, Volume 49, Issue 10, pp 2399–2418 | Cite as

Meshfree modeling of dynamic response of mechanical structures

  • Tomislav Kosta
  • Igor Tsukanov


Transient nature of the loading conditions applied to the structural components makes dynamic analysis one of the important components in the design-analysis cycle. Time-varying forces and accelerations can substantially change stress distributions and cause a premature failure of the mechanical structures. In addition, it is also important to determine dynamic response of the structural elements to the frequency of the applied loads. In this paper we describe the first application of the meshfree Solution Structure Method (SSM) to the structural dynamics problems. SSM is a meshfree method which enables construction of the solutions to the engineering problems that satisfy exactly all prescribed boundary conditions. This method is capable of using spatial meshes that do not conform to the shape of a geometric model. Instead of using the grid nodes to enforce boundary conditions, it employs distance fields to the geometric boundaries and combines them with the basis functions and prescribed boundary conditions at run time. This defines unprecedented geometric flexibility of the SSM as well as the complete automation of the solution procedure. In the proposed approach we will use SSM to enforce initial and boundary conditions, while transient behavior is enforced by time marching schemes used to solve systems of ordinary differential equations. In the paper we will explain the key points of the SSM as well as investigate the accuracy and convergence of the proposed approach by comparing our results with the ones obtained using traditional finite element analysis. Despite in this paper we are dealing with 2D in-plane vibrations, the proposed approach has a straightforward application to model vibrations of 3D structures.


Dynamic response Natural frequencies Finite element analysis Solution Structure Method Meshfree method Distance fields 



This research work was supported in part by the National Science Foundation Grant CMMI-0900219. The author Tomislav Kosta is also grateful for the following Grant 58940-RT-REP from the Army Research Office that enabled this work to be possible.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Mechanical and Materials EngineeringFlorida International UniversityMiamiUSA

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