Structural Problems, Computer Solutions

A Parallel DYNA3D (ParaDyn) simulation of weapons is only one example of finite-element analysis of structural behavior. Other finite-element problems include simulating car crashes and train accidents, falling nuclear waste containers, ground-shock propagation, aircraft-engine interaction with foreign debris, metal forming, biomedical interactions, and component designs for cars and aircraft.
The physics of structural behavior can be expressed in mathematical equations that can be translated into problems practicable for solving on the computer. Of the many computational techniques developed and used for solving structural mechanical problems, the one that became the most widely adopted by the 1970s--and the one that Laboratory computational scientists have advanced--has been the finite-element method.
In the finite-element method, a complex, solid object is divided into an assemblage of simple elements that become the basic units on which the computer calculates the structural behavior. Each element can be made as small and as irregularly shaped as needed to model the object being analyzed. Visually, the collection of elements resembles a wire mesh; the element boundaries are defined by lines that intersect at junctions called nodes. The nodes at each element corner define the movement and deformation of the elements.
The powerful versatility of finite-element codes is best exemplified in the numerous nonlinear material behaviors they can model: elasticity, plasticity, viscoplasticity, viscoelasticity, hyperelasticity, viscous flow, granular flow, thermomechanics, thermodynamic equations of state, composite behaviors, nonlinear foams and solids, void growth, and evolutionary damage accumulation. Simulating all of these behaviors is possible because the finite-element method uses constitutive equations to predict the element stress state based upon changing element deformations.

 The depiction of the blade fragments interacting with each other, as well as with following blades and the engine containment casing, posed special challenges. These "contact" problems required accurate mesh details at the interaction points, to more specifically calculate the material interactions there. Automatic contact algorithms were used for this large simulation. For his model, Kay explicitly defined the contact surfaces, but recent improvements in the code's ability to automatically define interacting parts would make that task easier today. Figure 2 shows the engine approximately one-third of a revolution after the fan blade had broken off. The simulations made by Kay demonstrate that the DYNA3D code can provide high-confidence simulations of blade failure. Based on those simulations, additional tasks, with the help of partners AlliedSignal and Pratt & Whitney, were begun in late 1997 to simulate the response of engine containment casings to the blade breakage and subsequent debris collisions.

 NIKE3D for Biomechanics Joint-replacement surgery, an increasingly common medical procedure, has been hampered by the inadequacies of today's prosthetic joint implants. Replacement prostheses sometimes do not reproduce normal joint movement and, because they have high failure rates, often cause their recipients to undergo additional costly, painful surgery. Attempts to improve the prosthetic designs have been based on limited information garnered from testing and failed implants. To obtain better information, implant designers have needed a way to quantitatively assess the stresses and loads on an implanted prosthesis and the wear and tear on its fabrication materials. Nonlinear, three-dimensional, finite-element modeling is a powerful tool for performing such quantitative assessment. NIKE3D, developed for studying dynamic, finite deformations, can model the behavior of joint tissues and bones subjected to different loads and joint movement with and without prosthetic implants. It is being used by Karin Hollerbach, Scott Perfect, and Elaine Ashby, a team of scientists from Livermore's Engineering and Computations directorates, to model both prosthetic implants and human joints. Data from the prosthetic simulations are providing useful information for prosthetic design and, when integrated with data from simulations of human joints, will provide information for evaluating the performance of implanted devices. Models of implants are based on computer-aided design (CAD) drawings of the prosthesis, from which the finite-element meshes are made. The models include numerical data that define the properties of the implant materials--including polyethylene and several metal alloys in the case of the prosthetic devices being studied--and the forces acting on the joints. For the thumb-joint models that the researchers have constructed (Figure 3), the loads produced during commonly used grasps (the key pinch, screwdriver grasp, and tip pinch) were used as the basis for assessing the performance of three thumb-joint designs. (See S&TR, September 1996, for more information on this project.) The stress predictions from the finite-element simulations were correlated against clinical findings. The agreement between simulations and clinical findings obtained by the researchers validates the modeling approach and pinpoints the most failure-prone designs. Thus, resulting modeling data can be used for selecting available implants as well as designing new ones.

 For the human joint models, the researchers had to develop a process for acquiring human data and converting it into a form suitable for finite-element analysis. They started by scanning a human joint, using computed tomography (CT) to acquire geometric data and bone surface definitions. To these data they added magnetic resonance imaging (MRI) data from collaborators that delineate soft joint tissues. Together, CT and MRI data define how bones and tissues attach to each other. Their resulting images were converted into three-dimensional surfaces using specially developed processing software, and those three-dimensional surfaces were then meshed for finite-element analysis (Figure 4). The researchers are currently working to integrate the data from the human and prosthetic joint models. These integrated models will be used to calculate the bone stresses resulting from the loads exerted by the implants and make bone-implant interface analyses possible.

 TOPAZ3D for Laser Heating Before scientists at the National Ignition Facility (NIF) begin performing laser experiments, they must fully understand how the various NIF components will behave in operation so they can design their experiments accordingly. One bit of crucial information they must know is how the NIF target chamber will expand and move as it heats up over the course of repeated laser shots. Attached all around the chamber are series of lenses that focus laser beams onto the target. Design analyses predicted the steady warming of the chamber and the equilibrium temperatures it would reach during various operating scenarios; the design of the lens assembly around the chamber allowed for these temperature increases. However, other transient temperature effects also must be taken into account, in particular, the periodic temperature spikes caused by individual laser shots. These temperature spikes cause a rapid thermal expansion of the target chamber. The chamber then slowly contracts, back to its equilibrium shape in time for the next laser shot. The concern is whether contractions affect the focus of the lenses. Just before a laser shot, these lenses must be in their positions to within tolerances of only a few millionths of a meter. Wayne Miller, a thermal analyst, was called on to model and simulate the temperature changes of an operating target chamber. He used the heat transfer code TOPAZ3D, developed by Art Shapiro of the Thermo-Fluids Group, in conjunction with NIKE3D to create an analysis model. The target-chamber model consists of an aluminum inner shell, a concrete outer shell, and aluminum ports through which laser beams are delivered. First, the finite-element geometry was created using TrueGRID, a commercial mesh-generation code. Then TOPAZ3D was used to predict the transient thermal behavior of the model, primarily due to laser energy deposited on the inner wall surfaces, which is then conducted through both shells and convected to the outside air. The thermal results were then given to NIKE3D, which predicted the thermal expansions of the chamber and prescribed the desired motion of the laser lenses for the next shot (Figure 5).

 The composite model was used to simulate thermal changes occurring in the chamber when laser shots are fired once every 4 or 8 hours. The 4-hour operating sequence, more challenging to the thermal stability of the chamber, was simulated under various conditions: with laser energies deposited uniformly and nonuniformly, with different outside air temperatures, and with different values for heat transfer from the chamber to the environment. Because one major goal of the overall analysis was to evaluate two ways of cooling down the chamber, simulations were performed with boundary conditions for passive cooling, in which heat transfers out through radiation and convection, and active cooling, and depends on the installation of a cooling system (Figure 6). The effects of the target chamber pedestal were also studied. A separate model provided data on how this pedestal grew taller and shrank back down and how this change affected the chamber and ultimately the focusing angle of the lenses. The results from the simulations for the different operating scenarios, cooling-down options, and pedestal influences were evaluated together to provide details on lens displacements--tangential, radial, or rotational--under different time and temperature conditions.

 DYNA3D Becomes ParaDyn The availability of massively parallel supercomputers, such as the IBM SP2, means that analysts now can solve problems larger by one or two orders of magnitude than was possible with other existing supercomputers. It is now possible and practical for engineering analysis codes to contain meshes with up to ten million elements. Now the limiting factor for problem size and complexity is the amount of time that analysts need to design the mesh rather than the raw speed of the computers. That boost in computing power depends on capable, efficient parallel codes. Because of the work of a code-developer team led by Carol Hoover, such a code, ParaDyn, is now available. As a result, parallel computing in solid and structural mechanics is becoming a powerful tool in computational engineering. To take advantage of the power of parallel computers, the mesh for a large problem must be partitioned so that the calculations for each part may be performed in parallel by the processors. The more processors working on the problem, the faster the solution is obtained. Multiprocessor calculations depend on the computer program to appropriately divide a problem, to logically sequence its calculations, and to allow communication among the processors so that their solutions can be integrated into a final correct answer. For computing efficiency, the workload must be evenly distributed among processors so that no processors are waiting on others. Furthermore, calculation time and processor communication time must be balanced; the latter must be limited to a small fraction of the overall computing time. Thus, for optimal efficiency and performance, a problem must be divided using a method that minimizes communication among the processors. The task of partitioning a problem may be needed more than once at the beginning of a parallel calculation. Because the problems are dynamic, the mesh may change significantly during the evolution of the deformation, affecting the parallel efficiency. When this happens, repartitioning the mesh and boundary conditions is often necessary. Developing methodologies for these repartitioning tasks is challenging, and research is still in progress in this area. ParaDyn's success has spun off several benefits to the weapons engineering programs at Livermore. Calculations that previously took several weeks are now performed in a day or less. New models are being generated for mesh sizes between one million and ten million elements--an order of magnitude larger than the largest models possible in the past. The Next Goals With the completion of ParaDyn, the development of parallel algorithms for NIKE3D and TOPAZ3D has begun. "This effort," Raboin explains, "is an even greater challenge. Developing efficient procedures for solving implicit matrix equations on single-processor computers is already difficult, so imagine the immensity of doing so for parallel processors. That's not to say that projects to couple the DYNA3D, NIKE3D, and TOPAZ3D codes to solve more complex physics problems will be any easier. Those are hard problems, too." With their experienced research and development, the Methods Development Group is helping to change the nature of engineering work and, in the long term, the very nature of problem solving. --Gloria Wilt

Key Words: computational mechanics, computer modeling and simulation, DYNA3D, finite-element method, nonlinear behavior, NIKE3D, ParaDyn, parallel computing, solid and structural analysis, TOPAZ3D.