This book contains the course schedule and material for the bridging course Structural Mechanics

Welcome to the submodule on the Matrix Method for Statics, part of Unit 2 of CIEM5000 Course base Structural Engineering at Delft University of Technology.

This book contains the material for the course.

Book for the course CTB3330 Structural Mechanics taught in the third year of Bachelor programme Civil Engineering at Delft University of Technology.

This manual is primarily designed for and by teachers for use in education, but should be a useful resource for anyone interested in creating and collaborating on Jupyter book. Our aim is to provide a simple way to start book-making for new users (it only takes 10 clicks!) through advanced usage for experienced users. We hope you find this resource useful and refer back to it often.

This book focuses on how to apply optimization algorithms to specific optimization problems. It does so using python, scipy and pymoo. It contains the preparations for the practical sessions in CME4501 Engineering Systems Optimization.

Het is mogelijk om lichte en goedkope staalconstructies te ontwerpen terwijl de rekenkracht ten opzichte van bestaande methodes beperkt is. Dit volgde, na parametrisch onderzoek, uit een afstudeeronderzoek vorig jaar aan de TU Delft, bij de faculteit Civiele Techniek. Deze methode is tevens toegepast op het constructief ontwerp van een ligger zoals ontworpen door Royal HaskoningDHV. Op verzoek licht de auteur toe hoe een optimaal ontwerp, volgens een nieuwe groeperingsmethode, met een beperkt aantal verschillende profielen goed toepasbaar is.

In the design of steel structures, optimization methods can find minimum weight solutions. However, the solutions tend to have a high diversity of profiles, thereby raising costs. Grouping methods provide a solution by limiting the number of unique profiles, while still providing an optimal solution. This study proposes a new grouping method and compares its performance to that of existing methods in eight benchmark problems. In current practice, the grouping is mostly performed manually, relying on an engineer’s expertise. This technique requires no additional calculations but fails in finding a light or cheap structure. In general, all other grouping methods perform better than manual grouping. Out of the compared methods, the cardinality constraints method finds the lightest solutions. However, this method requires solving a big optimization problem, thereby increasing computational costs and the variance in the outcome. The new method, ‘the fully stressed combinatorial search’, groups members by a combinatorial search, which evaluates the estimated weight of a restricted set of groupings based on the weight per unit length of the members of a fully stressed design. Subsequently, optimization of a small search space finds the corresponding optimum profiles. These steps are repeated, in which the fully stressed design uses the result of the previous optimization as its reference design. The loop repeats until the grouping is unchanged, or the result becomes less optimal. This new method finds similar results as the cardinality constraints with less finite element evaluations and higher consistency in the results upon repetition of the analysis.