Implementation and Analysis of a Mechanics Simulation Module for Use in a Conceptual Design System

Previously, we have described the theory of a general mechanics model for non-rigid solids (Jansson, Vergeest, 2000). In this paper, we will describe and analyze the implementation, i.e. algorithms and analysis of their time complexity. We will reason that a good (better than O(n2), where n is the number of elements in the system) time complexity is mandatory for a scalable real time simulation system. We will show that, in simplified form, all our algorithms are O(n lg n). We have not been able to formally analyze the algorithms in non-simplified form, we will however informally discuss the expected performance. The entire system will be empirically shown to perform slightly worse than O(n lg n), for a specific range and typical input. We will also present a working prototype implementation and show it can be used for real time evaluation of reasonably complex systems. Finally we will reason about how such a system can be used in the conceptual design community as a simulation of traditional design tools.