Compliant Mechanism 2D

The Compliant Mechanism 2D analysis optimizes a planar material layout that transmits force and motion between designated input and output regions. The solver uses AI-driven design optimization to find the best material distribution for your boundary conditions.

When to use this analysis

Use Compliant Mechanism 2D when:

• The mechanism operates primarily in a single plane.
• You need to convert an input force or displacement into a controlled output motion (grippers, inverters, amplifiers).
• You want fast iteration cycles. 2D solves complete in seconds to minutes on typical grids.
• The out-of-plane dimension (thickness) is constant and can be treated with plane-stress assumptions.

Do not use this analysis when:

• The mechanism requires out-of-plane motion or has significant 3D geometry. Use Compliant Mechanism 3D instead.
• The design is driven by thermal expansion from bolt-pad mounting. Use Decoupled Flexure instead.

Required boundary conditions

A valid 2D compliant mechanism analysis requires at minimum:

Condition	Object type	Purpose
Input	Input Preserve + Linear/Rotational Path	Where and in what direction force is applied
Output	Output Preserve + Linear/Rotational Path	Where and in what direction motion is desired
Fixed	Fixed Preserve or Boundary Fixed Preserve	Prevents rigid-body motion; anchors the mechanism

You may also add Obstacles (keep-out zones) and Preserve Pairs (to control which inputs drive which outputs in multi-pair designs).

Solver parameters

Optimization

Parameter	Type	Default	Range	Description
Volume fraction	float	0.3	0.01 -- 0.99	Target fraction of the design domain to fill with material. Lower values produce thinner, more flexible designs.
Penalization	float	5.0	1.0 -- 10.0	Controls design sharpness. Higher values produce crisper, more clearly defined solid-or-void designs.
Filter radius	float	auto	> 0	Feature size control radius in element widths. Controls minimum feature size. Larger values yield smoother, more manufacturable designs. When unset, defaults to 1.5x element size.
Iterations	int	20	1 -- 1000	Maximum number of optimization iterations.
Convergence tolerance	float	1e-5	> 0	Iteration stops when the maximum change in any design value drops below this value.

Design domain

Parameter	Type	Default	Range	Description
Design domain width	float	(from part)	> 0	Width of the rectangular design domain in mm.
Design domain height	float	(from part)	> 0	Height of the rectangular design domain in mm.
Element size	float	2.0	> 0	Edge length of each mesh cell in mm. Determines mesh resolution. Smaller elements increase accuracy and compute time quadratically.
Thickness	float	1.0	> 0	Out-of-plane thickness in mm. Used for plane-stress stiffness scaling.

Material

Parameter	Type	Default	Range	Description
Material	string	None	See Materials	Selected material from the database. Determines Young's modulus, Poisson's ratio, density, and yield stress.
Young's modulus	float	3.5e9 Pa (3500 MPa)	> 0	Young's modulus in Pa. Overridden when a material is selected.
Poisson's ratio	float	0.36	0.0 -- 0.5	Poisson's ratio. Overridden when a material is selected.

Compliant mechanism

Parameter	Type	Default	Range	Description
Formulation mode	enum	Nuanced	Robust, Nuanced	Solver formulation. Nuanced (default) is a fine-tuned stiffness control mode with a characteristic stiffness constraint. Robust is a general-purpose mode reliable for a wide range of mechanisms.
Mechanical advantage (J*)	float	-1.0	any	Ratio of output displacement to input displacement. Negative values produce inverting mechanisms (output moves opposite to input).
Max characteristic stiffness (K_p)	float	10.0	> 0	Upper bound on characteristic stiffness K_p (N/mm). Only active in Nuanced mode. Set per preserve pair.
Use summed constraint	bool	false	--	When true, sums K_p across all pairs into a single constraint. When false, each pair has an independent constraint.

Symmetry

Parameter	Type	Default	Description
Mirror vertical	bool	false	Enforce vertical (left-right) symmetry in the design result.
Mirror horizontal	bool	false	Enforce horizontal (top-bottom) symmetry in the design result.

Advanced

Parameter	Type	Default	Description
Use nonlinear analysis	bool	false	Enable geometric and material nonlinearity in simulation. Increases compute time significantly.
Material model	enum	Linear Plane Stress	Material model when nonlinear analysis is enabled. Options: Linear Plane Stress, Saint Venant-Kirchhoff, Yeoh Hyperelastic, Neo-Hookean.
Enable penalization scheduling	bool	false	Linearly ramp design sharpness from the base value to the final penalization over the last N iterations. Helps the solver produce cleaner, more defined designs.
Final penalization	float	15.0	Target penalization at final iteration when scheduling is enabled.
Enable stress constraint	bool	false	Activate a KS-aggregated von Mises stress constraint.
Yield strength	float	250.0	Material yield stress in MPa. Used with the factor of safety to compute the stress limit.
Factor of safety	float	1.5	Factor of safety: stress limit = yield strength / factor of safety.
Force preserve density	bool	true	Force full material density in preserve regions. Prevents the optimizer from removing material under boundary condition patches.

Solver output

Each completed iteration returns:

Output	Description
Material layout	Element material distribution across the design domain. 0 = void, 1 = solid.
Compliance	Structural performance metric value.
K_p values	Characteristic stiffness for each preserve pair.
Volume fraction	Actual volume fraction achieved.
Design change	Maximum design value change this iteration.
Converged	Whether the maximum change dropped below the convergence tolerance.

The final iteration additionally includes displacement field data for animation, and an STL mesh of the optimized design.