Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mechanical Engineering


Summers, Joshua D

Committee Member

Fadel , Georges M

Committee Member

Greenstein , Joel S


The lack of computational support to the conceptual phase of mechanical engineering design is well recognized. Function-based modeling and thinking is widely recommended in design texts as useful means for describing design concepts and using them in tasks such as solution search, problem decomposition, and design archival. Graph-based function structure models that describe a product as a network of transformative actions of material, energy, and information, are discussed as a potential tool for this purpose, but in the current state of the art, function structures are not formalized as a computational representation. Consequently, no computer tool exists with which a designer can construct grammatically controlled function structure models, explore design ideas by model editing, and perform automated reasoning on the model against the laws of nature to draw analytical inferences on the design. This research presents, verifies, and validates a formal representation of mechanical functions that supports consistent computer-aided modeling of early design and reasoning on those models based on two universal principles of physics: (1) conservation and (2) irreversibility. The representation is complete in three layers. The first layer--the Conservation Layer--is defined with nine entities, five relations, five attributes, and 33 grammar rules that together formalize the construction of function structure graphs and support conservation-based qualitative validation of design concepts. The second layer--the Irreversibility Layer--includes three additional attributes that support both conservation-based and irreversibility-based reasoning at qualitative and quantitative levels. The third layer--the Semantic Layer--is an extension of the previous two, where a vocabulary of nine verbs that describe mechanical devices and physical principles as functions is proposed. This layer supports feature-based modeling and semantic reasoning of function structures. The internal consistency of the representation is verified by logical examination and ontological consistency checking using Protégé-OWL. The coverage of the verbs is examined by constructing descriptive function structure models of a variety of existing physical principles and devices. The research is validated by incorporating the representation in a software tool using an object-oriented language and graphic user-interface, and by using the tool to construct models and demonstrate conservation-based and irreversibility-based reasoning.



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