Issue 29

F. Tornabene et alii, Frattura ed Integrità Strutturale, 29 (2014) 251-265; DOI: 10.3221/IGF-ESIS.29.22 258 where k w are the weighting coefficients. The integral of   f x over a given domain can be generally approximated by a linear combination of all the functional values in the whole domain as     1 j i x N ij k k k x f x dx w f x     (18) The limits i x , j x of Eq. (18) can be changed. When i a x  and j b x  Eq. (18) becomes a conventional integral (17). The GIQ weighting coefficients can be computed as ij k jk ik w w w   (19) The weighting coefficients for the integral are evaluated by inverting the matrix   1 (1)   W  , which depends on the matrix of the weighting coefficients of the first order derivative [7, 17] and they can be calculated by the following relations         1 1 1 1 1 for , for i ij ij ij ii j i x c i j i j x c x c             (20) a) b) Figure 6 : a) Static analysis for single element structural components varying the number of points N for a Membrane, a KL plate with  -points ( 5 10  ) and a RM plate using PDQ basis functions and Che-Gau-Lob grid distribution. b) Static analysis for structural components varying the number of elements e n with 7 N  for a Membrane and a RM plate using PDQ basis functions and Leg- Gau grid distribution. a) b) Figure 7 : a) Dynamic discrete spectra for single element structural components with 31 N  for a Membrane, a KL plate with  - points ( 5 10  ) and a RM plate using PDQ basis functions and Che-Gau-Lob grid distribution. b) Dynamic discrete spectra for various structural components with 7 N  and 64 e n  for a Membrane and a RM plate using PDQ basis functions and Leg-Gau grid distribution.