Alejandro R. Diaz

Checkerboard patterns in layout optimization

Effective properties of arrangements of strong and weak materials in a checkerboard fashion are computed. Kinematic constraints are imposed so that the displacements are consistent with typical finite element approximations. It is shown that when four-node quatrilateral elements are involved, these constraints result in a numerically induced, artificially high stiffness. This can account for the formation of checkerboard patterns in continuous layout optimization problems of compliance minimization.

Shape optimization of structures for multiple loading conditions using a homogenization method

A formulation for shape optimization of elastic structures subject to multiple load cases is presented. The problem is solved using a homogenization method. When compared to the single load solution strategy, it is shown that the more general formulation can produce more stable designs while it introduces little additional complexity.

Topology and Generalized Layout Optimization of Elastic Structures

An overview of the method of homogenization to find the optimum layout of a linearly elastic structure is presented. The work discussed here presents a formulation to address the simultaneous optimization of the topology, shape and size of the structure. The discussion includes optimization of plane, plate and three dimensional shell structures.

A method of grid optimization for finite element methods

A computationally useful criterion for grid optimization is derived, based on a measure of the interpolation error associated with the finite element model. The result is intended to be used to improve the quality of finite element solutions by changing the location of the nodes within a fixed number of degrees of freedom. Examples of the application of the criterion are provided. The finite element method has become an important tool of engineering analysis and design. Much of the popularity of the method is due to the freedom that it allows in the construction of the discretized model. It has long been realized, however, that this freedom must be carefully exercised since the quality of the finite element solution greatly depends on how the discretization is performed. Several methods have been proposed to improve the discretized model in an iterative manner. One such method is presented in this paper. A natural way of improving the quality of finite element solutions is to increase the number of degrees of freedom. The process is normally performed after an initial solution is already available. Several schemes have been devised to introduce the new degrees of freedom in a selective manner in order to produce the greatest possible improvement of the previous solution. This calls for the definition of criteria to identify the regions of the domain where the finite element approximation is poorer. The new degrees of freedom are added in these regions by either increasing the order of polynomial approximation inside elements, the so-called p-method, or by subdivision of elements, or h-method. The process is continued until a specified accuracy is achieved. The quality of the finite element solution may be improved also by optimizing the disposition of the nodes. Analysts often rely on their experience to construct grids that make an efficient use of the available degrees of freedom. It is also possible to improve the quality of existing meshes iteratively using predefined guidelines for the redistribution of the nodes. This paper considers the development of such guidelines.

Miniaturization of Patch Antennas Using a Metamaterial-Inspired Technique

A new design methodology for producing highly miniaturized patch antennas is introduced. The methodology uses complementary split-ring resonators placed horizontally between the patch and the ground plane. By optimizing the geometry of the split rings, sub-wavelength resonance of the patch antenna can be achieved with a good impedance match and radiation characteristics comparable to those of a traditional patch antenna on a finite ground plane. Construction of the optimized antenna is straightforward, requiring only the sandwiching of two etched circuit boards. High levels of miniaturization are demonstrated through simulations and experiments, with reductions of a factor of more than four in transverse dimension achieved for a circular patch resonant at 2.45 GHz. Although miniaturization is accompanied by a decrease in antenna radiation efficiency and a loss of fractional bandwidth, antenna performance remains acceptable even for a 1/16 reduction in patch area.

Optimal material layout for 3D elastic structures

The problem of optimal layout in three-dimensional elasticity is solved using a moment formulation to characterize the optimal orthotropy of the material at each point of the domain. Design for minimum compliance under a single constraint on the amount of material is considered.

A wavelet–Galerkin scheme for analysis of large-scale problems on simple domains

A wavelet–Galerkin scheme tailored to address the numerical solution of large-scale boundary value problems defined on domains of simple geometry is presented. The variation of parameters, e.g. material properties, within the domain is arbitrary but the method is specifically designed to solve problems where parameters vary in raster-like fashion. Boundary conditions are imposed via Lagrange multipliers using a fictitious domain approach. A preconditioner specially designed for this problem is developed to guarantee that convergence of conjugate gradient algorithms is quick and insensitive to problem size. The strategy is applied to the solution of steady state, heat conduction problems in 2-D, but it can be generalized without conceptual changes to 3-D problems and to problems in linear elasticity. Copyright

SYNTHESIS OF BISTABLE PERIODIC STRUCTURES USING TOPOLOGY OPTIMIZATION AND A GENETIC ALGORITHM

A formulation for the automatic synthesis of two-dimensional bistable, compliant periodic structures is presented, based on standard methods for topology optimization. The design space is parametrized using nonlinear beam elements and a ground structure approach. A performance criterion is suggested, based on characteristics of the load-deformation curve of the compliant structure. A genetic algorithm is used to find candidate solutions. A numerical implementation of this methodology is discussed and illustrated using simple examples.

Comparing the mathematical models of Lighthill to the performance of a biomimetic fish

The mathematical models for the performance of aquatic animals developed by M Lighthill are compared with the experimental performance of a biomimetic fish. The equations developed by Lighthill are evaluated at steady-state conditions. Equilibrium velocity and mechanical efficiency are calculated using Lighthills mathematical model and compared with experimental results. In both cases, a pattern is found wherein an optimum combination of tail frequency and amplitude maximizes equilibrium velocity. Differences between the theoretical and experimental results are attributed to mechanical limitations in the drive train.

An origami tunable metamaterial

The transmission characteristics of a folded surface decorated with a periodic arrangement of split-ring resonators is investigated. The folding pattern has one displacement degree of freedom, allowing motion that can be used to adjust the separation between the rings. When the geometry of the folded surface is varied by mechanical means, the change in spacing between the rings causes a shift in resonance frequency, making the surface mechanically tunable.