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Tortorelli, Daniel A.

Publications and source records attributed to Tortorelli, Daniel A..

4 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Level-set topology optimization with PDE generated conformal meshes

This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.

42 ENGINEERING↗
NASA NTRS1991

Optimal design of solidification processes

An optimal design algorithm is presented for the analysis of general solidification processes, and is demonstrated for the growth of GaAs crystals in a Bridgman furnace. The system is optimal in the sense that the prespecified temperature distribution in the solidifying materials is obtained to maximize product quality. The optimization uses traditional numerical programming techniques which require the evaluation of cost and constraint functions and their sensitivities. The finite element method is incorporated to analyze the crystal solidification problem, evaluate the cost and constraint functions, and compute the sensitivities. These techniques are demonstrated in the crystal growth application by determining an optimal furnace wall temperature distribution to obtain the desired temperature profile in the crystal, and hence to maximize the crystal's quality. Several numerical optimization algorithms are studied to determine the proper convergence criteria, effective 1-D search strategies, appropriate forms of the cost and constraint functions, etc. In particular, we incorporate the conjugate gradient and quasi-Newton methods for unconstrained problems. The efficiency and effectiveness of each algorithm is presented in the example problem.

Dantzig, Jonathan A.↗
NASA NTRS1990

A geometric representation scheme suitable for shape optimization

A geometric representation scheme is outlined which utilizes the natural design variable concept. A base configuration with distinct topological features is created. This configuration is then deformed to define components with similar topology but different geometry. The values of the deforming loads are the geometric entities used in the shape representation. The representation can be used for all geometric design studies; it is demonstrated here for structural optimization. This technique can be used in parametric design studies, where the system response is defined as functions of geometric entities. It can also be used in shape optimization, where the geometric entities of an original design are modified to maximize performance and satisfy constraints. Two example problems are provided. A cantilever beam is elongated to meet new design specifications and then optimized to reduce volume and satisfy stress constraints. A similar optimization problem is presented for an automobile crankshaft section. The finite element method is used to perform the analyses.

Tortorelli, Daniel A.↗