Issue 29

F. Tornabene et alii, Frattura ed Integrità Strutturale, 29 (2014) 251-265; DOI: 10.3221/IGF-ESIS.29.22 256 Uniform (Unif) Chebyshev-Gauss-Lobatto (Che-Gau-Lob) 1 , 1, 2,..., 1 k k k M M      1 1 1 1 , cos , 1,2,..., , 1,1 1 k k M k M r r k r k M r r r M                       Quadratic (Quad) (only for M odd) Extended Chebyshev (Extd Cheb) or (Cheb I) 2 2 1 1 2 1,2,..., 1 2 1 1 1 2 4 1, 1,..., 1, 1 1 2 k k k M k M k k M k M M M M                                              1 1 , roots of , 1,2,..., , 1,1 k k k M M r r r T r k M r r r            Extrema Chebyshev (Extr Cheb) or (Cheb II) Approximate Legendre (App Leg)   1 1 , roots of , 1,2,..., , 1,1 k k k M N r r r U r k M r r r            1 1 2 3 1 1 1 4 1 , 1 cos , 8 8 4 2 1,2,..., , 1,1 k k M k M r r k r r r M M M k M r                               Legendre-Gauss (Leg-Gau) Legendre-Gauss-Radau (Leg-Gau-Rad)   1 1 1 2 , 1, 1, roots of , 2,3,..., 1, 1,1 k k M M k M r r r r r r r P r k M r                     1 1 1 , roots of , 1,2,..., , 1,1 k k k M M M r P r r r P r r k M r r              Chebyshev-Gauss (Cheb-Gau) Legendre-Gauss-Lobatto (Leg-Gau-Lob)   1 1 1 1 2 3 , 1, 1, cos , 2 2 2,3,..., 1, 1,1 k k M M k M r r k r r r r r M k M r                               1 1 1 1 , 1, 1, roots of , 2,3,..., 1 1,1 M k k M k M dP r r r r r r r r dr k M r                 Hermite (Her) Laguerre (Lague)   1 1 , roots of , 1,2,..., , , k k k M M r r r H r r r k M r                1 1 , roots of , 1, 2,..., , 0, k k k M M r r r G r r r k M r             Jacobi (Jac) Chebyshev-Gauss-Radau (Cheb-Gau-Rad)     , 1 1 , roots of , 1, 2,..., , 1,1 k k k M M r r r J r r r k M r                1 1 1 2 1 , cos , 2 1 1, 2,..., , 1,1 k k M k M k r r r r r M k M r                         Jacobi-Gauss (Jac-Gau) Ding et al. [37] distribution     , 1 1 2 1 , 1, 1, roots of , 2,3,..., 1, 1,1 k k M k M M r r r r r J r r r k M r                   1 1 1 2 cos , 1,2,..., 2 4 2 1 k k k M M                     Chebyshev III (Cheb III) Chebyshev IV (Cheb IV)   1 1 , roots of , 1,2,..., , 1,1 k k k M N r r r V r k M r r r              1 1 , roots of , 1,2,..., , 1,1 k k k M N r r r W r k M r r r            Radau I (Rad I) Radau II (Rad II)       1 1 1 1 1 2 , 1, roots of , 1,2,..., 1, 1,1 M M k k M k M r r r r P r P r r r k M r                         1 1 2 1 , 1, roots of , 1,2,..., 1, 1,1 k M M k M k M r r r r r P r P r r k M r                 Table 2 : List of several grid distributions used in structural mechanics applications.