The dual requirements of accuracy and speed in analyzing structural systems with ever-tighter design tolerances and larger numbers of elements have been relentlessly driving forward research into methods that can achieve the Swift Analysis of Structures at a reasonable computational cost. The proviso of accuracy in the analysis is brought about by the need for demonstrating structural safety and material cost reductions. Unfortunately, more accurate analyses, with most conventional methods, lead to increased computational loads. Combined with the already heavy load of analyzing large and complex structures, conventional analysis methods turn into resource drains that are best avoided. In this book, we propose and validate a number of methods and shortcuts for frugal engineers by which they can shave off significant amounts from their computational budget in the analysis, reanalysis and thus structural design processes. A major class of methods for saving computational resources make clever use of symmetries or regularities within structures and have been presented in an earlier book by the first author published by Springer, titled Optimal Analysis of Structures by Concepts of Symmetry and Regularity. In the present work, we will concentrate on a set of methods which instead apply to a larger and more commonly seen subset of structures in which regularity or symmetry are violated by small changes such as cutouts or additional non-regular members. The value of the presented methods becomes more pronounced in situations where the analysis needs to be repeated hundreds or even thousands of times, as is the case with the optimal design of structures using different meta-heuristic algorithms. This book is of most interest to researchers and engineers who engage in computer-aided analysis and design of structures and to software developers in this field. The methods are not only applicable to skeletal structures but by extension also to continuum models. Many of the underlying concepts can be further applied to non-structural systems, such as hydraulic and electrical networks. This work aims to serve as a complementary book to the previous books published on optimal analysis of large-scale structures utilizing concepts of symmetry and regularity. v