FEA-3D |
Mixed solid elements (Icardi and Atzori (2004Icardi, U., Atzori, A. (2004). Simple, efficient mixed solid element for accurate analysis of local effects in laminated and sandwich composites, Advances in Engineering Software 35(12):843-859.)). |
MHR4 |
Mixed HR theory, displacements with Murakami’s zig-zag function (Icardi and Urraci (2018bIcardi, U., Urraci, A. (2018b). Novel HW mixed zig-zag theory accounting for transverse normal deformability and lower-order counterparts assessed by old and new elastostatic benchmarks, Aerospace Science and Technology 80:541-571.))(3.3). |
FSDT |
Equivalent first-order shear deformation theory, shear correction factor of 5/6 is assumed. |
MHR± |
MHR theory, where the right sign of Murakami’s zig-zag function is determined at each interface on a physical basis, (Icardi and Urraci (2018aIcardi, U., Urraci, A. (2018a). Free and forced vibration of laminated and sandwich plates by zig-zag theories differently accounting for transverse shear and normal deformability, Aerospace 5(4):108.))(3.3). |
HRZZ |
Mixed HR theory, , , (Icardi and Urraci (2018bIcardi, U., Urraci, A. (2018b). Novel HW mixed zig-zag theory accounting for transverse normal deformability and lower-order counterparts assessed by old and new elastostatic benchmarks, Aerospace Science and Technology 80:541-571.)) (3.3). |
MHR4± |
MHR4 theory, where the right sign of Murakami’s zig-zag function is determined at each interface on a physical basis (Icardi and Urraci (2018aIcardi, U., Urraci, A. (2018a). Free and forced vibration of laminated and sandwich plates by zig-zag theories differently accounting for transverse shear and normal deformability, Aerospace 5(4):108.))(3.3). |
HRZZ4 |
Mixed HR theory, , , (Icardi and Urraci (2018bIcardi, U., Urraci, A. (2018b). Novel HW mixed zig-zag theory accounting for transverse normal deformability and lower-order counterparts assessed by old and new elastostatic benchmarks, Aerospace Science and Technology 80:541-571.))(3.3). |
MHWZZA |
Mixed HW theory, displacements with Murakami’s zig-zag functions, stress and strains with Di Sciuva’s one (Icardi and Urraci (2018bIcardi, U., Urraci, A. (2018b). Novel HW mixed zig-zag theory accounting for transverse normal deformability and lower-order counterparts assessed by old and new elastostatic benchmarks, Aerospace Science and Technology 80:541-571.))(3.3). |
HSDT |
Equivalent third-order shear deformation theory. |
MHWZZA4 |
Mixed HW theory, in-plane displacements with Murakami’s zig-zag functions, transverse displacement, stress and strains with Di Sciuva’s one (Icardi and Urraci (2018bIcardi, U., Urraci, A. (2018b). Novel HW mixed zig-zag theory accounting for transverse normal deformability and lower-order counterparts assessed by old and new elastostatic benchmarks, Aerospace Science and Technology 80:541-571.))(3.3). |
HSDT_32 |
Enriched versions of HSDT, whose coefficients are redefined across the thickness, , (4.4). |
PP23 |
, zig-zag theory (Icardi (2001Icardi, U. (2001). Higher-order zig-zag model for analysis of thick composite beams with inclusion of transverse normal stress and sublaminates approximations, Composites Part B: Engineering 32(4):343-354.))(3.3). |
HSDT_33 |
Enriched versions of HSDT, whose coefficients are redefined across the thickness, , (4.4). |
ZZ |
, zig-zag theory (Icardi (2001Icardi, U. (2001). Higher-order zig-zag model for analysis of thick composite beams with inclusion of transverse normal stress and sublaminates approximations, Composites Part B: Engineering 32(4):343-354.))(3.3). |
HSDT_34 |
Enriched versions of HSDT, whose coefficients are redefined across the thickness, , (4.4). |
ZZA |
, zig-zag adaptive theory (Icardi and Sola (2014Icardi, U., Sola, F. (2014). Development of an efficient zig-zag model with variable representation of displacements across the thickness, Journal of Engineering Mechanics 140(3):531-541.))(2.2). |
HWZZ |
HW mixed version of ZZA (Icardi and Urraci (2018bIcardi, U., Urraci, A. (2018b). Novel HW mixed zig-zag theory accounting for transverse normal deformability and lower-order counterparts assessed by old and new elastostatic benchmarks, Aerospace Science and Technology 80:541-571.))(2.4). |
ZZA* |
, modified ZZA (Icardi and Urraci (2018aIcardi, U., Urraci, A. (2018a). Free and forced vibration of laminated and sandwich plates by zig-zag theories differently accounting for transverse shear and normal deformability, Aerospace 5(4):108.))(2.3). |
HWZZ_RDF |
Modified HWZZ theory(4.2). |
ZZA*_43 |
, modified version of ZZA* (4.3). |
HWZZM |
HWZZ with different zig-zag functions (Icardi and Urraci (2018aIcardi, U., Urraci, A. (2018a). Free and forced vibration of laminated and sandwich plates by zig-zag theories differently accounting for transverse shear and normal deformability, Aerospace 5(4):108.))(3). |
ZZA_X1 |
, modified ZZA theories, with different representation across the thickness(4.1). |
ZZA_X2 |
ZZA_X3 |
ZZA_X4 |
HWZZM* |
HWZZ with different zig-zag functions (Icardi and Urraci (2018aIcardi, U., Urraci, A. (2018a). Free and forced vibration of laminated and sandwich plates by zig-zag theories differently accounting for transverse shear and normal deformability, Aerospace 5(4):108.))(3.2). |
ZZA-XX |
Zig-zag general theory with exponential representation(4.1). |
HWZZM (♠) |
HWZZM theories, type A, B, B2, C, C2, 0, (Icardi and Urraci (2018aIcardi, U., Urraci, A. (2018a). Free and forced vibration of laminated and sandwich plates by zig-zag theories differently accounting for transverse shear and normal deformability, Aerospace 5(4):108.))(3.1). |
ZZA-XX’ |
Zig-zag general theory with power representation(4.1). |
MHR |
Mixed HR theory with Murakami’s zig-zag function, , lacking (Icardi and Urraci (2018bIcardi, U., Urraci, A. (2018b). Novel HW mixed zig-zag theory accounting for transverse normal deformability and lower-order counterparts assessed by old and new elastostatic benchmarks, Aerospace Science and Technology 80:541-571.))(3.3). |
ZZA_RDF |
Modified ZZA theory(4.1). |