FEM Model Review Checklist

Category: V&V・ベストプラクティス | 更新 2026-04-12
FEM model review checklist workflow diagram showing mesh quality, boundary condition verification, and reaction force balance checks
FEMモデルレビューの6大検証項目 — メッシュ品質、境界条件、材料特性、荷重条件、Free-Freeチェック、反力バランス

Theory and Physics

Overview — Why a Checklist is Necessary

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What exactly does a model review checklist check? It's something you look at before running the analysis, right?

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That's right. It's a list for systematically verifying mesh quality, boundary conditions, material properties, and load conditions as part of FEM model quality assurance, before executing the analysis. NASA's "FEM Best Practices" (NASA-STD-5002A) specifies a 35-item checklist, and structural analysis in aerospace must always go through this.

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35 items! But I don't hear of many teams in my field being that strict...

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Unfortunately, in many workplaces, it tends to become "generate the mesh, throw it to the solver, and if it converges, it's OK." But in reality, converged ≠ correct results. For example, in automotive crash simulation, it's not uncommon to approximate bolt connections with Tied Contact without verification, leading to results that don't match physical tests at all.

Even in your own team, creating a minimum checklist and making reviewer sign-off mandatory is a best practice. Having another engineer review, not the analyst themselves, prevents mistakes due to assumptions.

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I see, a double-check system is important. Specifically, what kind of items should we look at?

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They can be broadly divided into 6 categories:

  1. Mesh Quality Check — Metrics like aspect ratio, skewness, Jacobian, etc.
  2. Boundary Condition Verification (BC Verification) — Validity of constraints, presence of over-constraint
  3. Material Property Verification — Values of Young's modulus & Poisson's ratio, consistency of unit system
  4. Load Condition Review — Comprehensiveness of load cases, basis for load values
  5. Free-Free Mode Check — Verify connectivity with unconstrained modal analysis
  6. Reaction Force Balance Check — Confirmation of $\sum F = 0$, $\sum M = 0$

Mathematical Basis of the Checklist

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I have an image of checklists being like "procedure manuals," but do equations also relate to them?

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Of course. Many check items have quantitative criteria. For example, the reaction force balance check is evaluated using the following formula:

Reaction Force Balance Error
$$ \varepsilon_{bc} = \frac{\left|\sum R_{reaction} - \sum F_{applied}\right|}{\left|\sum F_{applied}\right|} \times 100\,[\%] $$
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This $\varepsilon_{bc}$ being below 0.1% is the general passing criterion. Furthermore, moment equilibrium is also checked:

Static Equilibrium Conditions
$$ \sum \mathbf{F} = \mathbf{0}, \qquad \sum \mathbf{M}_O = \mathbf{0} $$
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So we need to check both force and moment. Even if the forces balance, it's meaningless if the moment is off.

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Exactly. For example, when a concentrated load $P$ is applied to the free end of a cantilever beam, the reaction at the fixed end should be $R_y = P$ (force equilibrium) and the reaction moment should be $M = P \cdot L$ (moment equilibrium). This is verified in the FEM output. If the values are off, there is likely a mistake in boundary condition setup or a missing load definition somewhere.

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Regarding mesh quality, consider the global stiffness equation:

FEM Global Stiffness Equation
$$ [K]\{u\} = \{F\} $$
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This stiffness matrix $[K]$ is assembled from each element's stiffness matrix $K_e$. Element stiffness is calculated via numerical integration:

Gauss Integration of Element Stiffness Matrix
$$ K_e = \int_{\Omega_e} B^T D\, B\, d\Omega \approx \sum_{g=1}^{n_g} w_g\, B^T(\xi_g)\, D\, B(\xi_g)\, |J(\xi_g)| $$
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Here, $|J(\xi_g)|$ is the Jacobian determinant. When an element is distorted, the Jacobian deteriorates, and integration accuracy drops. That's why we check the Jacobian ratio in mesh quality checks. If a negative Jacobian appears, that element is inverted and physically meaningless.

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Ah, knowing the background of the equations makes me understand why criteria like "aspect ratio less than 5" exist. It's not just an empirical rule; it's directly connected to numerical integration accuracy.

NASA's Quality Assurance System

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What's in NASA's checklist? You said it has 35 items, right?

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It's detailed in NASA-STD-5002A "Structural Analysis and Test Requirements" and its supplementary document NASA-HDBK-5014. Summarizing the main items by category:

CategoryCheck Item (Representative Examples)Item Count
Geometric FidelityShape difference from CAD, justification record for simplifications4
Mesh QualityAspect ratio, skewness, Jacobian, connectivity7
Material PropertiesSource of Young's modulus/Poisson's ratio, temperature dependency, unit system5
Boundary ConditionsNumber of constrained DOFs, symmetry conditions, contact definition6
Load ConditionsComprehensiveness of load cases, application of safety factors5
Analysis ExecutionConvergence criteria, checking solver warnings4
Result VerificationReaction force balance, energy balance, Free-Free check4
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That's very systematic. Can it be used in fields other than aerospace?

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Absolutely. Many industries like automotive, nuclear, and medical devices also create their own checklists referencing NASA's framework. For example, automotive has similar requirements in the Euro NCAP crash analysis guidelines. The key is to identify "where the highest risk lies in your own analysis" and create a checklist focused on that.

Physical Meaning of the Reaction Force Balance Equation
  • $\sum R_{reaction}$ (Total Reaction Force): Sum of reaction forces calculated at all constraint points. Reaction force is zero for DOFs without constraint surfaces. Can be directly obtained from solver output files (.f06, .sta, .rst, etc.).
  • $\sum F_{applied}$ (Total Applied Load): Sum of all loads defined by the user. For distributed loads, calculated as the integrated value. If gravity is included, add total mass $\times g$.
  • $\varepsilon_{bc}$ (Balance Error): A large value suggests missing boundary condition definitions, mistakes in specifying load application surfaces, or numerical errors.
Relationship Between Jacobian and Element Quality
  • The Jacobian determinant $|J|$ represents the local "distortion degree" of the isoparametric mapping. For a square→square mapping, $|J| = $ constant (ideal value).
  • Elements with $|J| \leq 0$ are "inverted elements" and physically meaningless. Many solvers detect these as errors before analysis.
  • When the min/max ratio of $|J|$ (Jacobian ratio) is below 0.3, accuracy degradation becomes significant. For hexahedral elements, 0.5 or above is recommended.

Numerical Methods and Implementation

Mesh Quality Check

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For mesh quality checks, specifically which metrics should be checked against what criteria? The metrics that come out vary by software, and it's confusing.

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There are 5 main quality metrics. These are common regardless of solver:

MetricDefinitionIdeal ValuePassing CriteriaWhat happens if NG
Aspect RatioLongest side / Shortest side1.0< 5.0Stress accuracy degradation, especially in bending problems
Jacobian Ratio$|J|_{min} / |J|_{max}$1.0> 0.3Integration accuracy degradation; if negative, inverted element
Warping AngleNon-planarity of a face< 15°Incorrect stiffness evaluation for shell elements
SkewnessDeviation of internal angles from ideal0< 0.7Deterioration of convergence
Taper RatioDeviation of opposite side length ratios0< 0.5Distortion of stress distribution
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Do all elements need to meet the criteria? With complex shapes, some might exceed the criteria...

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Good question. Realistically, the guideline is that over 99% of elements meet the criteria. If NG elements exist, confirm that those elements are not in the region of interest (stress concentration area, failure evaluation area). If NG elements are in the area where stress is reported, those results are not reliable.

In practice, outputting a "quality histogram" and checking the distribution is standard. In Hypermesh, you can see it instantly in the Quality Index panel; in Ansys, use Mesh Metrics.

Boundary Condition Verification (BC Verification)

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Boundary condition checks... I thought you just look and see "this part is fixed," but what is there to check so much?

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Boundary conditions are the area with the most mistakes in FEM analysis. Always check the following:

  • Presence of Over-constraint: For 3D solid statically determinate problems, constraints are basically 6 DOFs (3 translation + 3 rotation). Constraining more than that generates artificial stresses.
  • Location and Direction of Constraints: Is the inner surface of a bolt hole fixed when the outer surface should be? Is the cylindrical coordinate system set correctly?
  • Validity of Symmetry Conditions: Are out-of-plane displacements constrained on symmetry planes? For anti-symmetric loads, are anti-symmetric BCs applied?
  • Validity of Contact Definitions: Selection of master/slave surfaces for Tied/Bonded contact, setting of friction coefficients.
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Over-constraint... I thought fixing more would be on the safe side, but is it bad?

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That's a common misunderstanding. Over-constraint inhibits the deformation the structure inherently possesses, calculating stresses that do not exist in reality. For example, if both ends of a thermally expanding pipe are fixed in all DOFs, huge fictitious stresses appear at flanges that would actually slide. The result is judged "dangerous," but in reality, it's not a problem at all — this is a false positive and distorts design judgment.

Free-Free Mode Check

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What is a Free-Free mode check? "Free-Free" means no constraints, right? Why deliberately remove constraints?

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Exactly. It's a test where you perform a modal analysis (eigenvalue analysis) without applying any boundary conditions. There are three purposes:

  1. Model Connectivity Verification: If all parts are correctly connected, there should be only 6 rigid body modes (3 translation + 3 rotation). If 7 or more appear, some part is floating (connection missing).
  2. Confirmation of Rigid Body Mode Frequencies: The natural frequencies of the 6 rigid body modes are theoretically zero. In FEM, they aren't exactly zero due to numerical error, but $f_{rigid} < 0.01\,\text{Hz}$ is a guideline. If above 1Hz, there's a problem.
  3. Confirmation of Mass Validity: Look at the 7th and subsequent elastic mode shapes from the Free-Free analysis and check if the deformation patterns are physically reasonable.
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Wait, if 7 rigid body modes appear, there's a missing connection? Are there actual cases where this helped?

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It happens all the time in practice. Especially with assembly models with 100+ parts, if there's even one missing Tied Contact definition, that part just floats. In static analysis, it might stop with a "singular matrix" error, but depending on the load case, it might coincidentally converge. The Free-Free check is a very powerful method to expose such "silent defects" beforehand.

The method is simple. In Nastran, use SOL 103 with no SPC specified; in Abaqus, use a *FREQUENCY step with no BC. The computational cost is less than 1/10th of a normal analysis.

Free-Free Mode Judgment Criteria
$$ \text{Number of Rigid Body Modes} = 6 \quad (\text{for 3D solids}) $$
$$ f_{rigid,\,i} < 10^{-2}\,\text{Hz} \quad (i = 1, \ldots, 6) $$
$$ f_{elastic,\,7} \gg f_{rigid,\,6} \quad (\text{must be orders of magnitude larger}) $$

Practical Guide

Material Property Verification

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Material property checks... isn't it just inputting Young's modulus and Poisson's ratio? I thought you could just use values from the MIL handbook...

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More than the values themselves, consistency of the unit system is the scariest. The most common fatal mistake in practice is "getting the unit of Young's modulus wrong." For example:

Unit SystemYoung's Modulus (Steel)Density (Steel)Common Mistake
SI (m, kg, s, Pa)2.1 × 1011 Pa7850 kg/m³Inputting as GPa → 1000x error
mm, t, s, MPa2.1 × 105 MPa7.85 × 10-9 t/mm³Inputting density as kg/m³
mm, kg, ms (impact)210 GPa → 210 kN/mm²7.85 × 10-6 kg/mm³Forgetting the time unit ms
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Wow, the density in the mm-t-s system is an extremely small number. What happens if you get this wrong?

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If you get the density wrong, inertial forces, gravity loads, and natural frequencies all go haywire. In static analysis without gravity, you might not notice, but in dynamic or modal analysis, the results become orders of magnitude wrong. The checklist verifies the following:

  • Record the source of input material properties (handbook name, test report number).
  • Calculate the model's total mass and compare it with the actual weight (within 2% error is a guideline).
  • For temperature dependency, check if data for the operating temperature range is correctly input.
  • For composite materials, check if the lamination sequence and fiber orientation angles match the design drawings.

Load Condition Review

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Load condition review...

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