Amazing Analyses

FEA software is capable of more than ever, except engineering judgment.

January saw the death of British mathe-matician Olgierd Cecil Zienkiewicz, an early pioneer of the finite element method who pushed for its computerization and who recognized the potential for using the method to solve problems outside solid mechanics, purview of the famous Euler-Bernoulli beam equation.

With his passing, we pause to assess FEA’s past—looking at the pros and cons of the leap the method has made into the software realm—and to look at what the future holds for finite element analysis and its applications.

From its inception in the 1940s until about a decade and a half ago, finite element analysis had been performed exclusively by specialized analysts who held Ph.D.s in the subject and had devoted their careers to the discipline. But the FEA field has seen great change over the past 15 years, with a jump in the number of computer technologies available to an increasing number of engineers. And like all changes, it has brought risks and rewards.

In his lifetime, Zienkiewicz saw the finite element method move from a powerful technique originally developed to solve complex structural mechanical problems to its use today across nearly all engineering fields, including bioengineering—and its stretch into unrelated fields such as the simulation of weather patterns. Beginning in the 1960s, FEA researchers began to extend the method beyond linear structural analysis to nonlinear FEA and other engineering disciplines such as fluid dynamics, heat transfer, soil mechanics, wave propagation, and electromagnetics.

Since its inception in the 1940s, finite element analysis—originally developed for numerical solution of complex problems in structural mechanics—has become established in nearly all engineering fields, including bioengineering, where it plays a role in studying many parts of the body, such as nasal passages.

Zienkiewicz himself sought to move the finite element method from a research tool to a computer-based analysis method that could be called upon by designers and engineers. And in 1968 he founded the first journal dealing with computational mechanics, the International Journal for Numerical Methods in Engineering.

Today, high-end FEA software packages are available to solve complex problems across many disciplines. But they’re still not perfect; that is, the engineers and researchers who use these tools can spend a lot of time kitting them out and programming them for their own unique use.

Other FEA packages introduced within the past 15 years are now commonly integrated with computer-aided design applications, allowing product developers to analyze as they design. The integration is intended to speed up the design cycle because designers can analyze, then immediately update, their designs.

easy access
Without a doubt FEA’s move to the computer allowed it to become the widely used tool it is today, said Samer Adeeb, an assistant professor in the department of civil and environmental engineering at the University of Alberta in Edmonton. By helping move the tool to the computer, Zienkiewicz enabled its popularity and its growth, Adeeb added.

In the early 1970s, FEA was run only on mainframe computers owned mainly by companies in the aeronautics, defense, and nuclear industries. With the rapid decline in the cost of computers and the concomitant increase in computing power, today’s personal computers can now produce accurate FEA results. Adeeb pointed out that many engineering technology vendors are currently marketing simplified analysis programs, which walk users through a series of steps that allow them to define the analysis they want to run and then interpret the results.

“FEA has been around forever, but it’s grown to be very powerful because of the computational power that exists right now in computers,” Adeeb said.

“The problems we’re now solving with FEA couldn’t have been done ten years ago because you would have needed a mainframe,” he added. “Now a desktop has enough computation power that anyone can run FEA.”

FEA is now used by disparate industries for a range of
applications. The packaging industry calls upon it to
analyze designs for blow-molded products, including
bottles, top. Bioengineers call upon the software for
their own use, such as studying the growth of a human
bone, bottom.

That jump to the desktop makes for the packages that allow CAD users to run more up-front analysis during design, but it can also mislead untrained analysts, who may not fully understand the finite element method and won’t exactly know how to best input information or how to interpret results, Adeeb added.

“FEA is becoming so easy to run and is so highly integrated with all the CAD software now, but the output from the analysis is still the numbers a designer uses to determine if the part is safe or not safe,” he said.

“It’s sometimes too easy to toggle back and forth between CAD and FEA without really knowing what you’re doing,” he said. “Some people abuse FEA because it offers such a nice animation; so they try to get to the animation they want rather than to actually solve a problem that returns useful information.”

According to Adeeb, FEA software shouldn’t be relied upon as a black box that spits out numbers. Designers still need to know the proper inputs and to understand what those numbers mean. The old adage holds true, he said: garbage in, garbage out.

To get meaningful analysis results, designers need to know how to identify the problem that needs solving in the first place. That requires at least a basic understanding of the finite method, he added. Before beginning analysis, designers will need to simplify the problem at hand, to ask themselves whether the problem is linear or nonlinear, and to identify the forces that need to be analyzed.

As an instructor, Adeeb knows this line of questioning doesn’t come intuitively to users who have little or no understanding of the finite element method.

As a numerical technique, FEA allows engineers to find approximate solutions of partial differential and integral equations. FEA software simulates where structures bend or twist and indicates the distribution of stresses and displacements. The software uses a complex system of points to form a grid, or mesh, across a model. The engineer assigns nodes at a particular density throughout the material, often depending on the expected stress levels of a certain area. The mesh contains the material and structural properties that define how the part will react to certain load conditions.

“The first question I ask my students on exams is: what is FEA and why do you need it?” Adeeb said. “If people can’t offer the correct definition of what it is I don’t trust them using FEA. Within the definition itself lies the understanding of what they’re doing.”

Companies that hire designers to perform both CAD and FEA should offer new employees an introductory course to FEA, Adeeb said.

“Otherwise what they’re doing is just an animation, and that doesn’t differ from a computer scientist who is just drawing on the computer,” he said.

the simple stuff
Though desktop FEA has come a long way in the past few decades, everyday users—even those well trained in FEA—still face everyday problems when trying to analyze designs and behaviors as part of their jobs, said Rick James, vice president of consulting at the SimuTech Group of Rochester, N.Y.

One problem is that while many FEA applications are integrated with CAD systems today, many of these calculate what James called “the simple stuff”; that is, they perform relatively basic stress and fatigue analyses. Users will need to purchase a third-party analysis application to run advanced fatigue analysis or other types of analyses on top of the simple stuff, he said.

“Most FEA desktop software doesn’t do the niche stuff like crack-growth propagation, where you’re watching a crack form and move on the screen,” James said.

And advanced FEA add-ons require that users have much more information to hand.

According to James, “This advanced fatigue stuff asks for this load history and that load history and then this residual stress from welding.”

Thus, the everyday CAD users will likely need advanced training to best use advanced packages. Training costs and software costs can quickly add up. According to James, extra analysis software on top of the already existing FEA application can run companies anywhere from $30,000 to $60,000 depending on the package, the number of packages needed, and user needs.

But the companies that really need advanced FEA capabilities simply can’t get by with everyday FEA software alone, he said.

already here

But the good news is that for many uses the everyday FEA software of the type integrated with CAD systems has advanced enough to be of great help. In fact, according to Adeeb, the software is very user friendly and—when properly programmed by the user—adept at analyzing most FEA engineering problems.

“For certain applications, like analyzing engineering structures that behave according to theories developed one hundred years ago, FEA software doesn’t need advancing,” he said.

But the story differs when high-end FEA packages are used for applications not strictly related to engineering, such as biomedical problems, he said. The human body, after all, is nonlinear in behavior. So not only is defining the complex problems related to the body a challenge for a researcher, so is determining how to call upon FEA software to best solve them, Adeeb said.

For example, as part of his research, Adeeb needed to create and analyze a model of a human bone as it grew. For this, he used Abaqus, software marketed by Dassault Systèmes of Paris, a powerful, high-end package used to solve complex physical problems.

Software for complex simulations isn’t plug and play, Adeeb said. The software programs meant to model complex or unusual problems are built to allow their users to configure the software—to a certain degree—to their own unique needs.

“I can do the analysis, but it takes me a lot of trying to fool the software and coming up with workarounds; it’s not something I can directly model, and it takes me a long time to try to model something like that,” he said.

Researchers can be assured the vendors of these customizable, high-end systems like Abaqus and Ansys of Canonsburg, Pa., will be stepping up with software to suit specialized needs in the future. But for new and specialized applications like biomedical software, development takes time, James said.

“But FEA software has proven to be very lucrative so it’s worth it for these guys to work on development,” he added.

Still, whether researchers and engineers call upon FEA software to solve complex problems or to analyze fairly straightforward structures as they design, they’ll need to bring their own judgment to the problem at hand, James said.

“FEA is never going to be the ultimate decision-making tool, nor should it be,” he said. “It’s still used for mathematical equations and modeling physics, and you still have to use engineering judgment when calling out a result you don’t think is true, even if your software can do amazing feats.”

But the mix of engineering know-how, engineering judgment, and amazing feats of software make for analysis and design never dreamed possible before the age of FEA.

In 1998, upon acceptance of the Timoshenko Medal from ASME, Zienkiewicz speculated about the future of FEA by referring to Charles Duell, commissioner of the U.S. Office of Patents in 1899, who famously speculated that everything that could be invented had already been invented.

“I do not share this pessimistic view, and I think we shall see many exciting developments in the coming years,” Zienkiewicz said. “It is evident that both applied mechanicians and mathematicians will continue to contribute to the numerical analysis field.”

He said that more than a decade ago, and it still stands.

Renewable Sea Power

Waves, tides, and thermals—new research funding seeks to put them to work for us.

For the first time in more than a decade and a half, on September 18, 2008, the U.S. Department of Energy announced the funding of projects dealing with renewable marine energy technologies. The program will address one of the great sustaining resources of our planet to see if it can yield benefit to mankind in new ways.

The ocean has always been a provider. Its fish and plants nourish a large portion of the Earth’s population. It is a vast recycling engine that replenishes oxygen in our atmosphere. It is also an immense store of energy, much of it derived from the sun and most of it untapped.

The DOE’s program will explore technology that aims to harness some of the ocean’s energy and put it to work for us. While several awards specifically were made to private companies for technology development and market acceleration, DOE also created two National Marine Energy Centers, one in Hawaii operated by the School of Ocean and Earth Science and Technology at the University of Hawaii and the other in the Pacific Northwest under a partnership of Oregon State University and the University of Washington. They will study various technologies designed to generate power from forms of energy in the ocean.

The portion of the solar energy absorbed by the ocean is initially thermal in nature. We find that the surface waters heat during the day and cool during the night. The air adjacent to the water surface is also heated and cooled, and thermal currents occur in both the air and water. Hence, the absorbed radiant solar energy is partially transformed to thermal energy and, then, to hydraulic and pneumatic energies, giving rise to winds. Winds and the Earth’s rotation create waves on the water surface. These energy transformations give rise to the fields of ocean thermal energy conversion, ocean wave energy conversion, ocean current energy conversion, and offshore wind energy conversion.

The tide is also partly solar. Tides are predictable energy forms at any site in the world, since they are due to the gravitational attractions of the moon and the sun.

Offshore wind energy is an established technology. Tides are site-specific, and there are plants producing electricity at places like the Bay of Fundy in Canada and the Rance Estuary in France. The other forms of energy conversion are in development.

A conception of a field of water mills designed by Marine Current Turbines that turn the currents of tides into electricity.

The new Marine Energy Centers will both be active in the promotion of wave power conversion; Hawaii also will lead efforts to advance ocean thermal energy conversion, while the Northwest will be involved in tidal energy development.

Jefferson W. Tester, Croll Professor of Sustainable Energy Systems at Cornell University, and four researchers from Massachusetts Institute of Technology, Elisabeth M. Drake, Michael J. Driscoll, Michael W. Golay, and William A. Peters, jointly wrote a book, Sustainable Energy: Choosing Among Options, published in 2005 by MIT Press. In it they estimate the relative potentials of ocean energy resources. According to the authors, the wave action of oceans deliver 2,700 gigawatts of power, and the power available for use totals about 500 GW. Currents are estimated at a total of 5,000 GW, of which perhaps 50 GW is of practical use for energy conversion. Ocean thermal resources may be as high as 200,000 GW, although practical exploitation would be about 40 GW. Tides represent 2,500 GW and maybe 20 GW can be used for energy conversion. 

Ocean thermal energy conversion (often abbreviated as OTEC) uses the temperature differences between warm surface waters of the ocean and the cold deep water. The temperature of ocean water at a depth of 1,000 meters is only slightly above freezing. If surface waters are at least 18 oC warmer, the heat of the warm surface water can evaporate a fluid such as ammonia, which can drive a turbine. The fluid is then condensed by up-welled cold deep-ocean waters to begin the cycle again.

The ideal regions of the world for ocean thermal energy conversion are between 20o north latitude and 20o south, where the average surface temperature in tropical oceans can rise above 30 oC. Although the ideal latitude band is well away from much of the industrialized world, we can take advantage of OTEC by creating a product other than electricity. For example, if we build a floating aluminum plant at the OTEC site, and make the aluminum from imported bauxite, then we have produced an energy-intensive product, relieving a nation’s power grid from that task.

The state of Hawaii is in the ideal band for OTEC. In the late 1970s, a modest effort was started to build a land-based OTEC power plant. The electrical power output from the original power plant was of the order of tens of kilowatts. Over the years, this effort has expanded. The state of Hawaii recently agreed to have a 10 megawatt OTEC plant constructed.

riding the waves

Wave energy conversion devices exploit the rise and fall of waves, often to produce electricity. There are prototype systems deployed around the world, but no commercial-scale installations.

Michael Pleas and Douglas Hicks of the University of Delaware recognized in the 1970s that the production of potable water, rather than electricity, might be a more efficient use of converted wave energy. Efforts in this direction are now under way in the United States, Ireland, and elsewhere.

The average U.S. citizen, who requires electrical power of 1 kW, also requires approximately 60 gallons (about 227 liters) of water per day. For electricity production, consider a sinusoidal wave approaching a mid-Atlantic U.S. state. The wave might have a wave height of 1.5 meters and a period of 7.5 seconds. For this wave, the power per crest width is about 16.6 kW/m. Let us assume that this power is to be converted into electricity with a bus-bar efficiency of 25 percent. The electricity supplied to the grid, then, is 4.15kW per meter of converted wave crest. For a coastal town of 1,000 citizens, approximately 241m of the wave crest must be addressed.

The population of the same coastal town would require 227 kiloliters of potable water per day. In the same sea, a wave-powered desalination system operating at an average pressure of 60 atmospheres and pumping 379 kL of salt water per day to obtain the 227 kL of fresh water would require about 26.3 kW of power. For a 25 percent efficient system, only 6.34 meters of crest width would be required.

The WaveBob generates power by using the out-of-phase heaving motions of the float and a submerged inertial body.

A promising wave-powered electrical generating system is the Pelamis of Pelamis Wave Power in Scotland. It is an articulated-body system with an internal closed hydraulic system that is part of the power takeoff sub-system. It has four components, each 45 meters long. Three Pelamis units have been constructed for deployment 5 km from the coast of Portugal. Each unit is rated at 750 kW.

Other systems for capturing wave energy are buoy-like designs. One, PowerBuoy from Ocean Power Technology, has been deployed in Hawaiian waters. Another, WaveBob from WaveBob Ltd., has been deployed in Galway Bay off the coast of Ireland.

The use of the tides to produce electricity has been done on a commercial scale, but the energy resource is site-specific. Although there are numerous low-capacity tidal power plants along the coastal waters of the Chinese mainland, there are few high-capacity plants in existence in the rest of the world. The best locations for tidal power plants are the Bay of Fundy in Canada, the Severn Estuary in the United Kingdom, Port of Ganville and the Rance River at San Malo in France, Puerto Rio Gallegos in Argentina and, in Russia, the Bay of Mezen on the White Sea and Penzhinskaya Guba on the Sea of Okhotsk.

Tidal energy plants are costly. The turbines must be bi-directional, to take advantage of incoming and outgoing tides. They must also be of high capacity. Most tidal plants require construction of a barrage as well. But the amortized cost of electricity is relatively small because the static tidal power systems are robust and have a long operational life.

The French built a tidal power plant at St. Malo in the Rance estuary, where the mean tidal range is 8.55 meters. That power plant delivers an average of 240 MW of power (240,000 kW) at a cost of about 1.8 cents per kilowatt-hour, which is quite inexpensive.

More recently, attention has been focused on the dynamics of the tides in the form of tidal currents. To convert the hydrostatic tidal energy into electricity, tidal water mills are deployed. For example, in the East River at New York City, the Verdant Power Co. has installed submerged water mills. According to Verdant Power, six turbines in the East River will generate approximately 10 megawatts. A British company, Marine Current Turbines Ltd., has installed a 300 kW plant in the English Channel off the coast of Cornwall.

The tidal energy resource is both reliable and predictable. With the escalating costs of oil and natural gas, it will become a viable resource in the near future.

research partnerships

The Department of Energy’s new program in marine renewable energies is an attempt to tap into a vast resource.

The proposed level of funding for the National Marine Energy Centers in Hawaii and the Pacific Northwest currently stands at $1.25 million annually for five years, but overall cost-matching from non-federal money must be achieved. This requirement is meant, in particular, to foster active cooperation between academia and the private sector. 

The Pelamis wave-power electricity generator has a closed hydraulic system inside its articulated components.

Electrical utilities (e.g., HECO and MECO in Hawaii) and private companies (e.g., Ocean Power Technologies and Lockheed Martin) have made early commitments to participate in the centers, The scope of planned activities is, however, quite broad.

While conducting their own research, the universities will assist in the establishment of ocean field testing sites and help the DOE keep a recently created marine renewable energy data base up to date. Research areas themselves are expected to cover different aspects of marine renewable energy conversion. In Hawaii, for example, such issues as wave resource forecasting, novel wave power device testing, wave power focusing, OTEC environmental impact, OTEC heat exchanger testing, corrosion mitigation, and electrical grid stability have initially been considered.

The world’s appetite for energy can only continue to grow. As Tester and his co-authors point out, there are tremendous energy resources in the world’s oceans if we can develop the technology to harness them. We are hopeful that with research we will see one or more of the ocean energy options achieve its great promise.