Decoupled Flexure

The Decoupled Flexure analysis designs compliant flexures that compensate for thermal expansion between bolted mounting points. It uses a two-stage approach:

1. Thermal stage -- A steady-state thermal simulation computes the displacement at each input bolt pad due to a prescribed temperature change.
2. Design optimization stage -- The computed thermal displacements become force directions for the standard compliant mechanism solver (structural optimization).

The result is a flexure design that routes thermal load paths from input bolt pads through an optimized material layout to a desired output motion.

When to use this analysis

Use Decoupled Flexure when:

• You are designing a thermally compensating flexure for a bolted assembly.
• Input loads come from thermal expansion at known bolt pad locations.
• You want to decouple the thermal problem (where forces come from) from the design optimization (how material is distributed).

Do not use this analysis when:

• Input forces are mechanical, not thermal. Use Compliant Mechanism 2D instead.
• You need 3D optimization. The decoupled flexure solver is currently 2D only.

Bolt pad configuration

Bolt pads are the primary boundary condition for decoupled flexure analysis. Each bolt pad has a role that determines how it maps to solver constraints:

Role	Solver mapping	Description
Input	Input preserve with thermal direction	Bolt pad where thermal expansion creates a displacement. The thermal stage computes the force direction.
Output	Fixed nodes (pinned)	Mount point for the output workpiece. Pinned to create reaction forces that drive load paths through the flexure.
Fixed	Fixed nodes (pinned)	Structural anchor point. Prevents rigid-body motion.

Bolt pad properties

Property	Type	Unit	Description
Center X	float	mm	X coordinate of bolt pad center
Center Y	float	mm	Y coordinate of bolt pad center
Width	float	mm	Width of the rectangular pad region
Height	float	mm	Height of the rectangular pad region
Role	enum	--	Input, Output, or Fixed

Output region

In addition to bolt pads, the analysis requires an Output Preserve that defines the desired output motion direction. This is distinct from output bolt pads (which are mount points). The output preserve has:

Property	Type	Description
Center position	float	X and Y coordinates of the output region center
Width, Height	float	Size of the output region
Direction	float	Desired output motion direction (X and Y components, normalized automatically)

Solver parameters

The decoupled flexure analysis accepts the same core optimization parameters as the compliant mechanism solver, plus thermal-specific settings.

Thermal stage

Parameter	Type	Default	Description
Delta temperature	float	-173.0	Temperature change in degrees C applied to the thermal simulation. Negative values represent cooling from ambient.
Thermal expansion coefficient	float	(from material)	CTE in 1/K. Automatically set from the selected material.

Optimization

Parameter	Type	Default	Range	Description
Volume fraction	float	0.3	0.01 -- 0.99	Target material fraction.
Penalization	float	3.0	1.0 -- 10.0	Controls design sharpness. Higher values produce crisper solid-or-void designs.
Filter radius	float	auto	> 0	Feature size control radius.
Iterations	int	60	1 -- 1000	Maximum optimization iterations.
Convergence tolerance	float	0.01	> 0	Convergence threshold on design value change.
Element size	float	2.0	> 0	Element edge length in mm.
Max characteristic stiffness (K_p)	float	10.0	> 0	K_p upper bound for the pair linking inputs to output.

Design domain

Parameter	Type	Default	Description
Design domain mode	enum	Manual	Manual (explicit dimensions) or Automatic (computed from bolt pad bounding box with padding).
Design domain width	float	--	Domain width in mm (Manual mode).
Design domain height	float	--	Domain height in mm (Manual mode).
Design domain padding	float	0.2	Fractional padding around bounding box (Automatic mode).

Material

Parameter	Type	Default	Description
Material	string	None	Selected material from the database. See Materials. When no material is selected, defaults to Ti-6Al-4V properties.
Thickness	float	1.0	Plate thickness in mm.

Advanced

Parameter	Type	Default	Description
Formulation mode	enum	Nuanced	Default is Nuanced (fine-tuned stiffness control) for decoupled flexure.
Force preserve density	bool	true	Force full density at preserve and bolt pad regions.
Mirror vertical	bool	false	Enforce vertical symmetry.
Mirror horizontal	bool	false	Enforce horizontal symmetry.

Solver pipeline

bolt pads + material + temperature change
        |
        v
  Thermal Simulation
  Computes displacement at each input bolt pad
        |
        v
  Input translation
  Maps bolt pads to input preserves with thermal directions
  Maps output bolt pads to fixed nodes
  Maps fixed bolt pads to fixed nodes
  Maps the output preserve to the compliant mechanism output
  Links inputs to output as a pair
        |
        v
  Compliant Mechanism Solver (design optimization)
  Structural optimization using translated boundary conditions
        |
        v
  Optimized material layout + convergence data

Solver output

Output is identical in structure to the Compliant Mechanism 2D output, including the material layout, compliance history, and K_p values. Additionally, the thermal stage visualization data (displacement vectors at bolt pads) is available for inspection.