FEA системы и реальные физические явления

Rectangular slices of soil were simulated using 1-in.-thick layers. But simulations revealed an irregular shape to the response field. So the soil geometry was modified using a Bezier curve tool to produce subdomains that precisely reflected the measured volume. This shortened run times.

Boundary Settings make it easy to select conditions for the relevant physics. Electric potential is measured by the value Vg and is specified in the model on boundaries 50, 51, 52,and 59.

Visualization Plots illustrate the performance differences between design options. Moving the ground plane increased the sensing depth.

The Plot Parameters dialog box allows changing the display. Up to seven plots types can be superimposed. This case shows the Streamline and Surface plots.

Femlab FEA software consists of a general-purpose multiphysics modeler plus optional specialized modules for electromagnetic, structural mechanics, and chemical-engineering applications. Although the physics in problems can be complex, the program is easy to use.

In a nutshell, building a FEA model for a problem goes this way: Users specify governing physics (electric fields, fluids, structures), build the geometry, assign material properties, mesh the model, solve, and postprocess results for interpretation. The developer has packaged these steps into a well-thought-out menu and toolbar system that lets users concentrate on the problem at hand rather than the peculiarities of the software. Default choices are made for many parameters, such as which solver to use for particular applications, and these only need tweaking in unusual situations.

To get users started, an extensive library provides well-documented examples for each application that illustrate key software features. In many cases, these models can be adapted to the user's geometry to quickly get up and running.

Documentation for each example contains model background, a discussion of the underlying physics, and step-by-step instructions to build the model and analyze the solution. If results require additional analysis capability, Femlab can be configured to run with Matlab (Versions 6.5 and later). However, Femlab does not require Matlab.

The best way to describe software features is to work through an engineering problem, such as a sensor redesign. Our company produces an asphalt sensor that measures to a depth of 4 in. We wanted to apply this sensor to measure soil to a 12-in. depth but needed to limit its diameter. (A previous article, MACHINE DESIGN, April 15, discussed modifications to the same sensor using Femlab to reduce measuring depth to 0.86 in.) The primary design parameters were the shape and configuration of the sensing plates and associated ground planes. As there is no closed form solution for the electric field for this configuration, we resorted to simulation with Femlab.

The software lets users model in 1D, 2D, and 3D, but because the soil-sensor concept is symmetric, we used a 2D axis-symmetric mode for the electrostatics applications. Two-dimension models minimize computation time and memory requirements, while still providing excellent insight into resultant field patterns. For example, sensor components and solids are represented by simple rectangular regions. After model building, the software translates the solid objects into subdomains and boundaries to which users assign material properties and boundaries conditions. Because the soil sensor consists of regions with different electromagnetic properties, such as conductivity and permittivity, they are placed into separate subdomains. To assist postprocessing, users may further subdivide homogeneous subdomains at important locations. In the sensor model, soil is subdivided into horizontal slices to assess values of interest at specified depths.

Boundary conditions are assigned by specifying external voltage and currents. Geometry boundaries must exist where boundary conditions will be applied. Boundary-condition values are specified in a dialog box or defined externally in the Options/Constants menu and symbolically specified in Boundary Settings. The software assists by assigning sensible defaults for each boundary, such as field continuity for internal dielectric boundaries between domains.

To build an adaptive mesh, users need only pick Initialize Mesh. If the automatic process does not produce an acceptable mesh, several levels of semiautomatic and manual controls are available to govern all aspects of mesh generation.

The solve step finds a continuous solution for the entire model. On a 2-GHz P4 processor with 1-Gbyte RAM and running XP, the sensor model took 8 sec to solve. The time to solution depends on the physics, model, and mesh complexity. (The same model solved in 44 sec using the previous version of Femlab.)

The software then presents a default solution plot. In this case, it was a surface plot of potential across the view plane. The software also superimposes an arrow plot of the electric-field vector. Values that would determine depth include the capacitance in each measurement subdomain and contour lines of the resultant displacement vector. To measure depth, the software calculates the capacitance in each subdomain measured by the sensor. A general formula for capacitance is:

where V = potential across the domain and W_e = energy density. The integral is computed using a Post/Subdomain Integration function. We arbitrarily define the measurement depth as that depth at which the integrated capacitance is equal to 99.5% of its final value. But the Subdomain Integration function only calculates total energy, so its value was exported into Matlab. At the Matlab command line, capacitance is calculated using the equation above.

One idea for increasing the measurement depth, without increasing sensor diameter is to remove the ground plane on the current sensor used for asphalt. We thought field lines from the transmitting element that are diverted to the ground plane would then pass into the soil. But the Femlab solution for the modified sensor model illustrated the opposite: the ground plane allowed

deeper penetration, the opposite of what was expected. Results showed field lines flowing from transmitter to ground penetrating deeper then those flowing from transmitter to receiver. This unexpected result steered the design in a different direction. Relocating and spacing the ground plane increased the penetration depth. The end result was a 100% increase in measurement depth with only a 10% increase in sensor diameter. Lab tests of a prototype agreed with simulation results.

In the design process, a problem developed with a boundary condition on an internal electrode that let the software technical support team demonstrate their quick response. The electrode has a floating potential that depended upon external circuits and properties of the material being measured. So this potential could not be specified prior to solving. Femlab's documentation and sample library did not provide a method to apply floating potentials. However, an e-mail describing the problem and a call to the regional technical representative produced a timely solution and explanation. An entry regarding the problem and solution was later placed on the developer's Web site so others can benefit from the experience.

The software is an intuitive, easy-to-use tool that provides insight to the detailed workings of complex devices. Potential users shouldn't be dissuaded by the price: $6,995 for Femlab plus $2,995 for each specialized module. We estimate the software paid for itself on the first project. Femlab comes from Comsol Inc., 8 New England Executive Park, Suite 310, Burlington, MA 01803 (781) 273-3322, www.comsol.com — Ronald W. Gamache