Radiolaria: often perfect geometric form and symmetry, radiolarians are single-celled organisms going back all the way to the early Cambrian Period (500 million years ago). Radiolaria can range anywhere from 30 microns to 2 mm in diameter. Their skeletons tend to have arm-like extensions that resemble spikes, which are used both to increase surface area for buoyancy and to capture prey. Most radiolarians are planktonic, and get around by coasting along ocean currents. Most are somewhat spherical, but there exist a wide variety of shapes, including cone-like and tetrahedral forms.

The skeleton is composed of amorphous silica. The complexity and architectural diversity of these glassy structures have long been a point of curiosity as to their mode of formation and function, in addition to amazement at their pleasing aesthetic properties. The delicateness of form and diversity of space-enclosing structures, including perforated spheres, ornate geodesic-like polyhedral lattice, and seemingly endless variations of combinations of solid geometric designs, bears clear witness to the adaptive plasticity and sophisticated phylogenetic development of these single-celled organisms. (source: radiolaria.org)

Questions: What makes these minute creatures develop into such complicated shapes? Does their shape have an influence on their species survival for hundreds of millions of years? Can we someday design devices as complex and efficient as biological entities?

Hint: biological structures are optimized entities; they maximize output using minimal resources to increase survival chances. If we are to succeed in replicating their performance in man-made structures, we need to optimize; we need Design Optimization

Skeletal structures of radiolaria. (source: radiolaria.org)
 
 

Project Description

The primary goal of this project is to develop mathematical and computer models and techniques capable of rendering novel designs for materials and structures that can dramatically increase the performance and reliability of man-made structures and devices. The applicability area is virtually unlimited: from efficient Micro-Electro-Mechanical-Systems (MEMS) to lightweight thermal protective coatings for high-speed aircrafts. These improvements will be obtained by altering the shape, material gradation, and topology of the new structures. Novel numerical methods (meshfree methods) are used to overcome the difficulties encountered in shape and material design by the classical Finite Element and Boundary Element Methods. Tools from Calculus of Variations, Continuum Mechanics, Nonlinear Optimization, Physics and Computer Science are used together in this approach.
 
 

Shape Optimization of Thermal Fins

A thermal fin is a structure that is attached to a system in order to dissipate heat from the system. The problem is: starting from an original fin of triangular cross-section, find the shape of the cross-section that maximizes the amount of heat flux flowing through the fin-base, while the cross-section area is limited to 60% of the original, triangular area. The finger-type shapes are obtained in just a few iterations of the nonlinear optimization program because of the use of a meshfree method. Previous studies carried out using the Finite Element Method (FEM) were unable to reach these results. The amount of heat dissipated into the ambient is increased by more than 50% compared to the FEM results. Such improved designs may be used as thermal sinks for cooling computer motherboards and reduce the need of using fans, significantly decreasing the power consumption. The ability to generate shapes that resemble natural occurring forms is achieved through the use of optimization algorithms coupled with an advanced meshfree analysis tool.

Reference: Florin Bobaru and Subrata Mukherjee, "Meshless Approach to Optimization of Shape for Thermoelastic Bodies," International Journal for Numerical. Methods in  Engineering. (in press).
 
 

Shape and Material Optimization of Functionally Graded Materials
 
 

Cross-sections through clam shells. Notice the variation of the material and the connection to the exterior shape

Teeth, shells, bamboo, bone, are just a few examples of how nature arranges the material microstructure by placing the strongest elements where stress and strain requirements are highest. Biological structures are designed to provide uniform strength at all positions to avoid localized stress peaks and thus extend the survival chances by minimizing the possibility for structural failure in case of thermal shock or impact.

Based on a similar idea, Functionally Graded Materials (FGMs) are materials that feature a gradual transition in microstructure and composition in order to meet performance requirements that vary with location within the component. It is well known that abrupt transitions in material composition and properties within a component often result in sharp local concentrations of stress that result in damage and failure of the material. With FGMs, these problems are eliminated in a manner that optimizes the overall performance of the component.

The aim of this project is to link the geometry (shape) optimization of a component to its material gradation and composition optimization in a way that can result in high-performance novel materials and structures capable of sustaining high thermal-shocks and load impacts without failure. As seen in the figure on the right, there are several ways to optimize FGMs: (1) material optimization (the shape is fixed and not allowed to change); (2) shape optimization (the inner gradation of the material follows the exterior shape changes); (3) combined shape and material optimization (both shape and material gradation are allowed to vary for obtaining the best structure). The latter strategy is the most general and seems to be employed by the natural FGMs.