Plenary speakers

The role of engineering analysis in product development is in the middle of a dramatic paradigm shift.

The first phase of engineering analysis was characterized by hand calculations and pioneering finite element calculations, suitable for little more than preliminary dimensioning and gaining engineering understanding of a product.

In the second phase, computer aided engineering, engineering analysis was used to predict hardware test results as accurately as possible. This has made product development more efficient and accelerated product development cycles.

The third phase is the complete digital transformation of the whole product life cycle:

• Virtual verification, validation, and certification eliminates the need to use hardware testing as the final confirmation of an OK result. Instead, we test to gather information in the most efficient way.

• Digital twins create interaction between the physical and virtual worlds, fusioning data from many sources.

• Creation of new, digital and digital-enhanced products.

• Convergence of different modeling domains: physical, statistical, ML / data driven.

This shifting role of engineering analysis makes simulation governance more and more important: We need to establish processes and quality management systems such as NAFEMS ESQMS to ensure the predictive power of simulation results, and we need to quantify the uncertainty of our predictions.

Bayesian machine learning methods are an ideal extension of engineering analysis to quantify uncertainty. They are the product of a similar transformation in the field of statistics, from frequentist hand calculations to solving general statistical models through numerical solution procedures such as Markov Chain Monte Carlo. This presentation will illustrate these general trends with specific application examples that show the convergence of physical and statistical modelling.

Virtual Product Development (VPD) is an interdisciplinary, finite element method based, alternative to the traditional, mostly empirical approach produce-try-correct a prototype. VPD or CAE (Computer Aided Engineering) is widely used in many industries for product development. Knowledge of mechanics, modelling of material properties, product design principles and use of dedicated software packages are needed for this interdisciplinary approach. To utilize its advantages entirely, it is smart to employ VPD early in the product development process for what-if parametric and sensitivity studies of design variants and material choices. Virtual prototypes of a product are virtually tested in obtain insight into performance of a product in conditions close to those in service. Less physical prototyping and testing, and less guesswork are needed. Increased design quality and reliability of products is achieved at reduced development costs. Geometry and elastomeric materials of rubber products exhibit mostly nonlinear behaviour. Elastomeric materials are nearly incompressible. Their progressive-degressive hyperelastic stress-strain relationship may be almost reversible upon unloading leaving a certain hysteresis. Such mechanical properties can be handled by finite elements of the Herrmann formulation. Mechanical and thermo-mechanical material properties are described by a material model, where parameters and exponents may be computed from experimental data. VPD of some technical rubber products and motorcycle tires are presented and explained along with experimental verification.

Fundamental mathematical features of external finite element approximations (EFEA) are discussed. It is shown that the features make EFEA well suitable for industrial software implementations. Robustness, speed, and accuracy of the simulations come from alternative definitions of degrees of freedom (DOF), use of always complete spaces of approximation functions, exact integration in a physical space, and decoupling of the function definitions from geometry. It is also shown that alternative DOF can be associated with arbitrary geometrical entities including ragged surfaces, point clouds, and sub-volumes. This makes software implementations extremely robust in handling assemblies with such classic geometry imperfections like misalignments, excessive gaps/penetrations, corrupt and untrimmed geometries, etc. Therefore, EFEA technology can be a perfect foundation for development of FEA software oriented towards users from almost none to a very modest experience in simulations. The alternative definition of DOF also allows to construct highly adaptive schemes of the computations which results in significant reduction in equation system size, speedup of the computations, and small memory footprint. Another benefit of geometry-functions decoupling is the possibility to construct approximation functions which are traditionally problematic for conventional Finite Element Analysis like divergence-free functions, or function which meet governing differential equations of a Boundary Value Problem. This results in further reduction of the equation system size, improved accuracy, and unconditionally stable numerical solutions.

The presentation will discuss the latest research results related to the implementation of the finite element method (FEM) - especially in its new, multi-stage approach - for the design, modeling, and analysis of systems with an electromagnetic field. The history of the development of numerical methods used in modeling electromagnetic phenomena will be presented. Next, field methods for describing electromagnetic phenomena and equations describing the electromagnetic field distribution in systems with conduction currents and dielectric shift currents will be discussed. The definition of the generalized element used in the multi-stage approach will be provided, along with mesh models of systems with electromagnetic fields used in modeling systems through the multi-stage FEM approach. However, special emphasis will be placed on the modeling and analysis of systems widely used in technology and industry, including electric drives (e.g., electric motors with permanent magnets), elevator systems (e.g., special converters, executive actuators, etc.), and systems used in power systems (e.g., variable inductance inductor); as well as in medicine, particularly in modeling the phenomena of magnetic hyperthermia, which finds applications in the destruction of cancer cells.