在有限元分析的行业中有很多商业化的软件，如ANSYS、COMSOL、ABAQUS以及ATILA，它们基本山可以分为显式求解和隐式求解两大类。以上软件超声方面的应用信息如下：

ANSYS、COMSOL、ATILA主要是基于隐式求解和谐波函数对于波的传播问题求解，ANSYS和 COMSOL相比于一般的有限元求解在压电/超声方面较弱。ATILA在超声方面有较多的经验，但是受限于窄带问题。

ABAQUS的确是拥有一个明确的时间域选项，但是其并不应用于压电/超声方面，不具备PZFlex那些功能和超高的效率。

PZFlex用于专门用于解决压电换能和超声波传播方面的问题，是我们几十年的经验的沉淀和积累，所以解决这方面的问题的确有很好的效果。与其它软件相比，我们的显式的基于时域的方法具有更快的计算速度，这得益于我们的专业的并行计算程序架构。

2. 显式与隐式求解器的区别为何？

有两种主要的时间积分方法：隐式和显式。隐式积分是经典的有限元分析方法，在求解过程中会产生一个或多个关于整个结构的矩阵，在求解一般的小问题时候能够很快进行求解，但是随着单元数量的增加，计算时间和内存要求是会迅速增长。显式的求解方式并不需要矩阵，这种方法能够节约时间与内存，用于求解中大型规模的问题，对于紧凑的2D和3D模型的边界上有数百个波长的问题的求解非常有用，尤其是超声波方面的应用。

3. 为什么对于时域的求解那么重要？

数学上有许多的有限元分析方法，但是适用于超声换能器中的压电元件和弹性波传播域分析的的主要的类型是谐波和瞬态分析方法。

当然！PZFlex是一个完整的瞬态分析包，并且精心设计了计算模型，使用了傅里叶变换技术可获得单一的瞬态响应并且可以提取任何感兴趣的频率，这本身就是一种宽带的方法。

5. 为什么PZFlex的网格与其它的有限元软件的网格不一样？

大多数有限元软件使用的是专门为自身定制的网格生成程序以便离散化他们的模型，这这些客制化的前处理尽可能地依照复杂模型的几何形状离散几何模型。与之不同的是，PZFlex是尽可能使用规则的矩形网格表述一个近似的几何形状。咋一看这些复杂的单元似乎描述了模型的精确形状，但事实并非如此。因为更少的复杂的单元网格的介入，使得采用标准网格的模型的计算速度快10-20倍。
有一个形象的比喻解释为什么矩形的网格能够保持较高的精度，如同一个显示器中的像素怎么组成一幅图像。当我们近距离看单独的一个像素，像素可辨，当我们退后一定的距离，这些像素构成了一幅无缝的图像。当波遭遇模型中的足够小的单元时，这个更大的图像或者外形，就是波“看到的”。

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.

任何有限元软件都有一个学习曲线，这是用户不可避免的，PZFlex亦是如此。 每种有限元软件都有自己的特点，PZFlex也有自己的特点。首先，PZFlex是一个基于语法的软件，所以需要用户具备一定的熟练的操作能力，尤其是建模、编程这方面。 然而，PZFlex也在努力改进GUI用户界面，使得它更友好。我们正在建立一些向导工具，用于引导用户建立基本的通用模型，并通过与SolidWorks公司合作开发SolidWorks的导入工具，实现CAD模型的导入（仅支持STL格式）。除此之外，我们还透过e-mail和电话为用户提供完善的技术培训和软件应用支持，类似于点对点的专用应用手册。如果您有应用技术问题，请联系我们：

http://www.pzflex.cn/about/show.php?lang=cn&id=95

FIELD II 是基于线性系统的，意味着如果你有一个换能器的脉冲响应或者声场里的反射信号和相互作用，你就能计算与输入对应的响应输出， FIELD II是一个使用简化的换能器模型作为输入信号，模拟线性、各项同性介质的高效的工具。但是，PZFlex与之不同。使用PZFlex您可以获得以下求解能力：

• 计算模型不再仅仅局限于线性模型，比如高能聚焦超声应用 (HIFU)
• 作为输入载荷的换能器可以直接放在求解模型中，用于捕捉超声波全面的传播特性。
• 使用各向异性材料描述各种媒质，比如脂肪、肌肉、内脏器官等。
• 可用于求解复杂三维模型
• 可用于模拟立体波形转换
• 热分析能力

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.

PZFlex软件及Flex系列在过去的30年里一直被美国政府应用在非线性波传播方面的研究。并在近20年里持续地开展医疗超声波、声纳和无损探测方面的声波传播问题。其他任何软件都不具备PZFlex拥有的超声波传播仿真经验。

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.cn

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.