There are a variety of commercial FE codes available on the market, the most common of which are ANSYS, COMSOL, ABAQUS and to a lesser extent ATILA. They can be generally categorised into implicit and explicit codes (see Q2). Some more detail with respect to ultrasonic applications and devices follows:

• ANSYS, COMSOL, ATILA are mainly implicit and harmonic based solvers which are inefficient for wave propagation problems. ANSYS and COMSOL are also less-specialised in the piezoelectric transduction/ultrasound markets and are more general use FE codes. ATILA is a little more experienced in ultrasound markets but is still limited to narrowband problems.
• ABAQUS does have an explicit time domain option but again do not specialise in the ultrasound/piezoelectric transduction markets and is not as efficient as PZFlex in terms of solve time.

PZFlex was designed to specialise in piezoelectric transduction and ultrasonic wave propagation problems and as a result of decades of experience we do these problems very well indeed. Our explicit time-domain approach results in rapid simulation times compared to the others, which is supported by our expertise in the applications themselves.

There are two main methods of time integration: implicit and explicit. Implicit time integration is the “classical” method of FEA, where one or more matrices are generated that couple the entire structure during solution. Although rapidly solved for small problems, an implicit approach results in a rapid increase in both computation power and memory requirements as the number of elements in a model increases. An explicit analysis does not require the matrices, which results in significant saving in computational power and memory required for medium- to large-scale problems. It is ideal for compact 2D and 3D models spanning tens of wavelengths on each side, which is typical for ultrasound applications.

There are many types of FEA, but the most useful types for the piezoelectric devices and elastic wave propagation dominant in ultrasonic transducers are “harmonic” and “transient” analyses.

Harmonic analyses examine steady-state device behaviour under continuous wave (CW) excitation. The data returned is the response at one particular frequency, so this is inherently a narrowband approach. Consequently, for commonly desired outputs such as electrical impedance versus frequency, multiple simulations must be performed. Transient analyses determine the time-domain response of a system to loading, whether impulse, constant, or CW. Output from such an analysis is identical to that which would be obtained from an experiment and so lends itself well to analyzing the response of real devices. In addition, time-domain techniques lend themselves well to such conditions as pulse-echo tests, non-linear responses, and non-sinusoidal drive conditions. The direct correlation to experiment and broadband potential of transient analyses make PZFlex the appropriate choice for analysis of ultrasonic devices.

From a single calculation:
- Pulse-echo or pitch-catch response
- Impedance/admittance spectra
- Displacement (mode) shapes
- TVR, FFVS, beam profile
- Pressure, displacement, stresses
- Voltage, charge, current

For more information see: http://www.pzflex.com/about.aspx

Of course! PZFlex is exclusively a transient analysis package, but given a well-designed model, Fourier techniques can take a single transient response and extract the device behaviour at all frequencies of interest—it is inherently a broadband approach.

Most other FE codes use their own custom meshing programs in order to discretise their models. These generate complex elements shapes that map to the exact shape of the device whereas PZFlex mostly uses rectangular elements to represent an approximation of the shape. At first glance these elements seem to represent a shape with more accuracy; however this is not always the case. If one removes the lines connecting the elements then the perceived differences between the two approaches quickly diminish and you are left with a collection of nodes contained within the shape you wish to model. The advantage of standard grid with rectangular elements now becomes clearer as both models have a similar amount of nodes but the standard grid can be 10-20 times faster to solve due to the less-complex elements involved.

A useful analogy for why rectangular grids retain accuracy for complex surfaces is how pixels in a monitor make an image. When one looks extremely closely the individual pixels are discernable, yet when one steps back to a distance they blend together to create seamless images. This larger image, or shape, is what a wave ‘sees’ when it encounters these sufficiently small elements in a model.  

Finite Difference methods are a simple and straightforward method of implementing a numerical solution method, however can result in some difficulties in practical use. The element size in the model is fixed across the entire grid, meaning the boundaries of materials can be difficult to place accurately, and excess meshing may be required if certain model components are particularly small. There are also some difficulties in applying boundary conditions in a straightforward manner.

While there are potentially some small reductions in efficiency, the versatility offered by Finite element approaches in ensuring the material boundaries are located exactly and that boundary conditions are simply applied, mean FE is a more practical method then FD for most problems.

With every FE software package there is a learning curve that must be tackled. Each package has their idiosyncrasies and PZFlex is no different. It is primarily a syntax based package (similar to ANSYS) and a degree of practice is required in order to get the most out of it. However, we at PZFlex are constantly striving to make the code more user-friendly.

To this end we have recently introduced an extremely palatable GUI front-end for text editing and file manipulation. This has been further augmented through Design Wizards for simple implementation of common problems and the addition of a SolidWorks license and model import tool for bringing CAD designs into the PZFlex environment.

We also provide comprehensive training and code support that is akin to one-to-one tutorials through e-mail and phone.

FIELD II is based in linear systems whereby if you have the impulse response of a transducer (or a reflector in the field and using reciprocity) you can calculate the linear output response generated by your chosen input. It is an effective package for simulations in linear isotropic media with simple representations of transducers acting as the source.

With PZFlex you can extend these capabilities significantly:

• models no longer limited to linear systems (e.g. HIFU)
• transducers in a load can be modelled directly in order to capture complete behaviour characteristics
• complex transmission media can be represented as can anisotropic materials
• full 3D models are accessible
• mode conversions is solids are simulated
• thermal analysis

In other words, if you would like to model not only the device itself, but the resultant field and any interactions with objects therein then PZFlex is preferable.

Modern Finite Element codes are significant efforts, usually totalling 10s of man-years of work, across multiple disciplines. Continuing Quality Assurance and development become full time efforts in themselves, and continuity of support over many years becomes critical in effective use. For small, simple projects where understanding the development procedure is important then writing your own FE code is viable – however in any situation where the aim is practical problem solving in the short term then a commercially developed and supported FE code is the simplest solution and most likely to yield useful results.

You can, as long as your problems are in 1D! Taking a piezoelectric transducer as an example, as 1D analysis only accounts for behaviour in a single direction the extensive lateral behaviour of such devices goes completely unrepresented. This has a significant impact on the final accuracy of metrics such electrical impedance plots, surface displacement profiles and ultimately field behaviour.

For more information and examples see: http://www.pzflex.com/support_papers_bysubject.aspx?s=1

Many packages use different algorithms to solve the physics of wave propagation in different media – for example the acoustic fluid may have a different formulation for pressure application than the piezoelectric solid – and so some form of coupling is needed to translate the behaviour of one component to the other. This is often due to features being added to packages over time for simulations they were never originally intended to do.

PZFlex was written for wave propagation from the outset and so simply solves for the appropriate physics in each material, with everything formulated in a common manner. This allows for seamless transition of waves from one type of material to the other with no need for user intervention.

Yes. PZFlex has a variety of data export options that are compatible with import into MATLAB. The most common of which is the comma delimited option. PZFlex also has its own post-processing software and GUI for those who do not have or require more advanced mathematical packages.

When you buy PZFlex you now receive a parts and assembly copy of SolidWorks at no extra charge. This allows you to:

• build your own 2D and 3D models
• view other CAD models in the SolidWorks environment
• convert other CAD formats to STL files for import into the PZFlex environment

Yes, providing material properties are known. There is also a simple tool in PZFlex that allows the orientation of the material with respect to the global axis. This is particularly useful when looking to simulate particular orientations of piezoelectric crystals and even weld grain structures for NDT purposes.

Yes, PZFlex allows users to input their own material properties for a wide range of materials including damping and thermal components. In recent versions of the package this has been simplified even further with the addition of the matrix conversions tools for translating between compliance and stiffness matrices for piezoelectric materials.

Quite simply FEA is only as accurate as the data that goes into the model and at the most fundamental level this data is contained within the material property definitions. We here are PZFlex are very aware of how material property variations can affect results. We therefore spend a great deal of effort to make sure that the material properties database we supply free provides information from the most reliable sources we have access to.

Most definitely not. As explained in the explicit vs implicit question (Q2) as wave propagation models get larger they are more suited to an explicit approach – the graphs below perfectly illustrate this distinction.

For more information see: http://www.pzflex.com/support_papers_bysubject.aspx?s=1

Only in special circumstances would we provide this option. As computing power increases and price decreases, the capabilities of PZFlex operating on a typical desktop PC increase substantially. For the majority of applications a high-end desktop PC will provide both enough RAM and CPU power for 100million element models to run in less than a day. For larger, complex, bespoke problems we would provide the option for the customer to purchase hardware along with the code. This would be decided upon consultation with PZFlex staff.

Yes. Due to our decades of experience in a variety of ultrasonic and related disciplines we have accumulated a library of example models to help users achieve their goals. We are happy to provide such examples to users as part of our extensive customer support package. If we don’t have a model specific to your application, chances are we would put an example together in order to get you started! Think of it like a ‘free’ consultancy when you purchase PZFlex.

Yes, there are a limited number of tutorials that describe the use of some of the Wizards in video format. As we extend the Wizard library we will also extend the tutorials. In the near future we will also be creating video tutorials/training for other aspects of PZFlex use outside the Wizards.

Flex has been used for nearly 30 years for analysing highly nonlinear wave propagation problems for the US Government, and for nearly 20 in the analysis of ultrasound for medical, SONAR, and NDT problems. No other commercial FE group has the combined experience of PZFlex staff in the modelling of ultrasound and piezoelectric devices.

There are numerous options with PZFlex, as well as significant discounts for academic use, and special payment terms are available upon request. We are very flexible on this and will do what we can to help as much as possible. Please contact your local distributor for detailed pricing information:

http://www.pzflex.com/about_licensing.aspx
http://www.pzflex.com/contact.aspx

Unfortunately we do not provide trial versions of the software as we have found that potential users do not get the maximum benefit out of the package without some degree of training from PZFlex engineers. To counter this, if you are interested in PZFlex and you can provide a simple example of what you would like to model then we will happily put one together to demonstrate capability. For more information contact us here: http://www.pzflex.com/contact.aspx

PZFlex is extremely efficient in the use of memory and can construct models far larger than any competing method. While model size can vary with what is being modelled, it is possible to run 3D models over 100 million elements in size on a desktop PC with 8 GB RAM in a few short hours.

PZFlex comes with a SolidWorks Parts and Assemblies license which you can then use to generate the .stl files required for importation into the model. Yes, you can modify the model in any number of ways if you choose. This does require some knowledge of how to write PZFlex models however, but the training and support will help you with this.

Yes, providing there is enough memory on the system (RAM) to facilitate. Remember that post-processing requires far less memory than the calculation.

Yes, we have the facility to 'batch' a number of jobs to run sequentially or in a looped sequence for parameter studies.