Finite Element Analysis Studies

SolidWorks Simulation | ME 328 | Cal Poly San Luis Obispo

Model Validation Mesh Convergence Structural Optimization Stress Concentrations Buckling

SolidWorks von Mises stress contour showing a stress concentration at a fillet

Finite element analysis is useful only when the model represents the real structure and its results can be defended. Across four studies, I built and validated SolidWorks Simulation models, compared element and boundary-condition choices, and used the verified results to evaluate stiffness, stress, weight, cost, and stability.

Model validation and convergence

Simply supported aluminum beam

I began with a simply supported beam under uniform pressure. Analytical beam equations predicted a maximum bending stress of 54 kpsi and a maximum deflection of 15.3 in. I modeled the same beam with solid, shell, and beam elements while changing the fixtures and mesh size.

Fully fixing the end faces made the model artificially stiff. Replacing those fixtures with edge constraints allowed the ends to rotate like pin and roller supports. With the corrected boundary conditions, mesh refinement brought the solid-element result to 54.02 kpsi and 15.32 in - closely matching the analytical solution.

54.0 kpsi Analytical maximum stress

54.02 kpsi Refined solid-element result

15.32 in Refined simulated deflection

Solid-element stress contour for the simply supported beam — Solid elements captured the full 3D geometry but required refinement to converge.

Beam-element stress contour for the simply supported beam — Beam elements reproduced the bending solution with a much simpler model.

Plot of stress and deflection convergence as solid-element size decreases — Reducing the solid-element size moved both stress and deflection toward the analytical values.

Key lesson: A visually convincing contour is not proof of a correct model. Fixtures, element selection, mesh convergence, and an independent analytical estimate all matter.

Wing-spar optimization

Geometry, material, weight, and cost trade study

I evaluated a conceptual 70 ft cantilever wing spar under a triangular lift distribution and a 500 lbf engine point load. I compared I-beam and hollow box sections in 7075-T6 aluminum and normalized AISI 4130 steel, iterating each geometry until tip deflection fell within the 9-10 in target range.

Cantilever wing spar with triangular lift distribution and engine point load — Final load case: triangular distributed lift with a 500 lbf engine load located one-third of the span from the root.

Cross section	Material	Deflection	Max stress	Weight	Est. cost
I-beam	7075-T6 Al	9.780 in	4,760 psi	1,969 lb	$13,783
I-beam	AISI 4130 steel	9.544 in	13,325 psi	2,596 lb	$25,960
Box beam	7075-T6 Al	9.378 in	3,259 psi	1,705 lb	$11,935
Box beam	AISI 4130 steel	9.300 in	6,694 psi	3,335 lb	$33,350

Recommendation: The 7075-T6 aluminum box beam was the lightest and least expensive option while meeting the displacement target. Its simulated stress also remained well below the assumed yield strength.

Stress concentrations

Fillet-radius sensitivity under axial and bending loads

A stepped bar showed how geometric discontinuities amplify local stress. The highest von Mises stress formed at the fillet where the cross section changed. I swept the fillet radius from 0.2 to 16 in and compared the response under axial and bending loads.

Increasing the radius reduced peak stress from 19.85 to 12.80 kpsi for the reported axial cases and from 29.56 to 20.24 kpsi for bending. Both curves approached a plateau, revealing diminishing structural benefit as the fillet became larger.

35.5% Reduction in reported axial peak stress

31.5% Reduction in reported bending peak stress

0.2-16 in Fillet-radius range evaluated

Design implication: A larger fillet can reduce local stress, but the benefit eventually levels off. The final radius should balance strength with packaging and manufacturing constraints.

Buckling and support conditions

Safety-factor-driven column sizing

I used Euler buckling theory to establish initial dimensions for 6.5 ft balsa-wood columns, then refined each model with a SolidWorks eigenvalue buckling study. Four cases combined pinned-pinned and fixed-pinned supports with 22,500 and 45,000 lbf compressive loads.

Every configuration was iterated into the required 2.5-2.6 safety-factor range. The fixed-pinned cases required smaller cross sections because the rotational restraint increased column stiffness. Doubling the load increased the required side length by roughly one inch because the square section's area moment of inertia scales with the fourth power of its side length.

Boundary condition	Applied load	Final side length	Safety factor
Pinned-pinned	22,500 lbf	5.67 in	2.50
Fixed-pinned	22,500 lbf	4.75 in	2.51
Pinned-pinned	45,000 lbf	6.75 in	2.52
Fixed-pinned	45,000 lbf	5.70 in	2.52

Pinned-pinned column buckling mode shape — Pinned-pinned mode shape with maximum lateral displacement near midspan. Deformation is exaggerated for visibility.

Fixed-pinned column buckling mode shape — Fixed-pinned mode shape showing the effect of added rotational restraint. Deformation is exaggerated for visibility.

What I learned

Engineering judgment before solver output

These studies reinforced that FEA is not a substitute for engineering judgment. A solver will return a result even when fixtures, element types, or mesh choices do not represent the physical problem. By pairing simulation with analytical estimates, convergence checks, and design iteration, I learned to separate visually plausible output from a result that can be defended and used for a design decision.

Lab 1 report: Validation → Lab 2 report: Wing spar → Lab 3 report: Stress concentrations → Lab 4 report: Buckling →