Advanced Techniques for Modeling Curved Structures in Risa

Understanding the Core Principles of Curved Structure Modeling in RISA

Modeling curved structures in RISA is a challenging but essential skill for engineers working on bridges, domes, arches, or any geometry that deviates from straight lines. At its core, RISA-3D and RISAFloor represent curved members through a series of straight, linear elements. This approach, known as a segmented or faceted approximation, requires careful planning to balance accuracy with computational efficiency. The fundamental principle is simple: the more segments you use to represent a curve, the closer the model matches the true geometry, but at the cost of increased solution time and model complexity.

Before implementing advanced techniques, it is critical to understand how RISA internally handles curved geometry. RISA does not natively support continuous curved beam elements; instead, it relies on straight beam elements connected at nodes. For shell and plate elements, curved surfaces are approximated by flat facets. This limitation means that engineers must consciously decide on the level of refinement needed for their specific analysis. For example, a shallow arch under uniform loading may converge adequately with relatively few segments, while a tightly curved beam with significant torsion will demand a finer mesh.

Key considerations when starting a curved model include:

Segment count versus accuracy – doubling the number of segments roughly quadruples the number of nodes and elements, increasing runtime. It is wise to start with a moderate segmentation and refine only where stress gradients are high.
Node placement – ensuring nodes lie exactly on the theoretical curve. RISA allows precise coordinate entry, but for complex curves, importing geometry from a CAD tool is more reliable.
Element aspect ratio – for plate meshes, avoid long, skinny facets with high aspect ratios, as they reduce solution accuracy. Use the built-in mesh quality checks.

With these fundamentals in place, engineers can proceed to master the advanced tools and workflows that RISA offers.

Leveraging RISA's Arc and Curve Creation Tools

RISA provides dedicated tools to streamline the creation of curved geometries, but many users underutilize their full capability. The primary tool is the Arc function, found in the modeling toolbar. This tool allows you to define an arc by specifying its start point, end point, and either a radius or a midpoint. Understanding the nuances of these parameters is essential.

Using the Arc Tool for Beam and Column Centerlines

To create a curved beam or column:

Select the Arc tool from the toolbar (often represented by a curved line icon).
Click to set the start point of the arc.
Click to set the end point. RISA will then ask for the radius or the midpoint. If you choose radius, enter a positive value; negative radius reverses the arc direction.
Once the arc is defined, RISA automatically meshes it into straight segments based on the current Mesh settings in Modeling Options.
Adjust the arc's properties (material, cross-section, release conditions) just like any other member.

A common mistake is forgetting to set a sufficient number of segments before creating the arc. To control segmentation, go to Modeling > Modeling Options > Arc Meshing and set either the number of segments per arc or the maximum segment length. A good starting point for structural steel arches is a segment length of 12 to 24 inches, but this depends on curvature radius and loading complexity.

Converting Arcs to Polylines for Advanced Control

Sometimes the automatic arc meshing does not produce the desired node arrangement, especially when you need to match points from adjacent curved members. In such cases, create the arc, then use the Explode command (right-click on the arc, select Explode) to convert it into individual straight segments. You can then manually reposition nodes or add additional nodes to refine the geometry. This gives you direct control over the nodal coordinates, enabling you to enforce continuity at intersections or to better represent a parabolic or elliptical shape by adjusting individual segment endpoints.

Creating Curved Shells and Plates

For curved surfaces such as cylindrical tanks, domes, or arch bridges, RISA does not have a direct "curved plate" tool. Instead, you must build the surface from multiple flat plates. The most efficient method is to:

Define the curve as a series of points (e.g., using the Point tool or importing coordinates).
Use the Generate Plate Elements command (under Generate > Plates by Contour or Plates by Axis).
Select the points in order to create a sequence of quadrilaterals or triangles that approximate the curve.
Apply Mesh Refinement to subdivide each plate into smaller elements for better stress resolution.

This approach is tedious for complex surfaces, which is why importing from CAD is often preferred. However, for simple curved panels like those in a roof skylight or a curved shear wall, the manual method is fast and gives you full control over mesh density.

Advanced Segmentation Strategies for Accuracy and Convergence

Segmentation is the backbone of curved modeling in RISA. The default settings may work for preliminary analysis, but for final design and code checks, you need to optimize the segment distribution. This goes beyond simply increasing the number of segments; it involves adaptive segmentation based on curvature and loading.

Curvature-Based Segmentation

For a circular arc, the segment length can be uniform. However, for compound curves (e.g., a parabolic arch or a spiral column), the curvature varies along the length. To capture the shape accurately, use a finer segmentation where the curvature is highest. In RISA, you can achieve this by manually subdividing the curve into multiple arcs or by importing a polyline with variable segment lengths from a CAD program. For example, a spiral staircase column might have 20 segments in the tightest turn and only 8 in the gentler portion.

Segment Count Sensitivity Study

A robust engineering practice is to perform a mesh convergence study specific to curved members. Start with a coarse segmentation (e.g., 4 segments for a 90-degree arc) and gradually increase until the maximum bending moment or deflection changes by less than 5% between successive refinements. This ensures that your model is neither over- nor under-refined. Document the chosen segment count in your calculation package to demonstrate due diligence.

Using the "Refine" Feature for Local Mesh Enhancement

RISA's Refine command (available in the Edit menu or right-click context menu) allows you to subdivide a selected member or a group of members into more segments without altering the rest of the model. This is particularly useful when a curved member experiences high local stresses, such as at a support or a concentrated load point. To use:

Select the curved member(s).
Right-click and choose Refine.
Enter the number of equal-length divisions you want to add (e.g., refine each existing segment into 2 or 4 pieces).
The newly created nodes will be placed precisely along the original straight line, so for curved members you must have already defined the arc with enough initial segments to preserve the curvature after refinement.

Alternative approach: instead of using Refine on a straight-segment model, you can create a polyline with more points upfront using the Divide Polyline feature when importing from DXF. This gives you a smoother curvature from the start.

Meshing Techniques for FEA Accuracy on Curved Surfaces

When using shell or plate elements to model curved surfaces, the mesh quality directly impacts the accuracy of stress results, especially near regions of stress concentration (e.g., cutouts, supports, or changes in curvature). Advanced meshing techniques in RISA include using higher-order elements, smoothing algorithms, and coupled analyses.

Choosing the Right Element Type

RISA-3D offers four-node quadrilateral (Q4) and three-node triangular (T3) shell elements. For curved surfaces, Q4 elements are preferred because they are less stiff in shear and bending compared to T3 elements, which are constant-strain triangles and tend to be overly stiff. However, in regions of high curvature or complex geometry, a mix of Q4 and a few T3 elements may be necessary for meshing. Avoid using T3 elements unless forced, and if used, ensure a fine mesh in that area.

RISA does not natively support higher-order (quadratic) elements like 8-node quadrilaterals. To approximate higher-order behavior, you must refine the mesh. A good rule of thumb: use at least four Q4 elements across a curved span to capture flexural stresses adequately.

Mesh Smoothing and Aspect Ratio Control

Irregular mesh shapes cause numerical errors. RISA's Auto Mesh function includes a smoothing algorithm (accessible under Mesh > Auto Mesh > Settings). Enable Laplacian smoothing to reposition interior nodes to produce more equilateral elements. Also, set a target aspect ratio (e.g., 4:1 maximum) – RISA will flag elements exceeding this ratio. Manually adjust nodes in problematic areas or remesh with different seed points.

For imported curved surfaces, it is common to receive faceted meshes from CAD with poor aspect ratios. Use RISA's Remesh Selected Plates command to rebuild the mesh with better quality. You can also use the Split Plate tool to manually divide a large quadrilateral into smaller ones, ensuring the new edges follow the curvature.

For a curved shell like a dome or arch bridge deck, stress gradients are typically highest at the supports and at the crown. Use a biasing technique: create a finer mesh near these regions by drawing auxiliary lines or using point loads as "seeds" for meshing. In RISA, you can also apply mesh density controls by selecting only the plates in the critical zone and using the Refine Plates command (which subdivides each plate into four). This avoids a uniform fine mesh over the entire surface, saving computational resources.

Importing Complex Curved Geometry from CAD

For structures with double curvature, non-uniform rational basis spline (NURBS) surfaces, or parametric shapes, manual modeling in RISA becomes impractical. The most efficient workflow is to create the geometry in a dedicated CAD or BIM tool such as Rhino, AutoCAD, Revit, or Tekla, and then import into RISA via DXF or IFC format.

Optimal CAD Model Preparation for RISA Import

The quality of the import depends heavily on how the CAD model is prepared. Follow these guidelines:

Use lines and polylines for frame members: RISA imports DXF linework as members. Ensure curves are drawn as polylines with a sufficient number of vertices (segments). Use the Divide command in CAD to add vertices along curves before export.
For plates: Draw surfaces as 3D faces (in AutoCAD) or closed polylines that will be converted to plates. RISA will automatically mesh these surfaces during import if you use the Import 3D Faces as Plates option.
Layer naming: Assign distinct layers for beams, columns, plates, and loads. RISA can map layers to member/plate properties during import.
Coordinate system: Use a single global coordinate system (typically origin at (0,0,0)) to avoid scaling or translation errors. Avoid using blocks or external references in the DXF – flatten all geometry.

Import and Post-Processing in RISA

After importing, always run the Check Geometry command to identify overlapping members, gaps, or duplicate nodes. For curved surfaces, you may find that imported plates are slightly disconnected – use Merge Nodes (with a tolerance of 0.01 to 0.1 inches) to connect them. Then, use the Auto Mesh command to subdivide the imported plates into a more uniform mesh for analysis. See RISA Official Documentation for detailed import settings.

For very complex shapes, consider using the RISA API (RISA-3D API) to programmatically create the model from data exported from a parametric design tool like Grasshopper. This is an advanced workflow but offers ultimate flexibility for adaptive geometry.

Exporting RISA Models for Verification and Collaboration

Sometimes the modeling of curved structures benefits from exporting the RISA model to a more advanced finite element package (e.g., SAP2000, ANSYS, or Abaqus) for detailed stress analysis, or to a BIM tool for fabrication and coordination. RISA supports export to DXF, CIS/2, and IFC formats. For curved members, be aware that RISA will export the segmented approximation, not the true curve. If the receiving software supports curved beams (like some CAD packages), you may need additional steps to regenerate the curve from node coordinates.

When exporting for code checking or connection design, ensure that the node coordinates are accurate. Use RISA's Export to Excel feature to create a spreadsheet of joint coordinates and connectivity, which can then be imported into custom scripts for generating parametric models in other tools.

Practical Workflow Example: Modeling a Curved Steel Arch Bridge

To tie all these techniques together, consider a typical steel arch bridge with a circular radius of 150 ft and a span of 300 ft. The arch is a tubular section (HSS20x20x0.5). The desired model refinement: 12 segments per half-arch (24 total for the entire arch).

In RISA, set Modeling Options > Arc Meshing to 12 segments per arc.
Draw the left half of the arch using the Arc tool from the start (0,0,0) to the crown (150,150,75) with a radius of 150 ft. Repeat for the right half.
Assign the HSS20x20 section to both arches.
Add lateral bracing between the two arches – these are straight members.
Run a preliminary analysis. Check deflection: if the vertical deflection at the crown is within tolerance, no further refinement may be needed.
For the deck, create a series of straight floor beams spanning between the arches, then add a concrete deck modeled as shell elements. Use the Generate Plates by Contour to create a curved deck surface following the arch profile.
Refine the deck mesh: use Refine Plates around the supports to capture local stresses.
Perform a mesh convergence study by increasing arch segments to 18 and checking if the maximum bending moment changes by less than 3%. If not, accept the 24-segment model.

This structured approach ensures accurate results without excessive runtime.

Common Pitfalls and How to Avoid Them

Even experienced engineers make mistakes when modeling curves in RISA. Watch out for these:

Disconnected nodes at arch intersections: Always use the Merge Nodes command after creating arcs that meet at a common point. A tiny gap will cause a mechanism.
Using too few segments for torsion: Curved members under torsion require a finer mesh because torsional warping is not captured by simple beam elements. Increase segments to at least 8 per 90-degree turn.
Ignoring p-delta effects – for slender curved arches, enable P-Delta analysis (large displacement) to capture second-order effects.
Importing splines as single polylines – a 3D spline imported as a polyline may have hundreds of tiny segments that make the model unwieldy. Simplify by reducing vertices using the CAD's Simplify command before importing.

For further reading, refer to the RISA 3D Tutorials and the Structure Magazine for case studies on curved bridge design.

Conclusion

Modeling curved structures in RISA is a blend of art and science. By mastering the arc tools, understanding segmentation trade-offs, applying advanced meshing techniques, and leveraging CAD import/export, you can produce models that are both accurate and computationally efficient. The techniques detailed here – from curvature-based segmentation to mesh convergence studies – will help you tackle complex geometries with confidence, whether designing a landmark arch, a spiral staircase, or a curved stadium roof. As with any finite element analysis, always validate your model against hand calculations or independent checks for critical structures. With practice, these advanced approaches will become second nature, elevating the quality and reliability of your structural designs.