Flexure Analysis
Flexure analysis designs monolithic mechanisms with thin, flexible joints (flexures) connecting rigid bodies. Unlike compliant mechanism analysis, which uses distributed compliance throughout the design, flexure analysis concentrates flexibility at specific hinge points. The result is a structure with clearly defined rigid links and narrow flexure joints.
The solver uses design optimization with an efficiency objective that favors thin, concentrated hinges over broadly distributed material.
When to use flexure analysis
Use Flexure when:
- You need distinct rigid bodies connected by thin hinges rather than a continuously flexible structure.
- The mechanism has well-defined degrees of freedom (translation or rotation at specific points).
- You want to minimize strain energy concentration for fatigue life.
- The design operates in 2D (planar).
Do not use flexure analysis when:
- The mechanism requires distributed compliance throughout the body. Use Compliant Mechanism 2D instead.
- The mechanism operates in 3D. Flexure analysis currently supports 2D only.
- The design is driven by thermal expansion. Use Decoupled Flexure instead.
How flexure differs from compliant mechanism
| Aspect | Compliant Mechanism | Flexure |
|---|---|---|
| Compliance distribution | Distributed throughout body | Concentrated at hinge points |
| Preserve layout | Separate Input + Output | Combined I/O (single preserve marks both actuation and desired motion) |
| Objective function | Displacement-based | Efficiency-based |
| Preserve mode toggle | Shown (Separate/Combined/Metamat) | Not shown (always Combined) |
| Obstacle support | Yes | No |
| Pair support | No | No |
Required boundary conditions
A valid flexure analysis requires at minimum:
| Condition | Object type | Purpose |
|---|---|---|
| I/O | Combined I/O Preserve + Path | Combined input/output point with motion direction |
| Fixed | Fixed Preserve or Boundary Fixed Preserve | Prevents rigid-body motion |
| Material | Material selection | Defines mechanical properties for the solver |
Flexure analysis does not support obstacles or preserve pairs.
Combined I/O preserves
The combined I/O preserve type is unique to flexure analysis (and Combined mode in compliant analyses). A single I/O preserve marks both where force is applied and where motion is desired. Each I/O preserve requires a part (defining geometry) and at least one path (defining the degree of freedom direction).
Combined I/O preserves appear in a single I/O section in the scene tree, rather than in separate Input and Output sections.
DOC indices
Each combined I/O preserve has a degrees-of-constraint setting that controls which DOC are active. The available DOC options are:
| Index | Label | Meaning |
|---|---|---|
| 0 | Perpendicular | Constrains motion perpendicular to the path direction. |
| 1 | Rotation (rz) | Constrains rotation about the Z axis. |
By default, index 0 (Perpendicular) is enabled. You can enable both indices for a fully constrained joint or select only rotation for a purely rotational flexure.
The DOC is auto-computed as perpendicular to the DOF (degree of freedom) path direction.
Solver parameters
Optimization
| Parameter | Default | Description |
|---|---|---|
| Iterations | -- | Maximum number of optimization steps. |
| Volume Fraction | -- | Target material usage as a fraction of the design domain (0.0 -- 1.0). |
| Max Strain Energy | -- | Global upper bound on stored elastic energy. Limits how much elastic energy the mechanism can store, controlling hinge flexibility. |
| Force Preserve Density | true | When enabled, preserve areas are forced to full material density (not optimized away). |
| Material Stress Limit | -- | Maximum allowable von Mises stress (MPa). |
Convergence
| Parameter | Description |
|---|---|
| Mean difference tolerance | Stops optimization when the average change in design parameters between iterations falls below this threshold. |
| Gray convergence tolerance | Stops optimization when the fraction of intermediate-value cells falls below this threshold. |
Symmetry
| Parameter | Description |
|---|---|
| Vertical mirror | Enforces left/right symmetry across the vertical axis. |
| Horizontal mirror | Enforces top/bottom symmetry across the horizontal axis. |
Design domain
| Parameter | Description |
|---|---|
| Mode | Manual (explicit dimensions) or Automatic (computed from preserve positions with padding). |
| Width / Height | Physical dimensions in mm (manual mode). |
| Element Size | Mesh element size in mm. Smaller values increase resolution and solve time. |
| Padding | Fractional padding around preserves (automatic mode only). |
Advanced
| Parameter | Description |
|---|---|
| Legacy optimizer | Use per-solver optimizer implementation instead of the bounded optimizer. |
| Nonlinear analysis | Enable geometric and material nonlinearity for more accurate simulation. |
| Material Model | Neo-Hookean (default), Linear Plane Stress, SVK, or Yeoh. Only relevant when nonlinear analysis is enabled. |
Validation requirements
Before running a flexure solve, the following must be satisfied:
- At least one combined I/O preserve with geometry (a linked part) must exist and not be suppressed.
- At least one fixed boundary condition (fixed preserve or boundary fixed preserve) must exist and not be suppressed.
- A material must be selected.
- No other solver job can be running or queued.
If any requirement is missing, the run button is disabled and a validation message indicates what is needed.
Related pages
- Preserve Modes -- Combined mode uses the same combined I/O preserve type
- Paths -- how paths define the degree of freedom direction
- Compliant Mechanism 2D -- distributed compliance alternative
- Results Interpretation -- reading flexure results