3. Parametric CAD and CAE model setup

Sensitivity analysis and response surface optimization both depend on a model that can be driven by numbers rather than by manual edits. The central task of this chapter is to convert a frozen CAD/CAE model into a parametric study model: a geometry and finite element setup in which a small set of controlled inputs (design variables) can be changed automatically, subject to physical and manufacturing limits (constraints), while a defined set of results (output responses) is extracted consistently after every solve. If this layer is built carelessly, no amount of optimization algorithm quality will recover the lost accuracy — the optimizer will simply converge faster to the wrong answer.

From a frozen model to a parametric model

A parametric model is not merely a CAD model with dimensions. It is a model whose regeneration path is stable: every design variable maps to a named parameter, every named parameter drives sketch dimensions, feature offsets, or mesh controls through an explicit dependency chain, and the CAE side re-meshes and re-solves without manual intervention. In practice this means three preparatory decisions before any variable is declared:

• Choose the driving sketch and feature hierarchy. Prefer variables that act on early, robust features (base sketch length, wall thickness, rib height) over variables that act on late cosmetic features. A variable that forces a fillet to fail at an extreme value will abort the entire DOE run.
• Separate geometry parameters from mesh and solver parameters. Mesh size, element order, and contact stiffness are legitimate study inputs, but they belong to a different class than geometry. Mixing them in one variable table makes the response surface uninterpretable.
• Decide the regeneration strategy. Fully parametric CAD with associative CAE (geometry regenerates, mesh updates) is preferred when shape changes are moderate. When topology changes (a rib appearing or disappearing), a scripted geometry rebuild or a morphing-based approach is more reliable.

Defining design variables

A design variable should be independent, physically meaningful, and bounded. Independence matters because two variables that both control the same wall thickness will produce a rank-deficient sensitivity matrix and misleading main effects. Physical meaning matters because the engineer must be able to defend the final design: "rib height 18 mm" is defensible, "shape parameter 3" is not.

For each variable, record at minimum: a unique identifier, the CAD parameter it drives, a baseline value, a lower and upper bound, and the unit. Bounds are not arbitrary — they encode manufacturing limits (minimum cast wall thickness), packaging limits (available envelope), and numerical robustness (the range over which the mesher still succeeds). A practical rule is to set the DOE range slightly inside the absolute feasible range so that corner points of the design space do not fail.

A representative variable table for a bracket study might look like this (values are illustrative, not measured):

Note that r_fillet has a lower bound of 1.5 mm rather than 0: a zero-radius fillet changes the topology of the feature and often breaks the mesh at the root. This is a numerical constraint disguised as a geometric one, and it must be documented.

Constraints: separating physics from the optimizer

In a sensitivity study, "constraint" is used in two distinct senses, and conflating them is a common source of error. Design constraints are limits on the inputs (the bounds above, plus coupling relations such as h_rib ≤ 0.8 · envelope_height). Response constraints are limits on the outputs (maximum von Mises stress ≤ yield/1.5, first natural frequency ≥ 120 Hz, mass ≤ 1.8 kg). The optimizer treats the first as the search space and the second as feasibility conditions.

Coupling relations deserve explicit attention. If two variables are linked — for example, rib thickness must not exceed web thickness — encode the relation in the parametric model itself (a formula-driven dimension) rather than relying on the DOE sampler to avoid the infeasible region. A sampler that draws independent uniform values will otherwise waste runs on geometry that cannot be built.

Output responses: what gets measured after every solve

An output response is a scalar (or a small vector) extracted from the solved model by a deterministic procedure. The keyword is deterministic: the same geometry and load case must yield the same response value, independent of who runs the extraction. Responses are typically defined as:

• Field extremes — maximum von Mises stress over a named selection, maximum displacement at a named node set.
• Global quantities — total mass, strain energy, first three natural frequencies.
• Derived indicators — safety factor (yield / max stress), stiffness (force / displacement at a probe point), or a compliance ratio.

Two practical rules keep responses trustworthy. First, scope every field response to a named selection, not to the whole body. A global maximum stress will jump to a contact edge or a singular re-entrant corner as soon as a variable changes the local geometry, producing a response surface dominated by mesh singularity rather than by design intent. Second, fix the extraction location: a probe node or a named vertex must be re-identified after each regeneration, otherwise the "displacement at point A" may silently refer to a different physical point in run 7 than in run 1.

How the pieces connect

The figure below shows the dependency chain of a well-formed parametric study model. Design variables feed the CAD regeneration, which drives the mesh and solve; responses are extracted from the solved field and passed to the sensitivity/RSM layer, while response constraints gate feasibility. The dashed feedback path is the coupling relation that keeps the input space physically admissible.

Verification before the study begins

Before committing to a DOE or RSM run, verify the parametric model with a small, deliberate test. Set every variable to its baseline, solve, and record all responses. Then perturb one variable by a small amount (for example, t_web from 4.0 to 4.4 mm), regenerate, and confirm three things: the geometry actually changed in the intended feature, the mesh updated without orphaned named selections, and the response changed in the physically expected direction (thicker web → lower stress, higher mass). If the response does not move, the parameter is not truly driving the model — a silent disconnect that would otherwise produce a flat sensitivity plot and a false conclusion that the variable is unimportant.

Repeat this single-variable perturbation for each variable in turn. This is the cheapest possible screening step, and it catches the majority of parametric setup errors — broken references, over-constrained sketches, and responses scoped to the wrong selection — before they are buried inside a 50-run study. Once all variables pass, the model is ready for the sensitivity and response surface work that follows.