Modeling Examples for tips on building plate element meshes. You can set all the element properties up front or you can modify these properties after you draw them. Modifying Solids is discussed in the next section.

The “Create Solids by Extruding Plates” window (shown below) lets you take any existing plate and extrude it out into a three dimensional object.

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Extrude Solids

To extrude solid elements:

1. If there is not a model view already open, then click the Open 3D Views icon in the ‘View’ ribbon.

2. If you do not already have a plate element mesh, then you must create one.

   See Drawing Plates for more information on this.

3. Click the Solids icon (as shown in the following image).and set the solid properties.

   

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   The Create Solids by Extruding Plates window opens.

   

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   The “Create Solids by Extruding Plates” window lets you take any existing plate and extrude it out into a three dimensional object.

4. Click the Material arrow and choose the solid material you want to extrude.

5. In the Extrusion Options section enter the extruding options:

   • Extrude Axes either globally or locally.

     The X, Y, and Z components of the extruding vector and the thickness of the extrusion vector.

   • The No. of Solid Elements (number solid elements) along the extrusion vector.

6. Choose one of the following options:

   • Extrude all selected plates - Choose this option to extrude an entire selection of plates at once.

     Select the plates in the 3D View panel first, then choose this option.

     All plates currently selected in the 3D View panel will be extruded. If you don’t have any plates selected, ALL plates of the same material in the model are extruded by default.

   • Extrude by clicking plates individually - Choose this option to extrude a single solid at a time or to select just a few plates to extrude.

     Choose this option first, then click on the individual plate(s) you want to extrude.

7. Click OK to extrude the plates.

Modify Solids

You can modify one or more solid elements at once using the Properties panel. The Properties panel lets you modify the properties of solids that already exist in your model. You can modify solids one at a time by selecting a single solid and modifying the properties, or you can modify entire selections of solids by selecting the solids first and then modifying the parameters for the entire set.

To modify solid elements using the Properties panel:

1. Click on one or more solids to view to display the properties in the Properties panel.

   

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2. In the Properties panel, edit the properties you want to modify.

   your changes are immediately applied.

Sub-Meshing Solids

You can submesh solid plate elements into a mesh of smaller elements. This new mesh can be any size up to the program limits for joints and/or solids. This is very useful for refining a coarse mesh of elements; just make sure that all adjacent solid elements (elements sharing an edge) maintain connectivity.

You can define different submesh increments in each direction. 

You can submesh the solids one at a time by selecting the Click to Apply option and then clicking on the solids you wish to submesh.  You may also modify entire selections of solids by selecting the plates and then using the Apply to Selected option.

Submesh Solid Elements

To submesh solid elements:

1. If there is not a model view already open, click the Open 3D Views icon in the View ribbon.
2. Select the Solids you want to sub mesh.

3. Click the Submesh Solids icon in the ‘Modify’ ribbon (as shown below).

   

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   The Solid Submeshing Options window opens.

   

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   This window allows you to define different submesh increments in each direction. 

4. Specify the number of pieces along the side.

5. Click OK to apply your options.

Solids Spreadsheet

The Solids Spreadsheet records the properties for the solid elements of the model and may be accessed by selecting Solids on the Data Entry menu.

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The following data columns hold the ‘Primary’ data for the solids.

Solids Primary Data Columns

Column	Description
Label	Display the unique name of each solid. You can assign a unique label to any or all of the solids. You can then refer to the solid by its label. Each label has to be unique. If you try to enter the same label more than once, you receive an error message. You can relabel solids at any time using the Relabel Allor Relabel Selected icons on the Modify ribbon.
Solid Nodes (A - H)	The A, B, C, D, E, F, G, and H node entries are used to define the 8 corner nodes of the solid element. These nodes are unable to be edited in the spreadsheet, since solids are created by extruding existing plates.
Material	The material label links the solid with the desired material defined on the Materials Spreadsheet.   Note: Solids are always defined with general materials.  This is because the other material sets (Hot Rolled, Cold Formed, Wood, and Concrete) are used to designate member code checking specifications. Since solids are only used for analysis, no code checking is provided and the material must be designated as a general material.
Activation	The Activation data column allows for solids to be set to 'Active', 'Inactive', or 'Excluded'. These choices can be made by selecting them from the drop down list or by entering an 'I' for 'Inactive' or an 'E' for 'Excluded'. If the cell is left blank the plate is 'Active' by default. See Inactive and Excluded Solids for more information.

Solid Information

Just as with the nodes, members, and plates you can click any solid to view it’s properties. All of the same information that is stored in the Solids spreadsheet is displayed for the solid you choose, and may be edited. This is a quick way to view and change solid properties.

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The following table describes the information provided in the Properties panel.

Solid Properties Panel

Property	Description
Material	The material set label links the solid with the desired material defined on the Material spreadsheet.
Solid Label	You must assign a unique label to all of the solids. You can then refer to the solid by its label. Each label has to be unique, so if you try to enter the same label more than once you will get an error message. You can relabel solids at any time by clicking the Relabel All icon on the Modify ribbon and selecting Solids. Click on image to enlarge it
Additional Properties (Corner Nodes)	The A, B, C, D, E, F, G, and H node entries, under the Additional Properties section, are used to define the 8 corner nodes of a hexahedral element.
Activation	Activation The activation state of the element may be changed. If the solid is made inactive, you will need to activate the solid from the solids spreadsheet, or by using the Criteria Select feature to find and select inactive solids. Note: If you have a plate that has a side of a length that is less than the merge tolerance that you specify in the Model Settings under the Solutions tab, then we will not extrude a solid element from that plate. If you come across this as being a problem, then your plates are probably not well meshed and you should think about cleaning up your mesh.

Inactive and Excluded Solids

Making an item such as a member or solid inactive allows you to analyze the structure without the item, without having to delete the information that defines it. This leaves data intact so the item may be easily reactivated. This is handy if you want to try a model with and then without certain items, without having to actually delete the data.

• Choosing "Inactive" makes the item inactive, i.e. the item is not included when the model is solved or plotted.

• Choosing "Exclude" will exclude it from the results list. So, an item set as "Exclude" will be treated like any other solid in the solution and plotting of the model, but the solid will not be listed in the solution results (forces, stresses etc.). This is useful if there are certain items whose results you're not interested in. You don't have to clutter up the results with these items and can concentrate on the items you're most interested in.

See Printing for more limiting printed results.

Solids Formulation

A reference for this element is Finite Element Procedures, by K.J. Bathe, Prentice-Hall, 1996.  Although the book does not complete the element derivations, it does provide many references for papers on the family of elements. In brief, the element formulation is standard 8-node ISO-parametric formulation.

Node Connectivity

The node connectivity in our current solid formulation follows the “left hand rule”. It means if the first 4 nodes are ordered counterclockwise in plane (as shown in the picture below), then node 5 has to be below node 1. However, if the first 4 nodes are ordered clockwise in plane, then N5 would have to be above node 1.

The node connectivity for solid element is listed in the following picture.

If the solid element is generated using the extrusion tool, the nodes will automatically be generated in the proper order. However, when you are modifying the location the nodes, it is important to keep the order the nodes to be consistent with the rules stated above. If not, then the local element matrix will be singular and an error message will be produced at solution time.

Degrees of Freedom

The Solid element activates the THREE translational degrees of freedom at each of its connected nodes. Rotational degrees of freedom are NOT activated. This element contributes stiffness to all of these translational degrees of freedom. If a rotational load or constraint is applied to a node that is only connected to the solid elements, it will be ignored. Modeling these types of rotations would be similar to modeling the "Drilling Degree of Freedom" for plates. Refer to the Modeling Tips section of the general reference manual for more information.

Coordinate System

For the time being, no local coordinate system is defined for the solid element. All the input and output, such as material properties, stresses, displacements are all defined in the global coordinate systems.

Solid Modeling Tips

Number of Elements

The standard ISO-parametric formulation needs at least 4 elements through the thickness in order to accurately simulate a bending dominant part (such as a thin beam or thin plate).

Aspect Ratio of Elements

Solid Elements are more sensitive to element distortion than plate elements. For this reason, it is a good idea to keep a solid elements relatively undistorted. The best formulation for a solid is a cube with equal length sides.

Loading

For the time being, only joint loads and self weight can be applied to the solid elements.

Verification Examples

Open the Solid_Cantilever.r3dfrom the Examples folder in the RISA directory.

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In this example, a straight cantilever beam (modeled with solid elements) is subjected to a unit force at the tip in the three orthogonal direction and the unit moments at the tip about the three orthogonal directions, each in a different load case. The tip displacements are compared with hand calculations as shown below:

The values shown in the table for the RISA output is an average of the 35 nodes at the tip of the cantilever.

Case	Equation	Theory	RISA	% Difference
Axial Extension	Delta = PL/AE	0.060"	0.060"	0
Strong Axis Bending	Delta = PL3/3EI	1.372"	1.361"	0.80
Weak Axis Bending*	Delta = PL3/3EI	4.322"	4.203"	2.75

From this table we can see that solid element deflections are in very good agreement with the theoretical values.