Exponential approximations in optimal design

One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis

The Machine that Changed the World: The Story of Lean Production

Nomenclature A = area E b = black body emission per unit area Fij or F sj = shape factor between surfaces i and j (including; = (') or between gas and surface j q = heat transfer m = mass flow rate N = number of surface elements on the wall and the solid T = temperature Az = size of each axial segment of the kil

MPI-enabled Shape Optimization of Panels Subjected to Air Blast Loading

The problem of finding the optimal shape of an aluminum plate to mitigate air blast loading is considered. The goal is to minimize the dynamic displacement of the plate relative to the test fixture, while monitoring plastic strain values, mass, and envelope constraints. This is a computationally challenging problem owing to (a) difficulty with finding optimal shapes with higher dimensional shape variations, (b) non-differentiable, non-convex and computationally expensive objective and constraint functions, and (c) difficulties in controlling mesh distortion that occur during explicit finite element analysis. An approach based on coupling LS-DYNA finite element software and a differential evolution (DE) optimizer is presented. Since DE involves a population of designs which are then crossed-over and mutated to yield an improved generation, it is possible to use coarse parallelization wherein a computing cluster is used to evaluate fitness of the entire population simultaneously. However, owing to highly dissimilar computing time per analysis, a result of mesh distortion and minimum time step in explicit finite element analysis, implementation of the parallelization scheme is challenging. Sinusoidal basis shapes are used to obtain an optimized 'double-bulge' shape.