Glossary

Active element An element in the material layout that is forced to full material regardless of the optimizer. Elements under preserve and bolt pad regions are typically active to prevent the optimizer from removing material where boundary conditions are applied.

Analysis A scene object that stores all solver configuration (parameters, references to preserves, material, domain size). Running an analysis creates a solver job. The analysis is the "blueprint"; the job is the "execution."

Bolt pad A rectangular region on a plate representing a bolted mounting point. Used in the decoupled flexure analysis. Each bolt pad has a role (input, output, or fixed) that determines how it maps to solver boundary conditions.

Boundary condition A constraint imposed on the solver model. In deFlex, boundary conditions include fixed nodes (zero displacement), input forces, and output motion requirements. Defined via preserves.

Characteristic stiffness (K_p) A scalar measure of how stiff the mechanism is at the output preserve. Computed as the ratio of reaction force to displacement at the output. Lower K_p means a more compliant (flexible) mechanism. Constrained by the max characteristic stiffness setting in nuanced mode.

Compliance The strain energy of the structure under load. The design objective in nuanced mode is to minimize compliance (maximize global stiffness) subject to stiffness and volume constraints. Lower compliance means a stiffer load path.

Compliant mechanism A mechanism that achieves motion and force transmission through elastic deformation of a monolithic part, rather than through rigid links and joints. Examples include grippers, snap fits, and living hinges.

Convergence The state reached when the design values stop changing significantly between iterations. Measured by the maximum change in any element's material value against the convergence tolerance. A converged design is stable and will not improve with further iterations.

Convergence tolerance The threshold on maximum design value change that triggers early stopping. When the largest change in any design value drops below this value, the solver declares convergence and stops.

CTE (Coefficient of Thermal Expansion) The fractional change in length per degree of temperature change (units: 1/K). Used by the decoupled flexure thermal stage to compute displacement directions at bolt pads.

Material layout The solver's primary output — a map of the design domain showing where solid material is placed and where voids exist. Values range from void (no material) to solid (full material). After optimization, the layout is converted to a manufacturable geometry.

Feature size filter A spatial smoothing operation applied to the design at each iteration. The filter radius controls the minimum feature size and prevents numerical artifacts. Larger radius means smoother, thicker members.

Design domain The rectangular (2D) or box-shaped (3D) region within which the optimizer distributes material. Defined by width, height (and depth for 3D), and element size.

Design value The material value of each element in the design domain. The optimizer adjusts these values (within [0, 1]) to achieve the best design subject to constraints.

Element A single cell of the solver mesh. In 2D, cells are quadrilateral. In 3D, they are hexahedral. Each cell has a design value that the solver adjusts during optimization.

Structural analysis The numerical method deFlex uses to compute displacements, stresses, and forces for a given design. Structural analysis runs at each optimization iteration to evaluate how well the current design performs.

Filter radius See Feature size filter.

Formulation mode The solver strategy used by the compliant mechanism solver. Robust mode is a general-purpose formulation reliable for a wide range of mechanisms. Nuanced mode is a fine-tuned stiffness control mode that gives precise control over mechanism stiffness.

Grayness The fraction of cells in the material layout with intermediate values (not clearly solid or void). A design with low grayness has crisp solid/void boundaries and is more manufacturable. Increasing the Penalization parameter reduces grayness by driving the design toward cleaner solid-or-void results.

Isosurface A surface at which the material layout equals a threshold value (typically 0.5). Used to extract a solid geometry (STL mesh) from the continuous result.

Iteration One cycle of the optimization loop: the solver analyzes the current design, evaluates performance, and updates the material distribution. Each iteration produces an updated material layout visible in the results viewer.

Mechanical advantage (J)* The ratio of output displacement to input displacement in a compliant mechanism. Negative values indicate an inverting mechanism (output moves opposite to input). A value of -1.0 is a unit inverter; -2.0 doubles and inverts the displacement.

Mesh The discretized representation of the design domain as a grid of cells. Mesh resolution is controlled by the element size setting. Finer meshes are more accurate but more expensive to solve.

Optimizer The algorithm deFlex uses to update the design at each iteration. It processes performance data from the structural analysis to determine where to add or remove material, while respecting constraints like volume fraction.

Node A point in the solver mesh where displacement values are computed. In 2D, each node has 2 degrees of freedom (x, y). In 3D, each node has 3 (x, y, z). Nodes are shared between adjacent cells.

Nuanced mode See Formulation mode.

Design objective The performance metric the optimizer seeks to improve. In deFlex, the design objective is typically compliance (strain energy) for nuanced mode, or a combined stiffness/flexibility measure for robust mode.

Obstacle A keep-out zone where the optimizer cannot place material. Elements inside an obstacle have their material forced to void at every iteration. Used for design constraints like clearance holes, cable routes, or pre-existing features.

Output path A direction vector (or rotation) that defines the desired output motion at an output preserve. Used by the solver to evaluate the mechanism's performance and compute K_p.

Pair See Preserve pair.

Part A geometric object in the scene. Parts serve as design domains (rectangles, boxes), preserve regions (where boundary conditions apply), and obstacle volumes. Types: Rectangle, Box, STEP, STL.

Passive element An element in the material layout that is forced to void (material value = 0). Elements inside obstacle regions are passive. The optimizer cannot place material in passive elements.

Path A scene object that defines a direction for force or motion. Linear paths specify a direction vector; rotational paths specify an axis and angle. Paths are referenced by preserves.

Penalization A solver parameter that controls design sharpness. At low values, the solver may produce designs with ambiguous regions that are neither clearly solid nor void. At higher values (default is 3--5 depending on analysis type), the solver drives the design toward clean, well-defined solid-or-void results that are easier to manufacture.

Preserve A boundary condition applied to a region of the design domain. Types: Input (force application), Output (desired motion), Fixed (zero displacement), Deformation Function (prescribed surface deformation), Flexure IO (combined input/output).

Preserve pair A grouping that links specific input preserves to specific output preserves. Allows multi-input, multi-output mechanism design where each pair has its own stiffness constraint.

Robust mode See Formulation mode.

Solver feedback Information the solver computes about how each cell's material value affects the overall design performance. This guides the optimizer in deciding where to add or remove material.

Design optimization method The solver's approach to determining optimal material distribution. Each cell's structural contribution is determined by its material value, with a sharpness parameter that drives the design toward clear solid-or-void decisions.

Solver job A scene object that tracks one execution of an analysis. Contains status (queued, running, completed, failed, cancelled), progress, iteration count, and a snapshot of all solver parameters used.

Stiffness constraint A constraint on the characteristic stiffness K_p at the output. In nuanced mode, K_p must remain below the max characteristic stiffness setting. This prevents the optimizer from creating infinitely stiff (non-compliant) designs.

Symmetry constraint Forces the material layout to be symmetric about one or both centerlines. The vertical mirror option enforces left-right symmetry; the horizontal mirror option enforces top-bottom symmetry. Reduces the effective design space and guarantees symmetric designs.

Design optimization A computational method that determines the optimal distribution of material within a design domain to satisfy given objectives and constraints. Unlike shape optimization (which adjusts boundaries) or sizing optimization (which adjusts thicknesses), design optimization can create or remove holes and form entirely new structural members.

Volume fraction The ratio of material volume to total design domain volume. A volume fraction of 0.3 means 30% of the domain is filled with material. This is the primary resource constraint in design optimization -- the optimizer must achieve the best performance using only the specified amount of material.

Workpiece spring A virtual spring placed at the output in robust mode. Its stiffness controls the trade-off between mechanism flexibility and output stiffness. Not used in nuanced mode.