Model Consistency for Mechanical Design: Bridging Lumped and Distributed Parameter Models With a Priori Guarantees
A major challenge in engineering analysis and design is to maintain consistency across models of the same engineered system at multiple levels of abstraction. For example, mechanical assemblies are commonly modeled at system-level (e.g., lumped-parameter networks of components) and component-level (3D models with detailed geometry and materials), whose comparison is nontrivial due to different representations and semantics. We present a novel, simulation-free approach to quantify consistency across a subset of such models; namely, linear time-invariant mass-spring-damper networks and corresponding elastic 3D objects deforming under mechanical loads. Their behavior is described by a finite vector of temporal signals, governed by systems of ordinary differential equations (ODEs), and spatio-temporal fields, governed by partial differential equations (PDEs), respectively. A major benefit of our approach is its ability to perform a priori consistency analysis rapidly (e.g., 5x faster than a posteriori comparison after solving ODEs and PDEs for state space dimensions larger than 30,000) even as the model complexity increases (e.g., only 2.2x slower when the number of equations is doubled). Our approach is validated through several mechanical design analyses, demonstrating its effectiveness in bridging the gap between different modeling abstractions and facilitating the integration between system-level and geometric designs.
