Prediction & Analysis

Numerical modelling predicts the response of a system to certain conditions to analyse the physics of complex real-world situations. Using this approach, engineers and designers can study behaviours that are impractical or impossible to realise experimentally, with complete control and in comprehensive detail.

Full Matrix offers simulation services as well as more in-depth analysis from experienced scientists.

Finite Element Analysis

Finite element analysis (FEA) is a computational method for simulating the physics of complex systems and is commonly used for acoustics, mechanical, thermal and electromagnetic calculations.

For problems specific to ultrasonic inspection of pipes or plates, Full Matrix has developed its own in-house code, FM-FEM.

Significant cost and performance advantages are achieved with FM-FEM by making use of open-source solvers to run efficiently on multiple cores. Alternatively, several different models can be calculated in parallel to generate significant quantities of training data for machine learning approaches.

For problems with more complex requirements Full Matrix offers bespoke FEA modelling services.

Finite element simulation tools are invaluable for understanding the interaction of waves in complex geometries. At Full Matrix, this modelling capability is employed to design and optimise new inspection procedures, as well as understanding the behaviour of scattering caused by defects.

FEA simulations capture details which are not easily derived from analytical calculations, such as the influence of irregular geometries, or the complex behaviour of mode conversion at interfaces.

The natural frequencies of an object dictate how it will move when excited. FEA can reveal the modal behaviour and deflection patterns of components with complex geometries, to better understand their dynamic response.

The results of this analysis allow designers to predict resonant conditions to be avoided, and modify components to mitigate the risk of failure from excessive vibrations. In appropriate conditions, it is even possible to calculate the guided waves modes in certain structures, and infer their velocity and dispersion.

Finite element analysis can be used to predict the way heat flows through structures, taking into account losses such as radiation and convection. Additionally, FEA can be used to predict the resulting stresses caused by mechanical loading.

One example of combining the two is simulation of welding where user-subroutines are generated to simulate a moving heat source that represents the welding torch. Then, the predicted thermal history can be fed into a stress analysis to predict the residual stress and distortion. Models like this can be used to optimise processes for reducing stress and/or distortion such as trailing cooling behind the weld.

Numerical simulations are extremely valuable for calculating electric and magnetic fields, currents and forces around components. The finite element technique particularly excels at simulating electromagnetic phenomena at high-frequencies, such as the inductive forces produced by EMAT transducers.

The results of these simulations are core to the design process of Full Matrix EMAT transducers, reducing the need to expend energy on costly physical prototypes. Equally, electromagnetic FEA calculations offer great utility for the design of other electrical or magnetic systems.

Analytical and Semi-Analytical Modelling

In cases where the geometry of a problem can be simplified, alternative methods can significantly reduce computation time. These include reduced order models that are highly suited to pipes with long straight sections coupled with bends and an analytical method for rapid dispersion curve computation of pipes.

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