Finite Element Solutions

Push the limits of Finite Element Analysis

Weidlinger Associates, Inc. (www.wai.com), is a 300-person structural engineering firm that designs and rehabilitates buildings, bridges, and infrastructure and provides special services in applied science, forensics, and physical security. The firm, which celebrated its 60th year in 2009, is recognized worldwide for its innovative and practical design solutions and for its long-term commitment to advancing the state of the art in engineering. Headquartered in New York City, the firm has branch offices in the United States and the United Kingdom.

PZFlex® is the registered trademark of Weidlinger’s Finite Element software, which is first in world markets for medical therapeutics and sonar. It is the program of choice for all major U.S. and Japanese medical transducer manufacturers, as well as for scientists at prominent academic institutions engaged in studies of diagnostic and therapeutic medical ultrasound. Developed in the 1980s to improve the modeling of ultrasonic probes, PZFlex quickly became the most versatile member of a family of codes (Flex) used to solve huge wave-propagation problems for the U.S. government. During the past two decades of intensive development, PZFlex has spawned numerous applications and attracted increasing numbers of clients.

4 Introduction

6 FEA for Ultrasound

8 Medical Ultrasound

10 Therapeutics and HIFU

12 NDE/ NDT

14 Sonar

16 MEMS

18 Sensors and Actuators

20 Academic Research

22 Solvers

28 Add-On Modules

30 Features

32 Capabilities

38 Feature Matrix

39 Additional Information

4

Welcome to the world of PZFlex, the premier finite element analysis software specifically designed for piezoelectricand wave-propagation applications.

PZFlex was originally developed to model ultrasonic probes, but it has proven a popular choice for creative engineers everywhere. Designed by engineers with advanced degrees in acoustics and more than 30 years of modeling experience, it can be used to simulate any product: commercial, esoteric, fully developed, or only in the dream stage. Whether you are new to virtual prototyping or an old hand, we invite you to find out more about PZFlex and join the community of dedicated professionals who use it.

Pressure field from a piezoelectric HIFU transducer

6

FEA for Ultrasound

Finite element modeling (FEM), sometimes referred to as finite element analysis (FEA), is used to simulate real-world objects for a variety of purposes—from designing new engines to visualizing the effects of loads on building components. FEM paints a very precise picture of a structure and its effects by breaking it down into millions of pieces and subjecting the pieces to real-life stresses and strains. A PZFlex model, rich in detail and localized to small groups of elements, allows you to look inside a device and understand better what is happening to it as you experiment with different design parameters and configurations. The simulations you construct are excellent substitutes for physical models, which are kept to a minimum. With in-depth knowledge of how your device operates in multiple environments, you can optimize performance and pinpoint problems that may compromise production.

“The speed and versatility of PZFlex for piezoelectric device modeling is astounding.” David J Powell, PhD, Project Manager, Sparton Electronics

Develop new products in hours, not weeks.

DesignProcess Improvement

Rapid identification of process-induced defects and how they alter performance metrics from specification is invaluable in today’s competitive world of fabrication. PZFlex provides a powerful tool for predicting how deviating from the ideal can affect performance. By leveraging the speed and versatility of PZFlex, customers can predict the effect common fabrication problems may have on the final product and gain a better understanding of acceptable tolerances.

Blue Sky Ideas

PZFlex offers the user a virtual laboratory with which to conduct wide ranging tests that would be too expensive or time-consuming to perform at the conceptual stage. This allows the user to generate tangible results from “blue sky” designs that would otherwise not be possible. Couple this with the processing power offered by PZFlex, and new ideas can be progressed from concept to prototype in a vastly reduced time frame.

Product Design Optimisation

Delivering a product to market can be a long and expensive journey, especially for small to medium sized companies. Reducing the number of prototypes required in a particular product cycle is a guaranteed method of minimising cost and exposure to dynamic market forces. PZFlex has been a pioneer in product design optimisation in the ultrasound industry for over 20 years and can help reduce the number of prototypes in a cycle by over 90%.

8

Medical Ultrasound

Although ultrasonic investigations took place in Japan as early as 1917, the pioneering work of Heiichi Nukiyama and others was relatively unknown in the U.S. and Europe until the 1950s. Japan shared its research on detecting masses inside the body, then researchers in the U.S., Sweden, and Scotland advanced the field in the late 1950s. At the time, their machines produced only still pictures of the body, whereas today’s machines can turn out real-time moving images.

PZFlex has played a significant role in this progress. The software has won widespread acceptance in the biomedical imaging industry and is used by large international companies such as Philips, GE, Siemens, and Hitachi. It has supported years of ultrasonic probe design and experimental verification studies, earning the confidence of designers who depend on the accuracy of its theoretical predictions. It has facilitated the development of new imaging arrays and the optimization of designs, while reducing dependency on the building of costly physical test devices.

Improve your focus.

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Sub-diced high-frequency array Catheter probePressure in catheter elements

10

Therapeutics and HIFU

PZFlex is the medical industry’s premier tool for modeling ultrasound’s pulsed and continuous-wave operation, nonlinear propagation (using B/A properties), frequency-dependent attenuation, and thermal effects over time. The software is used to design and improve HIFU transducers and plays an important role in gathering 3D anatomic information for exact tumor targeting. It is used to visualize the beam path through tissue layers and to predict, monitor, and control the probe’s motion, tracking, and heat generation. Forecasting the beam’s absolute location and its effects ensures more precise positioning of the focal point and better control over exposure times, increasing patient safety.

PZFlex has also added capability for acoustic radiation force (ARF) calculations, which compute the small DC force that accumulates on particles due to the mechanical energy deposited over thousands of cycles. These stresses can then be used to simulate realistic tissue deformation and displacement (shear wave imaging).

Power new treatments.

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HIFU Beam in Tissue Map3D Curved ArrayNonlinear Pulse in Tissue

12

NDE/NDT

PZFlex is used in various NDE/NDT applications, from modeling transducers to predicting acoustic wave propagation through structures. Substantial work has been carried out regarding the propagation of Lamb waves and their interaction with defects in plate and pipe structures. PZFlex is also well suited to aid in the NDE/NDT community’s application of imaging techniques developed by the biomedical industry, such as multi-element arrays and acoustic beam steering, for which traditional analytical methods are inadequate, especially when performed on advanced structures and materials such as carbon-fiber composites and anisotropic welds.

PZFlex’s rapid simulation times have eliminated the requirement for expensive bespoke test pieces for creating new inspection techniques. Inspection scenarios can now be rapidly simulated in the virtual environment. For example, full matrix capture (FMC) datasets for 1D and 2D arrays are available in minutes using proprietary parallel processing techniques.

Find the hidden flaws.

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Inspection of Turbine BladeShear-Wave Phased Array with WedgeMultiple Phased Array Inspection of Rail

14

Sonar

PZFlex has been used extensively in the design of sonar arrays for mine hunting and the underwater detection and evaluation of surface ships and submarines. Dependence on substantial submarine fleets is a key factor in sonar remaining a top priority for major world powers. PZFlex was substantially improved by tightly tying our development process to feedback from commercial sonar manufacturers. The specialized manner in which the software was implemented facilitates solving large numerical problems, giving designers valuable insight into sonar’s theoretical capabilities.

PZFlex provides the users with a set of intuitive GUI transducer design wizards that incorporate many of the common transducer arrangements found in sonar devices. These toolkits were developed in conjunction with the U.S. Navy and have been validated by suppliers. In addition, PZFlex now also boasts a rapid 3D extrapolation and visualisation tool to supply users with a simple means to create and display their beam profiles.

Sound out the obstacle.

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Nine-element hexagonal tonpilz array Stave projector displacementLarge curved projector

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MEMs and Fi lters

From the accelerometer that deploys the airbag in your car to the filter in your cellphone, micro-electro mechanical systems (MEMS) are all around you and increasing in number. They are built to scales of a few microns or even less (the diameter of a human hair is about 100 microns) using semiconductor manufacturing processes. Of growing interest to sensor, actuator, and transducer design engineers, MEMS are welcomed for the new and exciting opportunities they offer.

Unfortunately, today’s engineers with an eye on the MEMS of the future find market entry blocked by the significant investment in manufacturing equipment required. Unlike previous generations of inventors, who could build and develop new devices in their garages on shoestring budgets, these designers are at a significant disadvantage compared with the large industrial corporations. Fortunately, PZFlex’s simulation capabilities extend to MEMS and support rapid virtual prototyping, permitting development of a new design on a desktop PC within hours.

Build a miniature world.

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Phononic Crystal CellTypical 2D SMRDisplacement from membrane sensor

18

Sensors and Actuators

Sensors and actuators are transducers that respond to physical stimuli and transmit the impulses to another medium for measurement where the active element is typically a piezoelectric ceramic. The first piezoceramic in general use, made of barium titanate, was superseded in the 1960s by one made of lead zirconate titanate (PZT). Newer materials, such as piezopolymers, single crystals, and composites, have presented a range of new challenges for designers.

PZFlex provides accurate and quantitatively meaningful results for the increasing numbers of sensors and actuators for which piezoceramic materials are the active component. Acoustic beam patterns, impedance characteristics, and thermal properties are obtainable from its fast and efficient electromechanical solvers, designed to handle this particular class of modeling problem. Applications range from piezoelectric stacks used by astronomers in deformable mirrors, to needle hydrophones used in acoustic calibration.

See inside the problem.

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Displacement from matrix array element 3D Piezoelectric Horn Transducer2D Array Element Displacement

20

Academic Research

Technological innovation and development is continuing at an ever-increasing pace. As markets grow and diversify, so too does the scientific research that underpins them. However, bridging the gap between theory and practical use remains a challenge. It is often said that “engineering is the art of turning science into technology,” and here at PZFlex we provide tools that allow engineers to do this more effectively than ever.

With new research streams ranging from bio-inspired imaging systems, new implementations of piezoelectric materials for high-frequency arrays, and novel RF filter designs, to developing NDE inspection methods for the nuclear industry – and everything in between – PZFlex is at the forefront of acoustic innovations across the globe. We provide researchers with the ability to conceptualise and test their ideas rapidly and accurately, and strive to work closely with academic institutions to ensure they have the tools they need at their disposal, with the support necessary for new applications.

Turn science into technology.

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3D multiprobe pipe inspection CT import of bat earsParametric Sonar Field

22

The Unlimited Elements module allows users to run multi-million, and even multi-billion element models if they have enough computational power available. The only real limitation on the number of elements is the amound of RAM supported by the Operating System, and as PZFlex is extremely efficient with memory usage (1 GB RAM = 10-15 million elements), users have the ability to run very large models on a standard laptop.

Unlimited ElementsThe Piezoelectric module provides a fully coupled electro-mechanical solver. This is key to simulating piezoelectric ceramic transducers in all their forms and is extremely useful in all major applications that involve piezoelectric transduction. It also allows electric fields to be simulated in dielectric materials. Due to the underlying method used in PZFlex, coupling piezoelectric materials to other non-piezoelectric materials is extremely simple and requires no boundary interfaces to be defined.

Piezoelectric

Solvers

24

Solvers

The Large Deformation module allows for geometric nonlinearities and more advanced solid mechanics to be simulated. It provides the simulation capability for very large strain levels in addition to mechanical contact, slip, debonds, erosion and much more. It is primarily useful for structure analysis but has found great use in multi-physics acoustic problems when looking at nonlinear NDE, thermal expansion/deformation of materials and transducer response to large hydrostatic forces.

Large Deformation

The Steady-State Flow module provides users with the ability to import steady-state flow fields from CFD codes and simulate the effect these will have on an acoustic pulse propagating through it. This will be particular useful for a range of sensing applications, in particular acoustic flow monitoring.

Steady-State FlowThe Thermal module allows for both the coupled thermo-mechanical and purely thermal solutions. Thermal only is very useful for HIFU simulations to calculate the temperature rise in tissue under focused ultrasound conditions. It also allows users to gain a better understanding of the thermal behaviour of their transducer arrays under a variety of drive conditions. The thermo-mechanical solution is fully coupled and can simulate the mechanical deformation caused by the thermal expansion of constituent materials.

Thermal

26

Solvers

The CMUTs module expands the range of simulation

possibilities for capacitive micromachined ultrasonic transducers and other electrostatic devices, matching the accuracy and versatility of the original PZFlex piezoelectrics package.

It captures the full range of dynamic behavior—transmitting and receiving, biasing, crosstalk, and collapse and collapse/snapback operation contact—and accounts for the material and geometrical nonlinearities that dominate the operation of these devices.

CMUTs

The SPFlexTM module is a specialized time-domain solver for computing waves that propagate through acoustic media over

long distances or that are focused and intense. The software has a wide range of applications in medical diagnostics, therapeutics, and sonar. Its “pseudospectral” formulation eliminates the numerical dispersion common to traditional finite-element and finite-difference formulations, providing results that are highly accurate for thousands of wavelengths. SPFlex may be purchased as a standalone package as well as an add-on to PZFlex.

There are distinct advantages to buying SPFlex as part of the PZFlex package rather than as a standalone. For example, SPFlex can be initialized with the pressure field produced by a piezoelectric device, which can be computed using PZFlex, and then used to compute the long-range propagation of this pressure. Using PZFlex and SPFlex together creates a feedback loop between a device and its effects that is helpful to the designer and benefits the design.

SpectralFlex

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Add-On Modules

GPU EXTRAPOLATIONThe GPU Extrapolation module bring the computational power of GPUs to bear on PZFlex’s extrapolation algorithms. The ability to rapidly calculate the predicted pressure in the far-field without the requirement to run a full FE model, provides an effective means of generating beam profiles in both the time and frequency domain. It also allows for ‘domain

segmentation’ of models, whereby only the complex regions of a problem need to simulated in FE and extrapolation can be used in the intermediate path.

TRAININGAs with any FEA code, there is a learning curve associated with attaining a level for proficient use and PZFlex is no different. We

PZFlex modules are available as add-ons to any PZFlex package and can be purchased individually or combined into a bundle. This structure is designed to provide greater flexibility and clarity, ensuring that each license encompasses the capabilities that meet the specific needs of the user, at the best price.

offer 2-day training sessions at our sites (UK and US) as part of any purchase of a Platinum or Professional license. Standard customers can choose this option as an add-on. As we typically run small, dedicated training sessions for select customers, they offer a great deal of value for targeted use of PZFlex. On-site training is available at an extra cost, contact the PZFlex Support Team for more information on your specific situation.

TECHNICAL SUPPORT & MAINTENANCEDevelopment is ongoing, as our designers do extensive consulting and are very conscious of the marketplace. After the first year, you may choose to take advantage of our extended maintenance contract, which costs 15% to 20% of your initial outlay per year per site. It entitles you to receive continuing code maintenance and

telephone/email support, as well as any feature updates or program upgrades made during your contract period. We strongly advise taking the technical support option as we pride ourselves on our support levels. The Support Team has over 50 years of acoustic and FEA experience, which coupled with practical knowledge of many applications, ensures an extremely effective service.

NETWORK LICENSING AND ADDITIONAL PROCESSORSPZFlex now supports a network licensing option for an annual fee. This can be used to replace the standard hardware dongle system for customers who operate a shared computing facility. Please contact PZFlex Support for more information on this option as it relates to your particular arrangement.

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Features

Created in collaboration the National Institutes of Health (NIH), the Food and Drug Administration (FDA), and George Washington University, MediFlex is the result of a 2010 SBIR grant awarded to Weidlinger to develop and apply “simplified GUI toolkits for high-fidelity simulations of therapeutic ultrasound.” The user creates a material palette and draws regions and layers in a tactile GUI environment. This makes the design of models and definition of outputs considerably easier.

The MIDAS FX+ module is a very powerful and intuitive pre-processor that is now offered with PZFlex. MIDAS FX+ allows users to bring CAD models from a wide variety of sources, allocate constituent materials, mesh and export into PZFlex for solution. It also offers a comprehensive solid modelling tool that rivals most basic CAD packages.

The SolidWorks Parts & Assemblies module offers users more CAD power, but no pre-processing capbilties.

An important new feature in PZFlex 2014 is the addition of MPI for mechanical problems. This allows large problems to be divided into many parts, taking full advantage of modern computing hardware. This makes it possible to run PZFlex models with billions of elements, opening up a whole new range of simulation possibilities.

MPI stands for Message Passing Interface, and is an efficient language-independent communication protocol, which has become the de-facto standard in parallel high performance computing. PZFlex’s explicit solver is ideally suited to making full use of MPI, and we have seen super efficiency as a result of improved use of memory and storage bandwidth.

Pre-processors MPI

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Features

PZFlexCloud extends the market reach and performance of PZFlex’s award-winningengineering software by exploiting the power, elasticity, and ubiquity of the cloud. PZFlexCloud also makes advanced FEA available to a broader market. New users who have had to compromise on functionality can now use the PZFlex suite on a pay-as-you-go basis without the costs and complexities of building and maintaining capital-intensive physical

computing resources. PZFlexCloud extends the unmatched performance of PZFlex by exploiting the power of state-of-the-art cloud computing.Run hundreds of models in parallel, or combine the power of many cloud nodes to run massive models faster than ever before.

With flexible access and prices starting at $5,000, PZFlexCloud represents a step change in FEA capability.

Finite Element Solutions on the Web.

© ISTOCKPHOTO.COM/MBORTOLINO

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Capabi l i t ies

File Format Extension Read WritePZFlex Model .flxinp (text) Yes Yes

Binary Data .flxdato, flxhst Yes Yes

File Format Extension Read WriteJPEG .jpg, .jpeg Yes Yes

PNG .png Yes Yes

BMP .bmp Yes No

.tif, .tiff .bmp Yes Yes

AVI1 .avi No Yes

PZFLEX

NUMERICAL DATA, IMAGES, AND MOVIES

File Format Extension Read WriteAutoCAD®2 .dxf Yes No

Autodesk Inventor®2 .ipt, .iam Yes No

Pro/ENGINEER® .prt, .asm Yes No

Solid Edge®2 .par, .asm Yes No

SolidWorks®2 .sldprt, .sldasm Yes No

Parasolid®2 .x_t, xmt_txt, .x_b, .xmt_bin Yes Yes

ACIS®2 .sat, .sab, .asat, .asab Yes No

STEP2 .step, .stp Yes No

IGES2 .iges, .igs Yes No

CATIA® V52 .CATPart, .CATProduct Yes No

STL .stl Yes Yes

File Format Extension Read WriteNASTRAN Bulk Data .nas, .bdf, .nastran, .dat Yes Yes

STL .stl Yes Yes

CAD

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Capabi l i t ies

PHYSICS & COMPUTATION• Piezoelectric effects• acoustics and solid mechanics• Elastic waves & mode Conversions• nonlinear geometric effects• Contact and large deformation• Sophisticated absorbing

boundary conditions• Both linear and nonlinear waves• Coupled Thermo-Mechanical effects• Nonlinear Propagation• Element Erosion• Steady-State Flow• Electrostatics (cMUTs)

• Electromagnetics• Circuits• MPI on local and cluster-based systems• Multi-Billion element models• 10-15 million elements per GB RAM• Cloud computing resource available

MESHING & FINITE ELEMENTS* • 1D, 2D and 3D element types• Axisymmetric Constraints• 2D and 3D Hexahedral elements• 2nd order linear elements• Skewed elements and grids• Automatic Standard Partition

Meshing options

• General Connectivity supported• Specialised elements such as: Shell, Beam,

Bar, Spring, Contact elements• Tetrahedral, Hexahedral, Prism, Pyramid

element interpolation options• Refined Grid capability• Structured Grid supported

GEOMETRY MODELLING* • Primitive solid objects: block, cylinder,

torus, elipse, cone, etc• Extrude, revolve, sweep• Boolean operations: fuse, cut etc• Combination of points, lines, surfaces,

solids etc• Work plane with 2D modelling• Image to material map importation• 2D ‘paint’ package for simple drawing features• CAD Importation and manipulation

• Create geometry from arbitrary arrays• Copy and duplicate geometry and structures• Local axis positioning and referencing

MATERIALS• Linear Elastic• Anistropic Materials• Piezoelectric Materials• Electrostrictive Materials• Magnetostrictive Materials• Nonlinear Tissues• Comprehensive Damping Models

(Frequency Dependent)• Time varying materials• Nonlinear material properties available as

functions (e.g. dependance on stress)• Thermal properties• Viscosity & plasticity effects

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Capabi l i t ies

RESULTS & TOOLS• Visualisation• Interactive 3D Graphics• Embedded Graphics for runtime plotting• Vector Plots• Surface and isosurface Plots• Splining and slices• Contours

CUSTOM TOOLS• Extrapolation Tools• GUI Wizards for rapid model creation and

simulation• HIFU Wizard tool

• Scripting• Interactive HTML Help• Damping Analysis Tool• Material Property Convesion Tool• 3D Interactive Graphics• Over 500 example models• Extensive material database

POST-PROCESSING & ANALYSIS • Impendance & Admittance Calculations• FFTs• Beam Profiles• Displacement Shapes• Pulse-Echo Simulations

• Broadband Analysis• Harmonic Analysis (Mode Shapes)• Radiation Force Calculation• Loss Calculations• Transmit Voltage Response• Averages, Integration, Max/Mins, Flux

of fields over arbitrary surfaces, lines, volumes and objects

• Custom functions for mathematical operations, spatial locations, field extraction and more

IMPORT• Text• Excel• Images• Meshes (via Nastran Format)

• CAD formats• 3rd Party FE meshes• Matlab• Python

EXPORT• Text• Excel• Images• STL• Matlab• Python• Animations

* Some features availble only with MIDAS FX+ add-on or other 3rd party pre-processor.

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PZFlex Standard – CMUT*

PZFlex Standard – Piezoelectric*

PZFlex Stan-dard – Me-

chanical Only*

PZFlex Professional

PZFlex Platinum

PZFlexCloud Starter Pack

Number of Elements 500,000 500,000 Unlimited Unlimited Unlimited Unlimited

Large Deformation

Piezoelectric Solver

Unlimited elements

CMUT Electrostatic Solver

Thermo-mechanical Solver

PsuedoSpectral Solver

Steady-State Flow

MIDAS FX+ Preprocessor or SolidWorks Parts & Assemblies***

GPU Extrapolation

MPI Module

One Year Maintenance and Code Updates

Two-Day Training

Modeling Support

Notes on applicationsCMUT transducer design, both 2D

and 3D.

Piezoelectric transducer design, both 2D and 3D.

NDT, Biomedical, and structural applications.

All large-scale acoustic-trans-

ducer and application modeling.

Complete suite of PZFlex

tools.

Access to all PZFlex solvers on pay-as-you-

go basis.

Packages

PremiumPZFlex PlatinumPZFlex Professional

Standard*PZFlex Standard – PiezoelectricPZFlex Standard – ElectrostaticPZFlex Standard – MechanicalCloud**PZFlexCloud BasicPZFlexCloud Starter

Support and Training1-year support & updatesModelling support (PZFlex Standard)2-day Training (UK or US offices) On-site training

Modules & Options

SolversPiezoelectric solverUnlimited elementsElectrostatic solver (CMUT)Thermo-mechanical solverPsuedoSpectral solverSteady-State Flow

Other Add-onsMIDAS FX+ Pre-processorSolidworks Parts & Assemblies***GPU Extrapolation moduleMPI ModuleNetwork LicenseAdditional CPUsAdditional Licenses

PZFlex prices are applicable to all operating systems and are valid for up to two (2) physical processors, although multi-cores are supported.

PZFlex Standard comes with maintenance and code updates for one (1) year, but excludes modeling support. Further maintenance and technical support may be purchased for an annual price of 15 percent of the total package price.

PZFlexCloud is a pay-as-you-go FEA service. The Starter Pack includes 100hrs simulation time, Flexlab environment and 1 day of modeling support time. The Basic pack is only 100hrs simulation time. For information on PZFlexCloud services, contact PZFlex: support@pzflex.com

Users may choose between the MIDAS FX+ Preprocessor and Solidworks Parts & Assemblies. MIDAS FX+ includes solid modeling and CAD capability (no parametric CAD), meshing, material assignment, and loading options for import into PZFlex. SolidWorks Parts & Assemblies is full parametric CAD, with import into PZFlex via STL importer tool.

PZFlex is the premier FEA package for ultrasound and wave-propagation problems. Its specially designed algorithms are optimized to provide accurate, complex, fully coupled simulations in minutes, not days.

*

**

***

PZFlex Support Group399 West El Camino Real, Suite 200Mountain View, CA 94040–2607www.pzflex.com

Weidlinger Associates, Inc.www.wai.com

California, USA+1 650 230 0210

Glasgow, UK+44 (0)141 303 8303

PZFlex® is part of the Weidlinger Associates group. © 1985-2014 All Rights Reserved