Date of Award

Fall 2019

Document Type


Degree Name

Master of Science (MS)


Mechanical & Aerospace Engineering


Aerospace Engineering

Committee Director

Gene Hou

Committee Member

Brett Newman

Committee Member

Miltos Kotinis


Numerical analysis of constrained static and multibody dynamic systems has become an integral part of engineering analysis with the continued improvements in technology and software availability. Many methods currently exist for numerically solving constrained static and dynamic systems. The applicability of a penalty method for constrained static solutions is observed in many academic texts and papers. The appeal for using a penalty method in statics pertains to its ease of implementation, computational suitability, and accuracy. This thesis extends a static penalty method for use with constrained multibody dynamics to observe if the penalty method’s benefits are similar for a dynamics solution.

This thesis discusses formulations that are used in extending the static penalty method for use with constrained multibody dynamics. Example problems are then solved using the static penalty method and compared with a projection method. Example problems are selected to provide a solid foundation for implementing the static penalty method with many other constrained multibody systems. Constraints are purely holonomic for simplification of problem statements.

The goal of this thesis was met, in that the static penalty method is successfully applied to constrained multibody systems with favorable results. In comparing the penalty method with a projection method for each example, computational time and accuracy are comparable. Coding of the penalty method is found to be no more difficult than that of the projection method. The static penalty method is shown to be useful in solving constrained multibody dynamics. Application of the penalty method was not tested with non-holonomic constraints. Future work is necessary to assess the penalty method’s applicability with non-holonomic constraints, as well as increasingly complex multibody dynamic systems.


In Copyright. URI: This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).