Battery Module Structural Analysis

Click "Open in Colab" to experiment with different parameters

These hand calcs translated into a script allowed for quick iteration and structural optimization of our FSAE Battery Segments. The initial version was made back in 2024 (in MATLAB).

This document includes current SES calculations, SES calculations to be introduced in 2026, and calculations deemed to help verify solid mechanical design.

Constants and Geometry
Load Cases & Bending Stress
Fasteners: Tension, Shear, and Bearing
Bond Strength Analysis
Euler-Johnson Buckling Analysis
Passive Thermal Properties
Summary Results Table
Sources Referenced

1. Constants and Geometry

We establish the physical foundations and material properties here.

Segment Assembly Diagram

             ____________________________________________________________
            /                                                           /|
           /                     POLYCARBONATE LID                     / |
          /___________________________________________________________/  |
         |                                                           |   | <--EneSegHeight
         |                                                           |   |      (105.6mm)
         |___________________________________________________________|   |
         |                                                           |  /
         |                                                           | / <--EneSegmentWidth
         |___________________________________________________________|/        (81.2mm)
           <------------------- EneSegmentDepth ------------------->
                                 (417.0mm)

Cell Layout (Top View)

         _________________________________________________________
      | | [ o o ]   [ o o ]   [ o o ]   [ o o ]   [ o o ]   [ o o ] |
      | | [ o o ]   [ o o ]   [ o o ]   [ o o ]   [ o o ]   [ o o ] |
      | | [ o o ]   [ o o ]   [ o o ]   [ o o ]   [ o o ]   [ o o ] |  (81.2mm)WIDTH
      | | [ o o ]   [ o o ]   [ o o ]   [ o o ]   [ o o ]           |
      | |_________________________________________________________| |
      |                                                             |
        <---------------------- DEPTH (417.0mm) ------------------->

Input Parameters

Parameter	Value	Unit
Module Width	20.3	mm
Segment Height	105.6	mm
Module Depth	69.5	mm
Module Weight	0.278	kg
Segment Depth	417.0	mm
Segment Width	81.2	mm
Garolite Thickness	3.175 (1/8")	mm
Polycarbonate Thickness	9.525 (3/8")	mm
Total Modules	23	-

Material Properties

Material	Property	Value
Garolite G10	Strength	262 MPa
	Modulus	16.5 GPa
Polycarbonate	Flexural Strength	93 MPa
	Modulus	2.21 GPa

2. Load Cases & Bending Stress

Calculated for 20g vertical and 40g lateral crash loads per SES requirements.

Assuming a uniformly distributed load where total force $F$ is related to the distributed load $w$ by $F = w \cdot L$ :

Maximum Bending Moment

M_{m a x} = \frac{w L^{2}}{8} = \frac{F \cdot L}{8}

Bending Stress

σ = \frac{M \cdot c}{I}

Maximum Deflection

δ_{m a x} = \frac{5 w L^{4}}{384 E I} = \frac{5 F \cdot L^{3}}{384 E I}

Results - Polycarbonate Lid

Parameter	Value
Vertical Force (20g)	1254.5 N
Bending Moment	65.4 N·m
Lid Safety Factor	1.75

Verifies that our polycarbonate lid will survive a 20g vertical crash load - cells will not break the lid or fly out.

3. Fasteners

Tensile Stress Area

For a threaded rod subjected to pure tensile loading, strength is defined by the average of minor and pitch diameters. The tensile-stress area $A_{t}$ is:

A_{t} = \frac{π}{4} {(\frac{d_{p} + d_{r}}{2})}^{2}

For ISO metric threads (M6):

d_{p} = d - 0.649519 p, d_{r} = d - 1.226869 p

Where:

$d$ = major/outside diameter (6.0 mm)
$p$ = thread pitch (1.0 mm)

Axial Tensile Stress:

σ_{t} = \frac{F}{A_{t}}

Ref: Norton, R. L. (2020). Machine Design: An Integrated Approach. 6th ed., p. 907.

Fastener Results (M6 Bolts)

Load Case	Safety Factor
Bolt Tension (20g Vertical)	39.83
Bolt Plug Shear (20g Vertical)	23.88
Bolt Shear (40g Horizontal)	3.32
Bolt Tear-out (40g Horizontal)	2.65

4. Bond Strength Analysis

Given simple loading, how strong is the bonded G10? This does not account for finger joints (which add additional strength).

Parameter	Value
FR4/G10 Bond Strength	15.2 MPa
40g Horizontal Force	2509.0 N
Bond Safety Factor	2.80

5. Euler-Johnson Buckling Analysis

Euler-Johnson Buckling Criteria

Critical Slenderness and Radius of Gyration:

C_{c} = π \sqrt{\frac{2 E}{σ_{y}}}, k = \sqrt{\frac{I_{x x}}{A}}

Johnson (Inelastic) Buckling if $S R < C_{c}$ :

P_{c r} = A [σ_{y} - \frac{1}{E} {(\frac{σ_{y} \cdot S R}{2 π})}^{2}]

Euler (Elastic) Buckling if $S R \geq C_{c}$ :

P_{c r} = \frac{π^{2} E I_{x x}}{L^{2}}

(Ref: Norton, Machine Design, 6th Ed., p. 231)

Results

Parameter	Value
Buckling Mode	Johnson (Inelastic)
Buckling Safety Factor	120.70

6. Passive Thermal Properties

Calculating the heat dissipation capacity of the segment casing through conduction.

Parameter	Value
Total Surface Area	0.156 m²
Garolite Conductivity	0.288 W/m·K
Passive Heat Transfer Rate	14.13 W/K

7. Summary Results Table

Section	Load Case	Safety Factor
2.4	Lid - 20g Vertical	1.75
3.2	Bolt Tension - 20g Vertical	39.83
3.3	Bolt Plug-out - 20g Vertical	23.88
3.4	Bolt Shear - 40g Horizontal	3.32
3.5	Bolt Tear-out - 40g Horizontal	2.65
4.1	Bond Strength - 40g Horizontal	2.80
5.2	Casing Buckling - 40g Horizontal	120.70

All safety factors > 1.0 - Structure passes SES crash load requirements.

Code

Python Implementation (click to expand)

import math
import pandas as pd

# Conversion Constants
PSI_TO_PA = 6894.76
MM_TO_M = 1/1000
INCH_TO_M = 25.4/1000
G = 9.80665

# 1.1 Module Dimensions
ene_mod_width = 20.3 * MM_TO_M
ene_seg_height = 105.6 * MM_TO_M
ene_mod_depth = 69.5 * MM_TO_M
module_weight = 0.278  # kg

# 1.2 Segment Assembly
ene_segment_depth = 6 * ene_mod_depth
ene_segment_width = ene_mod_width * 4
garolite_thickness = (1/8) * INCH_TO_M
segment_modules_weight = module_weight * 23

# 1.3 Material Properties
garolite_strength = 38000 * PSI_TO_PA
garolite_modulus = 2400000 * PSI_TO_PA
poly_thickness = 3/8 * INCH_TO_M
poly_strength = 93e6  # Pa
poly_modulus = 2.21e9 # Pa

# 2.1 Load Cases
top_force = segment_modules_weight * 20 * G  # 20g vertical
side_force = segment_modules_weight * 40 * G  # 40g lateral

# See full implementation in Colab notebook

Sources Referenced

Enepaq VTC6 Module Datasheet - Module dimensions and weight specifications.
Laminated Plastics G-10/FR4 Data - Material strengths, bonding data, and tear-out limits.
MatWeb Polycarbonate Data - Mechanical properties for the module lid.