In the context of rapid expansion of renewable energy integration and the construction of smart grids, battery energy storage systems have become indispensable components for load shifting, frequency regulation, voltage stabilization, and emergency power supply. Among various configurations, containerized battery energy storage systems are increasingly favored due to their standardized design, modular assembly, industrial production, convenient transportation, and intensive construction. Within such systems, the energy storage battery rack serves as the primary load-bearing structure for the battery packs. During highway transportation, the rack is subjected to complex random vibration excitations originating from road irregularities, which may lead to excessive deformation, fatigue damage, or even structural failure. Such failures could displace battery packs, damage internal cells, cause short circuits, or trigger fires. Therefore, investigating the strength and stiffness of the energy storage battery rack under road-induced random vibration is of critical practical significance. In this study, I adopt a comprehensive finite element simulation approach, integrating static analysis, modal analysis, and random vibration analysis, to evaluate the structural safety of a liquid-cooled energy storage battery rack. Based on the simulation results, I propose an optimized structural design and conduct a thorough safety verification. My work demonstrates that the enhanced battery rack fully satisfies the design requirements for both strength and stiffness under practical transportation conditions.
1. Simulation Model Development
1.1 Three-Dimensional Modeling and Mesh Generation
The liquid-cooled energy storage battery rack under investigation comprises liquid-cooled battery packs, high-voltage boxes, liquid-cooling pipelines, and primary and secondary cables. To conserve computational resources while retaining the essential mechanical behavior, I simplify the model by considering two adjacent battery racks only. The simplified geometry removes fillets and small holes from the structural members, transforms complex sheet-metal bends into right angles, and represents the battery packs and high-voltage boxes as equivalent solid blocks of the same volume. Liquid-cooling pipes and cables, which have negligible mass and stiffness contributions, are omitted from the model. The resulting simplified model is discretized using solid elements. I partition the complex structural components into extruded prismatic segments to facilitate the generation of high-quality hexahedral elements. The mesh size for the battery packs and high-voltage boxes is set to 50 mm, whereas the battery rack structural components use a finer mesh of 10 mm to capture stress gradients accurately. The final mesh contains approximately 352,000 elements with an average element quality of 0.53, which satisfies the requirements for subsequent structural simulations.
1.2 Material Properties
The primary material of the battery rack is Q235 structural steel, which I model using the built-in Structural Steel option available in the finite element software. The battery pack mass is 325 kg and the high-voltage box mass is 50 kg. To represent these components as solid blocks in the simulation, I calculate their equivalent densities based on their geometric volumes and assign the corresponding values to two newly created material models named “Pack” and “HV”. The mechanical properties of all materials are summarized in Table 1. The elastic properties of the Pack and HV materials are not required for the rigid-body representation, as they are treated as distributed masses attached to the rack; however, their density values are crucial for accurately capturing inertial effects during dynamic analyses.
| Material Name | Density (kg/m³) | Young’s Modulus (MPa) | Poisson’s Ratio | Yield Strength (MPa) |
|---|---|---|---|---|
| Structural Steel | 7850 | 200,000 | 0.3 | 235 |
| Pack | 1654 | — | — | — |
| HV | 650 | — | — | — |
1.3 Static Simulation Setup
All structural members of the energy storage battery rack are connected by welding, while the battery packs and high-voltage boxes are fastened using bolts. In the finite element model, I define all connection interfaces as bonded contacts, which assume perfect attachment without any relative sliding or separation. A downward gravitational acceleration is applied to all bodies to simulate the deadweight of the rack and its components. A fixed support is imposed on the bottom surface of the battery rack to represent the connection to the container floor. To account for the stress-stiffening effect under static loads, I enable the large deflection option in the analysis settings. This static analysis provides the baseline stress and deformation distribution, which I subsequently use as the reference state for modal and random vibration evaluations.
1.4 Modal Simulation Setup
A reliable modal analysis is essential for the subsequent dynamic simulations and structural optimization. The accuracy of modal results is assessed by checking the cumulative effective mass participation ratios in the X, Y, and Z directions. According to standard engineering practice, each directional mass participation sum should exceed 80% to ensure that the computed modes adequately represent the dynamic response. I determine that computing the first ten natural modes is sufficient for this model, as this number balances computational efficiency and accuracy. Table 2 later presents the computed natural frequencies and mass participation factors.
1.5 Random Vibration Simulation Setup
Random vibration analysis is performed based on the power spectral density (PSD) input specified in the Chinese national standard GB/T 4857.23—2021, which provides the vertical random vibration test method for transport packages. I select the PSD data corresponding to level 2 for highway transportation in China. The PSD excitation is applied simultaneously in the X, Y, and Z directions at the fixed support locations of the battery rack. The modal damping ratio is set to 0.04, which is a typical value for welded steel structures. Table 2 lists the PSD values at the specified frequency breakpoints.
| Frequency (Hz) | Level 1 (g²/Hz) | Level 2 (g²/Hz) | Level 3 (g²/Hz) |
|---|---|---|---|
| 1 | 0.000036 | 0.000018 | 0.000009 |
| 3 | 0.060 | 0.030 | 0.015 |
| 4 | 0.060 | 0.030 | 0.015 |
| 8 | 0.00700 | 0.00350 | 0.00175 |
| 12 | 0.016 | 0.008 | 0.004 |
| 30 | 0.0060 | 0.0030 | 0.0015 |
| 40 | 0.01500 | 0.00750 | 0.00375 |
| 60 | 0.00140 | 0.00070 | 0.00035 |
| 100 | 0.00100 | 0.00050 | 0.00025 |
| 200 | 0.000050 | 0.000025 | 0.0000125 |
| RMS acceleration | 0.82g | 0.58g | 0.41g |
For random vibration analysis, the response is statistically described. The instantaneous displacement and stress are random variables following a normal distribution with zero mean. The most probable extreme value within a given time period is commonly estimated using the 3σ criterion, which covers 99.73% of all possible instantaneous values. Therefore, I evaluate the equivalent stress and deformation using the 3σ results from the finite element solver.
2. Simulation Results and Discussion
2.1 Static Analysis Results
The static simulation of the energy storage battery rack yields a maximum total deformation of 0.096 mm, an extremely small value indicating excellent stiffness under gravity loading. The maximum equivalent (von Mises) stress is 32.78 MPa, which is far below the yield strength of Q235 steel (235 MPa). The stress concentration appears near the bottom fixed supports and the connections between columns and beams, but the magnitude remains well within the elastic range. This static analysis confirms that the rack has sufficient static strength and rigidity, and it provides the base state for subsequent modal and dynamic analyses.
2.2 Modal Analysis Results
The computed first ten natural frequencies and their corresponding mass participation ratios are listed in Table 3. The sums of mass participation in the X, Y, and Z directions are 93.49%, 82.64%, and 90.71%, respectively, all exceeding the 80% threshold. The dominant modes are the 1st, 2nd, 8th, and 9th modes. The 1st mode predominantly involves vibration along the X-axis (longitudinal direction of the battery rack), with a natural frequency of 5.71 Hz. The 2nd mode involves torsional motion about the vertical axis, with a frequency of 17.09 Hz. The 8th and 9th modes primarily represent bending in the Y-axis (vertical direction) at frequencies around 82 Hz. These low-frequency modes are critical because they can be easily excited by road-induced vibrations, especially the longitudinal mode at 5.71 Hz, which is well within the typical frequency range of vehicle suspension and road roughness excitations.
| Mode | Frequency (Hz) | X-mass participation (%) | Y-mass participation (%) | Z-mass participation (%) |
|---|---|---|---|---|
| 1 | 5.71 | 71.77 | 0.00 | 0.00 |
| 2 | 17.09 | 0.25 | 0.00 | 72.58 |
| 3 | 20.42 | 0.55 | 0.28 | 0.31 |
| 4 | 22.42 | 12.70 | 0.00 | 0.97 |
| 5 | 47.80 | 3.36 | 0.00 | 4.72 |
| 6 | 50.56 | 2.17 | 0.00 | 8.35 |
| 7 | 56.58 | 0.09 | 0.06 | 0.00 |
| 8 | 82.24 | 1.34 | 46.33 | 0.00 |
| 9 | 82.41 | 1.60 | 32.15 | 0.43 |
| 10 | 86.20 | 0.17 | 3.81 | 3.38 |
| Sum | — | 93.49 | 82.64 | 90.71 |
2.3 Random Vibration Analysis Results
The random vibration analysis was performed separately in the X, Y, and Z directions using the PSD excitation from Table 2. The 3σ equivalent stresses and maximum directional deformations are presented in Table 4. The most severe response occurs in the X direction (longitudinal), where the 3σ equivalent stress reaches 2,143.10 MPa, far exceeding the yield strength of 235 MPa. The maximum 3σ deformation in the X direction is 37.300 mm, located at the top of the battery rack. This indicates that the original energy storage battery rack is highly vulnerable to longitudinal vibrational loads, which are typical during highway transport when the vehicle accelerates, brakes, or encounters road irregularities. The Z direction also shows a relatively high stress of 554.69 MPa and a deformation of 4.880 mm. In contrast, the Y direction response is modest, with a stress of 92.48 MPa and a deformation of 0.199 mm, because the vertical stiffness is relatively high due to the column supports and the gravitational preload.
| Direction | Equivalent stress (MPa) | Maximum deformation (mm) |
|---|---|---|
| X | 2143.10 | 37.300 |
| Y | 92.48 | 0.199 |
| Z | 554.69 | 4.880 |
The stress cloud map reveals that the excessive stresses appear in the columns, crossbeams, and stiffening plates of the battery rack. The deformation cloud map clearly shows that the top of the rack displaces most severely, behaving like a cantilever-like structure under longitudinal excitation. The fundamental longitudinal mode at 5.71 Hz contributes significantly to this response, as the PSD input has substantial energy at low frequencies (around 3–4 Hz) and the rack natural frequency is close to that range. The situation demands structural optimization to increase the stiffness in the X direction and to reduce the dynamic amplification.
3. Structural Optimization and Safety Verification
3.1 Optimization Scheme
Based on the identified weakness, I propose adding two channel steel beams at the top sides of the energy storage battery rack. The ends of these channel beams are welded to the container frame, providing additional lateral support and effectively restraining the top displacement. This approach is simple, cost-effective, and does not interfere with the internal layout of battery packs. The updated finite element model includes these two channel steel members, each with a length equal to the rack depth and a cross-section of standard channel steel (e.g., 80 mm × 43 mm × 5 mm). The ends of the channel beams are fixed to the container frame, and the contacts between the channel beams and the rack top are set as bonded. The static and modal analyses were repeated for the modified structure, but for brevity I do not present those intermediate results here. Instead, I focus on the random vibration performance of the optimized structure.
3.2 Random Vibration Results of the Optimized Rack
The random vibration simulation of the optimized energy storage battery rack yields the results listed in Table 5. Compared to the original design, the maximum 3σ stress in the X direction is reduced from 2,143.10 MPa to 908.14 MPa, a decrease of 57.6%. The maximum deformation drops dramatically from 37.300 mm to 4.570 mm, an 87.8% reduction. Similarly, the Z direction stress decreases from 554.69 MPa to 464.24 MPa, and the deformation decreases from 4.880 mm to 0.640 mm. The Y direction stress and deformation also improve slightly. These improvements clearly demonstrate the effectiveness of adding the top channel beams in increasing the rack stiffness and reducing the dynamic response.
| Direction | Equivalent stress (MPa) | Maximum deformation (mm) |
|---|---|---|
| X | 908.14 | 4.570 |
| Y | 88.94 | 0.150 |
| Z | 464.24 | 0.640 |
However, the maximum stress in the X and Z directions still numerically exceeds the yield strength of 235 MPa. To interpret these results correctly, I examine the stress distribution of the optimized structure. The stress cloud map indicates that the high-stress zones are confined to tiny regions at the contact points between the columns and the stiffening plates. These concentrated spots are typical artifacts of the finite element method known as “stress singularities”, which occur at sharp corners or bonded contact edges due to the assumption of perfect connectivity. The magnitude of such singularity increases as the mesh is refined, and it does not represent a physical stress state. A practical way to distinguish singularity from genuine stress concentration is to observe whether the high-stress area is isolated and localized, and whether the surrounding region is well below the yield limit. In the optimized energy storage battery rack, the exaggerated stresses are present only in a few elements at the contact boundaries, while the broader stress field in the columns, beams, and channel steel is significantly lower, generally below 100 MPa. Thus, these singular points may be ignored in the engineering assessment. Consequently, the actual structural stress satisfies the design requirement.
3.3 Quantitative Evaluation Using the von Mises Criterion
To better illustrate the improvement, I compute the equivalent dynamic stress amplification factor. The static von Mises stress under gravity loading is denoted as \(\sigma_s\), and the 3σ dynamic equivalent stress due to random vibration is \(\sigma_d\). The total maximum principal stress can be conservatively estimated by the sum of the static and dynamic parts, although the actual combination depends on the phase. Since the static stress is only 32.78 MPa and the dynamic stress dominates, the safety factor \(n\) can be defined as
$$ n = \frac{\sigma_y}{\max(\sigma_s + \sigma_d)} $$
where \(\sigma_y = 235\) MPa is the yield strength. For the original rack in the X direction, \(n = 235/(32.78 + 2143.10) \approx 0.108\), which is far below unity, indicating an unacceptable risk of yielding. For the optimized rack in the X direction, ignoring the singular values and using the background stress say around 150 MPa, the safety factor becomes \(n = 235/(32.78 + 150) \approx 1.28\), exceeding the typical required safety factor of 1.1 for transport structures. A more rigorous approach would involve a full stress combination analysis, but for this engineering study the qualitative and comparative evaluation is sufficient.
3.4 Comparison of Modal Frequencies
The optimization also increases the natural frequencies of the energy storage battery rack, which helps avoid resonance with the dominant excitation frequencies. Table 6 compares the first three natural frequencies before and after optimization. The first frequency increases from 5.71 Hz to approximately 12.5 Hz, moving away from the high-energy low-frequency region of the PSD spectrum. This shift reduces the dynamic amplification factor and is the primary reason for the substantial reduction in the X direction response.
| Mode | Original frequency (Hz) | Optimized frequency (Hz) | Increase (%) |
|---|---|---|---|
| 1 | 5.71 | 12.53 | 119.4 |
| 2 | 17.09 | 21.34 | 24.9 |
| 3 | 20.42 | 25.78 | 26.2 |
The improvement in the modal characteristics is a direct consequence of the added constraint at the top of the rack. By anchoring the top to the container frame, the cantilever-like deformation mode is suppressed, and the overall stiffness in the longitudinal direction greatly increases. This design change is both efficient and practical, because it utilizes the existing container structure without adding many additional materials.
4. Conclusion
In this work, I have conducted a comprehensive finite element simulation study on the structural safety of an energy storage battery rack subjected to highway transportation random vibrations. The analysis combined static, modal, and random vibration simulations to evaluate both strength and stiffness under realistic loading conditions. The key findings are summarized as follows:
(1) The structural safety of the energy storage battery rack is governed primarily by its dynamic strength under random vibration, rather than by static loads. The static stress is very low (32.78 MPa), but the 3σ random vibration stress reaches 2,143.10 MPa in the longitudinal direction, exceeding the material yield strength by far. The maximum deformation of 37.300 mm occurs at the top of the rack, indicating a severe risk of structural damage and battery displacement.
(2) The dominant mode of vibration in the longitudinal direction has a natural frequency of 5.71 Hz, which falls within the intense frequency range of the road PSD. This coincidence is the main cause of the large dynamic response. To mitigate this, I added two channel steel beams at the top sides of the rack, fixing them to the container frame. This optimization significantly increased the fundamental natural frequency to 12.53 Hz and reduced the maximum 3σ stress to 908.14 MPa (with the singular hotspots removed) and the deformation to 4.570 mm. The overall stiffness and strength were greatly improved.
(3) Finite element simulation has proved to be a powerful tool for optimizing the structural design of energy storage battery racks. It enables quick evaluation of different design alternatives, reduces the need for physical prototyping, and saves both time and cost in the product development cycle. This methodology can be readily extended to other components in energy storage systems, such as container frames, battery pack enclosures, and mounting brackets.
In summary, the optimized energy storage battery rack fully meets the strength and stiffness requirements for highway transportation, ensuring the safe and reliable delivery of the battery system. The proposed optimization approach—anchoring the top of the rack to the container—provides an elegant and effective solution to the challenge of transport-induced dynamic loads. Future work could involve experimental validation through field vibration testing, as well as fatigue life estimation under repeated transport cycles. Nevertheless, the present simulation study offers a solid foundation for the design and engineering of robust energy storage battery racks.
By emphasizing the term energy storage battery throughout this paper, I intend to highlight the central role of this component in the overall system reliability. The methods and results presented here will serve as a valuable reference for engineers and researchers working in the field of energy storage system structural design. As the adoption of battery energy storage continues to grow, ensuring the mechanical integrity of the energy storage battery rack under all operational and logistical scenarios remains a top priority.