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Document Type



Master of Science (MS)


Mechanical Engineering

First Advisor's Name

Igor Tsukanov

First Advisor's Committee Title

Assistant Professor

Second Advisor's Name

George S. Dulikravich

Second Advisor's Committee Title


Third Advisor's Name

Cesar Levy

Third Advisor's Committee Title

Department Chair and Professor


meshfree, solution structure method, vibrations, structural dynamics, modal analysis, dynamic response, finite element method

Date of Defense



In this work, a pioneering application of the Solution Structure Method (SSM) for structural dynamics problems is presented. Vibration analysis is an important aspect of any design-analysis cycle for which reliable computational methods are required. Unlike many meshfree methods, SSM is capable of {\it exact treatment of all prescribed boundary conditions}. In addition, the method is capable of using basis functions which do not conform to the shape of the geometric model. Together, this defines an unprecedented geometric flexibility of the SSM.

This work focused on the development of numerical algorithms for 2D in-plane and 3D natural vibration analysis and 2D in-plane dynamic response. The convergence and numerical properties of the method were evaluated by comparing meshfree results with those obtained using traditional Finite Element Analysis implemented in Solidworks and ANSYS.

The numerical experiments presented in this work illustrate that the Solution Structure Method possesses good convergence and in some cases, such as geometries with partially fixed boundaries, this method converges much more rapidly than traditional FEA. Finally, in addition to complex boundary conditions, this method can easily handle complex geometries without losing favorable convergence properties.





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