Finite Element Analysis with Cloud-Based High-Performance Computing

The Importance of Finite Element Analysis in Engineering

Finite Element Analysis (FEA) has become an indispensable tool in engineering, enabling professionals to predict how products will perform under real-world forces, vibration, heat, and other physical effects. However, the computational power required to conduct complex simulations has historically been a limiting factor. Enter cloud high performance computing (HPC), changing the landscape by providing scalable, turnkey, and cost-effective computational capabilities. 

This blog delves into the synergistic relationship between FEA and cloud HPC, exploring how this pairing propels industries into a new era of innovation and efficiency.

Understanding Finite Element Analysis

Finite Element Analysis (FEA) is a sophisticated computational technique for predicting and analyzing the physical behavior of structures and systems under various conditions. It starts by defining the geometry of the solid in its unloaded condition and considering other factors like initial stress fields, elastic constants, thermal expansion coefficients, and body force distribution. The boundary conditions specify displacements or tractions on the solid’s boundary.

The core principle used in FEA is the principle of virtual work, which allows for the calculation of displacements, strains, and stresses in an integral form, replacing the derivatives in the partial differential equations of equilibrium with an equivalent integral. This approach is adaptable to dynamic problems, other stress-strain laws, and significant shape changes. In essence, the principle of virtual work states that the work done by external forces on a virtual displacement is equal to the work done by internal stresses on a virtual strain. This principle simplifies the complex problem of equilibrium into a more manageable form, making it easier to solve numerically. Additionally, it provides a robust framework for handling various types of loading and boundary conditions in FEA.

To implement FEA, the displacement field is discretized, meaning, it is calculated at a set of discrete points (nodes) within the solid. The displacement field at any point within the solid is then interpolated between these nodal values. This approach requires a careful choice of interpolation scheme. For instance, linear interpolation might be used between nodes on a 2-noded element, and quadratic interpolation for a 3-noded element.

The finite element method involves substituting these interpolated fields into the virtual work equation. This leads to the forming of a stiffness matrix and a force vector, which are fundamental components in FEA. The stiffness matrix is a function of the elastic properties of the solid, its geometry, and the interpolation functions and nodal positions. The process of FEA involves defining element stiffness matrices and element force matrices for each element, based on their geometry, interpolation functions, and material properties. These individual element matrices are then summed to form the global stiffness matrix.Finally, numerical integration techniques, such as the quadrature formula, compute the integrals for each element stiffness matrix. This step involves mapping the integration domain and calculating the shape function derivatives in the element stiffness matrix. Learn more about finite element analysis from solidmechanics.org

Commercial Finite Element Analysis Solutions vs Open Source Solutions

The history of FEA software began in the 1940s with the development of methods for calculating aircraft structures. It evolved in the 1960s with the creation of NASTRAN by NASA, a significant milestone that made FEA more accessible. Since then, both commercial and open-source FEA tools have proliferated, driven by advancements in computing power and a growing understanding of complex materials and phenomena. 

The rise of open-source FEA software is largely driven by its cost-effectiveness and the growing community of users and developers who contribute to its improvement. As computational resources become more accessible and the need for concept testing with simulations grows, engineers and researchers are turning to open-source options that allow them to run a massive number of simulations without licensing costs. This trend is further bolstered by the sharing of knowledge and solutions within the community, promoting innovation and making advanced simulation capabilities more accessible to a wider audience.

Rescale offers a library of different software that is already integrated with the latest cloud providers. For example, Abaqus is a popular FEA software package for highly nonlinear finite element analysis like the deformation in soft deformable materials like seals. Ansys Mechanical is very popular for linear dynamics like vibrating turbines, while Ansys Ls Dyna is popular for high velocity dynamic events like crash testing of cars. Other related simulations include MSC Adams which is a multi-body dynamics software that can work in combination with FEA to calculate the motion of objects such as cars, trains and aircraft. For example, MSC Adams can be used to predict handling and roll-over possibilities given different driving scenarios.

New Developments in FEA: Hybrid FEM-NN (Finite Element Method – Neural Network)

Hybrid FEM-NN (Finite Element Method – Neural Network) models represent a cutting-edge approach in computational physics, merging the robustness of traditional FEM with the adaptive learning capabilities of neural networks (NNs). By combining the structured, physics-based modeling of FEM with the adaptive, data-driven capabilities of neural networks, these hybrid models can offer improved accuracy, efficiency, and generalization over complex domains. This makes them particularly valuable for solving problems where traditional methods are computationally intensive or where the underlying physics are partially unknown or difficult to model.

This methodology involves integrating NNs into the FEM framework to enhance the modeling and prediction of complex systems governed by partial differential equations (PDEs). It allows for the training of neural networks while adhering to the constraints of PDEs, leading to more accurate and efficient solutions for both stationary and transient problems. Hybrid FEM-NN models are particularly effective in recovering coefficients and missing PDE operators from observations, demonstrating their potential in various complex applications, including dynamic and nonlinear systems. To learn more about an overview of neural networks and the potential of AI Physics, check out our other blog here.

Accelerate Finite Element Analysis with Cloud HPC

Cloud HPC provides on-demand, scalable computing resources ideally suited for heavy workloads like FEA. Because FEA requires solving large matrices of equations, it can be a heavy workload, meaning it can benefit from parallel processing of the matrices. It offers a significant shift from traditional on-premise HPC solutions, eliminating the need for massive capital investments in infrastructure and reducing the time to procure and set up hardware. Cloud HPC platforms like Rescale offer tailored environments for FEA applications, ensuring optimal performance and efficiency.

Scalability and Flexibility

Unlike on-premises infrastructure, Cloud HPC is inherently elastic, meaning it can scale up and down as needs change. This elasticity allows organizations to subscribe for more computing power as needed, ensuring full utilization without the constraints of capped capacity. This scalability is crucial for cost-effective operations, ensuring that organizations only pay for the resources they need when they need them.

Enhanced Performance

With access to cutting-edge processors and high-speed networks, FEA tasks on Cloud HPC are completed faster, leading to quicker design iterations and reduced time to market. The ability to run multiple simulations in parallel further accelerates the R&D process.

Collaborative and Secure Environment

Cloud platforms facilitate collaboration among distributed teams by providing centralized access to data and tools. Advanced security measures protect sensitive data, which is crucial for industries with stringent compliance requirements.

Challenges and Considerations for Finite Element Analysts and Engineering Managers

Data Management

Majority of organizations that use FEA for simulation face significant challenges in maintaining a coherent connection between their engineering data and the activities that generated it. This disconnect renders the data only as useful as the memory of the creator, leading to substantial risks and inefficiencies if that knowledge is lost, for instance, due to staff turnover​​. Cross-functional teams encounter difficulties in obtaining a comprehensive view of product efforts, hindered by fragmented and siloed data storage and a lack of shared context. The use of different simulation tools across teams further complicates data sharing and alignment​​.

Furthermore, many R&D activities are found to be redundant or unnecessary, consuming valuable resources without contributing meaningfully to innovation. This inefficiency is largely attributed to opaque product decisions, where the rationale behind design choices is undocumented or unclear to other teams. As the move towards AI-generated designs and decision-making accelerates, the need for high-quality, traceable data to ensure the accuracy of AI models becomes paramount​​. These challenges underscore the need for a more integrated and strategic approach to Metadata management in R&D, one that can support the swift and innovative development processes required in modern engineering environments.

Integration of Finite Element Analysis with Existing Workflows

Integrating cloud-based high-performance computing (HPC) with existing finite element analysis (FEA) workflows can be seamless with the right approach. By leveraging cloud HPC, organizations can enhance their existing processes without significant disruptions. Cloud HPC platforms are designed to integrate with popular FEA software, ensuring compatibility and ease of use. Engineers can continue using their familiar tools while benefiting from the added computational power and scalability of the cloud. This integration not only boosts productivity but also enables more complex simulations that were previously not feasible due to hardware limitations.

Cost Management

Managing costs is a critical consideration when adopting cloud HPC for FEA. While cloud solutions can offer significant savings by eliminating the need for large capital expenditures on hardware, they also introduce variable costs based on usage. Organizations need to implement effective cost management strategies to maximize the benefits. This includes optimizing resource usage, leveraging spot instances, and taking advantage of cloud provider discounts. Additionally, using cloud management tools to monitor and control spending can help ensure that the cloud HPC usage remains within budget, providing a clear understanding of the cost-benefit ratio of cloud-based FEA.

Application Management 

Application management on the Rescale platform is designed to streamline the deployment and oversight of complex engineering and scientific applications in the cloud. With Rescale, users can seamlessly integrate and optimize applications for high-performance computing (HPC) environments, ensuring efficient performance across various cloud providers. The platform supports a wide range of software, from commercial packages to open-source tools, and offers automated updates and robust version control to keep applications current and secure. Additionally, Rescale facilitates comprehensive benchmarking to evaluate and optimize application performance, enabling users to select the best configurations for their workloads. License management is also simplified, allowing for the tracking and allocation of software licenses to ensure compliance and cost-effectiveness. With Rescale’s intuitive interface and powerful orchestration capabilities, users can easily manage scaling, monitoring, and resource allocation, allowing engineers and scientists to focus on innovation rather than infrastructure management. By leveraging these features, organizations can accelerate their R&D efforts, reduce time-to-market, and achieve greater computational efficiency.

Real-world Applications of Finite Element Analysis

Aerospace and Defense

In an industry where safety and precision are paramount, FEA on Cloud HPC enables engineers to simulate and analyze complex components and systems, from jet engines to entire aircraft structures, leading to safer, more efficient designs. See how Exosonic is revolutionizing supersonic travel.

Automotive

Car manufacturers use FEA and Cloud HPC to simulate crash tests, aerodynamics, and engine performance. This reduces the need for physical prototypes, saving time and money, and leads to vehicles with better performance and safety features. See how Rescale is helping a global auto parts maker become more agile and competitive.

Energy

For renewable energy sources like wind turbines, FEA helps optimize designs for maximum efficiency and durability. Cloud HPC’s scalability allows for the simulation of various environmental conditions to ensure reliability and performance. See how NOV goes all-in on cloud HPC to unlock engineering productivity and manage growth.

Conclusion

Integrating Finite Element Analysis with Cloud High-Performance Computing is ushering in a new era of engineering and design. The scalability, speed, and cost-effectiveness of Cloud HPC make it an ideal partner for FEA’s computationally intensive tasks. As industries continue to embrace this powerful combination, we expect to see more innovative designs, faster time to market, and efficient use of resources. The future of engineering is here, and it’s powered by the synergy between FEA and Cloud HPC.