Exploring Finite Element Analysis in a Parametric Environment

Abstract

This thesis is Exploring Finite Element Analysis in a Parametric Environment, with the intent of building a functioning Finite Element Analysis (FEA) program within the Grasshopper parametric environment. A motivation for this is to provide tools for designers and architects to roughly and swiftly assess structures within the Grasshopper environment.

In order to attain a deeper understanding of how the Finite Element Method can be implemented in a parametric design environment, some Finite Element Analysis software packages are created to gain some experience with the inner processes of the Finite Element algorithms and to help locate eventual implementation issues.

The results are four functioning programs for calculation of displacements, strains and stresses within truss, beam and shell structures. In addition, analysis is performed on each of the programs to assess their performance in terms of running time and accuracy. To measure accuracy, the software packages has been compared to analytical solutions and a well-established Finite Element Analysis program.

All the created software packages display sensible deformation patterns and are in accordance with the established Finite Element Analysis comparison tool. In terms of running time, the simpler software bundles are executed within satisfactory time limits, but the heavier software bundles struggle with larger structures.

In general, the processing parts could benefit from utilization of sparse storage formats and better optimized solving algorithms. The software packages are very close to analytical solutions, with the exception of complicated shell structures. The Shell software would benefit from implementation of more advanced elements, especially for the membrane part of the element.