Implicit functions with guaranteed differential properties
Proceedings of the fifth ACM symposium on Solid modeling and applications
Transfinite interpolation over implicity defined sets
Computer Aided Geometric Design
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Lanczos Method: Evolution and Application
Lanczos Method: Evolution and Application
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Geometrically adaptive numerical integration
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Field modeling with sampled distances
Computer-Aided Design
Finite element analysis in situ
Finite Elements in Analysis and Design
Engineering analysis in imprecise geometric models
Finite Elements in Analysis and Design
| Hi-index | 0.00 |
Determination of resonance frequencies and vibration modes of mechanical structures is one of the most important tasks in the product design procedure. The main goal of this paper is to describe a pioneering application of the solution structure method (SSM) to 2D structural natural vibration analysis problems and investigate the numerical properties of the method. 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 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 analytical methods or traditional finite element analysis. Despite in this paper we are dealing with 2D in-plane vibrations, the proposed approach has a straightforward generalization to model vibrations of 3D structures.