Fractal finite element mesh generation for vibration problems
J.-H. Jeng, V. V. Varadan, Vijay K. Varadan · The Journal of the Acoustical Society of America · 1987
A new approach for solving plate vibration problems has been formulated by using the Pascal–Sierpinski gaskets and finite element method. The Pascal–Sierpinski gaskets are geometric fractals that are self-similar under scale transformation. Modeling a finite plate element with the basic Pascal–Sierpinski gasket unit, the equations of motion of the basic unit are derived. A buildup process is formed by linking three identical units together. Finally, systematic recurrence relations are generated. The advantage of this approach is that the dynamic matrix of the system has the same dimension at each buildup step. The basic vibration properties, computation time, and memory requirements are discussed and critically compared with traditional finite element methods by discussing a specific example. In general, finite element mesh generation based on geometric fractals offers much promise in reducing storage requirements and computation times significantly.