The Basics

Prior to using OnScale for the first time, it is important to understand some fundamental information about how OnScale works:

Types of Models

2D Plane Strain - Assumes effectively infinite model in the z-direction (into the page) i.e. zero strain is generated.

2D Axisymmetric - Assumes 360 degree rotation around the X or Y axis (no partial rotations)

3D - Complete model geometry specified with no approximations beside symmetry conditions, if they exist

Type of Elements

OnScale mainly uses 2D and 3D 'Cartesian' elements

• 90 degree vertices (rectangles, cubes)
• Skewed elements possible, although ~5x more expensive computationally
• Elements are first order linear

• Computationally cheap
• Accurate

2D elements are Quadrilateral, or 'Quads and have 4 nodes

3D elements are Hexahedral, or Hexes' and have 8 nodes

OnScale also supports a selection of other elements, such as Shells, Bars, Tetrahedrals and others.

Type of Grid

OnScale most commonly makes use of a 'Standard Partition' approach when setting up grids for solving. The simplest way to visualize such a grid is to think of the structure of graph paper, although the spacing throughout the grid does not have to be regular.

The key component to a regular standard partition grid are:

• The elements interact at right angles to each other
• All nodes are at known positions
• There is no need to calculate fields AND positions

This combination makes for an extremely efficient solution for small deformation models (<1% strain) and is ideal for wave propagation.

Despite the advantages of standard partition for the majority of ultrasound and wave propagation problems encountered, OnScale also supports 'Skewed' and 'Non-structured' grids. Skewed grids are still structured, although the vertices need not be at 90 degrees. The skewing of the elements often compromised accuracy to some degree, and speed.

Non-structured grids are also known as General Connectivity and are generally much slower and less accurate than Structured grids.

Meshing in OnScale

Unlike most FEA programs, meshing in OnScale is NOT automatic. Users have control and must create a grid before allocating materials to elements on this grid. In general this is straight-forward as most geometries in acoustic applications can be very well represented by a fine regular mesh.

It is important to know the guidelines when setting mesh size in OnScale, which has the accurate sampling of a wave at its core throughout.

• Highest Frequency of Interest
• Slowest velocity
• 15 elements per wavelength at the slowest velocity

More elements per wavelength can be used to increase accuracy, however, this MUST be traded off against additional computational times. For example, in a 3D model, doubling the amount of elements per wavelength with multiply the model size by a factor of 8.

Therefore, the effect of diminishing returns must be considered. Unless it is absolutely necessary, a small increase in accuracy is not necessarily worth the x10-20 increase in simulation time.

Broadband Signals

As OnScale is a time-domain code and intrinsically broadband, input signals are generally pseudo-impulse and therefore broadband in nature. FFT techniques can be used to verify spectral content.

It is vital to ensure that any input signal applied has energy at frequencies of interest:

Numerical Dispersion

Numerical Dispersion is inherent in all numerical codes and is a small cumulative error that is caused due to sampling a wave in space and time. Here are some of the attributes of numerical dispersion:

• Non-physical phenomenon
• Higher frequencies disperse more
• Different frequencies travel a different velocities
• Cannot be avoided
• Phase errors
• Amplitude errors

Type of Solver

FEA solvers can generally be categorized in one of two types

IMPLICIT:

• Best for Static solutions, very low frequency problems
• Generate matrix for entire structure, set timestep, then solve
• Considers the effect of each node on all the others

EXPLICIT:

• Ideal for mechanical wave propagation
• Nodes effectively 'de-coupled' from one another
• Often x100-1000 faster than Implicit

Note: OnScale uses an Explicit approach for the majority of problems

Despite the obvious advantages of Explicit solvers for mechanical wave propagation and non-linear problems, OnScale also considers the electro-mechanical effects associated with using Piezoelectric materials.

As the electrical field calculation is instantaneous, OnScale adopts a hybrid approach where regions of the mesh are identified as having Piezoelectric properties.

The is commonly referred to an 'Electric Window', where the electrical calculations take place. The explicit regions are for purely Mechanical Wave propagation.

Key points to note:

• Field changes are instantaneous in the electric window
• Implicit approach used for this region
• Explicit approach maintained for mechanical only aspect
• Implicit region is much more computationally intensive
• Always minimise Electric Window as much as possible for efficient runs
• Always include Piezoelectric materials in the Electric Window

Analysis Types in FEA

OnScale is a time-domain code and primarly performs transient analyis which allow a large amount of useful data to be extracted. Note that the transient approach yields the same outputs as the all other types of solver, NOT vice versa.

Discrepancies in FEA

There will always be differences between results obtained from FEA and those in experiment. As long as the reasons for these discrepancies are well understood then this is not problematic.

Main causes for discrepancies are:

• Material Properties
• Real Life Defects
• User error

FEA will ALWAYS be 'too perfect' in comparison to experimental results due to faults/defects/inhomogeneities not being simulated. However, if these effects are known and can be quantified then they can be modeled.

An example of a PZT pillar in an ultrasonic transducer is below. The left image shows the perfect representation in OnScale, while the right image shows some of the possible defects/faults that may exist but not be considered in the simulation.

Training Material

All the default training material given as an introduction to OnScale can be downloaded here