Mesh size of a finite element model

Question

Hi everyone, 
 When calculating the average element size, Kuhlmeyer & Lysmer (1973) suggested to assume a size of element not larger than &lambda;/8, where &lambda; is the wavelength corresponding to the maximum frequency f of interest. Therefore, Average element size = &lambda;/8 = (Vs)/(8)(fmax). fmax is the maximum frequency of interest. 
 Does anyone know, how to calculate fmax (maximum frequency of interest)? 
 Thanks and regards, Mihimal.

Faseel Khan · Answer

The mesh generation in PLAXIS is fully automatic and is based on a robust triangulation procedure. The dimension of the triangular elements needs to be controlled and the mesh refinement allows to get a specific value of the average length of the element size. Kuhlemeyer & Lysmer (1973) suggest to assume a size less than or equal to one-eight of the wavelength associated with the maximum frequency component fmax of the input wave (i.e. the highest frequency component that contains appreciable energy): Average element size = &lambda;/8 = (vs min)/(8.fmax) 
 Based on the shear stiffness profile and the unit weight of soil, it is possible to calculate the shear wave velocity profile with depth from where you can get vs min. From the Fourier spectrum, the maximum frequency component fmax can be found. PLAXIS will automatically perform the fourier analysis on the input signal for generating the Fourier spectrum of the time series. In the graph, the corner and maximum frequencies (fmax) of the source spectrum model are found. This curve has three different parts, first part is rising part and then a part approximate quasi-constant and then the third part is descending part. The inflection point between the first part and second part gives the corner frequency and the inflection point between the second part and third part gives the maximum frequency.