University of Michigan
College of Engineering

Department of Naval Architecture and Marine Engineering

ENGINEERING for the MARINE ENVIRONMENT


Structural Redesign



Description of the Project



Figure 1



Figure 1.

As an introductory example, consider the design of a simple strut; its function is to transmit a tensile force from one point (or region) to another. We suppose further that a Selective Laser Sintering (SLS) device constitutes our manufacturing capacity. The fabrication of the strut will then involve sintering layers of material sequentially from one end of the part to the other. A rough sketch of a possible part design is shown in Figure 1.



Figure 2


Shown in Figure 2 is a schematic diagram of the planned approach indicating the linkage of macrostructural properties and performance with microscale material characteristics and the fabrication process. A global optimization of material and geometry (topology, shape, and size) must address the issues of production efficiency and quality of the product. The design process will require establishing the spacial distribution of the material. Thus, the material stiffness which is represented by the elastic modulus, E , would be a function of position E . Similarly, the density and strength of the material must be established, , and respectively. These parameters are related to the microstructure of the layered material which are described by, for example porosity, P , crack distribution . The functional relations between the macro- and the micro-scale required parameters are being established within the scope of the project. Here we show for example the dependency of the strength on layer thickness and scan direction.



Figure 3



Figure 3.


Simulation based design is represented schematically in Figure 3. Operational requirements are established at what we refer to as a global level, these requirements are considered fixed throughout the design process. Models of the processes and products are used in the simulation in order to analyze the performance and judge their suitability based on the specified requirements. Production costs and throughput or build rates are also analyzed. These analyses are used to redesign the products and processes. More detail of the integrated product and process design procedure are provided in Figure 4.



Figure 4



Figure 4.

Product model design variables and process model design variables are denoted as X and Y vectors, respectively, in a synthetic environment such as CAD/CAM models. Particular simulation models are denoted Si and in general require a translation from the product and process models in order to provide the system properties used within the simulation. The time variable used within the simulation in manufacturing endeavors can range from nanoseconds when simulating laser sintering processes to months and years when simulating ship fleet operations. Generally however the performance of the product or process is judged by some time independent parameter which we refer to as a Response Quality Metric. Some specific examples follow in Figures 5 and 6.


Figure 5



Figure 5.

The product model example shown in Figure 5 involves a Finite Element Analysis. The product here is a cantilever beam analyzed for stresses and displacements. The Response Quality Metrics (RQMs) are listed as the displacements (ui) at discrete points and the maximum stresses, [[sigma]]max . The product design variables are the density and modulus of the material for the n finite elements.


Figure 6



Figure 6.

The process model example shown in Figure 6 involves Selective Laser Sintering. The process design variables could include parameters such as layer thickness, energy density, scan speeds, and scan spacing. Examples of process simulations could include densification, shrinkage, porosity, and a host of other important process analyses. To illustrate our methodology for linking the process variables with the product design variables, the following examples show how a single process parameter, the build plane angle, can influence the product and process design optimization.


Figure 7



Figure 7.

In the stress analysis of the product, say the cantilever beam of Figure 5, the stress is related to the strain through the stiffness tensor, K. In a nonlinear analysis the stiffness may vary as a function of strain as indicated in Figure 7. The strength of the part is formulated as a function of stress, perhaps a history of the deformation, and also the design variables X. Inherent in these relationships is a dependency on the process used to manufacture the part. The dependency is described for example by including the build angle of the part.


Figure 8



Figure 8

Because of the directional nature of the sintering process, the material may show anisotropic mechanical properties. Hence the stress strain relations, often most conveniently described a by global coordinate system, may require knowledge of the local process variables such as [[phi]] the build plane angle as shown in Figure 8. Both the stiffness and the strength of the material is therefore a function of the [[phi]].


Figure 9



Figure 9.

Having established the dependency of the material stiffness on the process variables, Figure 9 illustrates the methodology used in the structural optimization or redesign for, as an example, displacement constraints. Changes in response are expressed in terms of changes in design variables.


Figure 10



Figure 10.

The local stiffness matrices, K, of individual finite elements are shown in Figure 10 as the integral result of the elastic modulii. The modulii are again however linked to the anisotropic stress strain relations of the material and hence functionally related to the fabrication process. The code RESTRUCT can then be used to find changes in either process variables or product variables to achieve the improved state of performance.


Figure 11



Figure 11.

Several problems in structural analysis and design (see Figure 11) - including the problem of redesign or inverse design - can be cast as two-state problems. State S1 is the initial state which is known and for which all required finite element analyses (modal dynamics, static buckling, etc.) have been performed. It is assumed that State S1 has undesirable characteristics or performance and should be improved to satisfy the designer's specifications. State S2 is the objective unknown state modeled by the same finite element grid but defined by different design variables.


Figure 12



Figure 12.

Figure 12 shows a simple two-dimensional topology redesign problem which has been used in the literature as a bench mark problem. The results produced by Code RESTRUCT which implements the LEAP algorithm for topology optimization of solid elements are consistent with those published in the literature. The starting structure (State S1) of a solid plate is redesigned to become a multiply connected structure at State S2.





The Team




Standing: Left to right: John Ferris, Dale Karr, Michael Bernitsas
Seated: Left to right: Danet Suryatama, Byungsik Kang, Ralph Seguin, Constance Savander, Stephanie Wimmer




Project Personnel

Michael M. Bernitsas, Professor
Dale G. Karr, Associate Professor
Byungsik Kang, Research Fellow
Basem Alzahabi, Ph.D. Candidate
John Ferris, Ph.D. Candidate
Danet Suryatama, Ph.D. Pre-candidate
Stephanie Wimmer, Ph.D. Pre-candidate
Constance Savander, Master's Student




Resulting Papers