Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, J Appl Mech ASME, vol.18, pp.31-39, 1951. ,
Free vibration analysis of symmetric laminated composite plates by FSDT and radial basis functions, Comput Methods Appl Mech Eng, vol.194, pp.4265-78, 2005. ,
Stability and vibration of isotropic, orthotropic and laminated plates according to a higher order shear deformation theory, J Sound Vib, vol.98, pp.157-70, 1985. ,
A simple higher-order theory for laminated composite plates, J Appl Mech ASME, vol.51, issue.4, pp.745-52, 1984. ,
A higher order theory for free vibration of orthotropic, homogeneous, and laminated rectangular plates, J Appl Mech ASME, vol.51, pp.195-203, 1984. ,
A unified formulation of laminated composite, shear deformable, five-degrees-of-freedom cylindrical shell theories, Compos Struct, vol.25, issue.1-4, pp.165-71, 1993. ,
High order triangular sandwich plate finite element for linear and nonlinear analyses, Comput Methods Appl Mech Eng, vol.185, pp.305-329, 2000. ,
URL : https://hal.archives-ouvertes.fr/hal-01366943
Mechanics of laminated composite plates and shells -theory and analysis, 2004. ,
A family of sinus finite elements for the analysis of rectangular laminated beams, Compos Struct, vol.84, pp.56-72, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-01366937
On the use of the murakami's zig-zag function in the modeling of layered plates and shells, Comput Struct, vol.82, pp.541-54, 2004. ,
A higher-order theory of plate deformation. Part ii: Laminated plates, J Appl Mech ASME, vol.44, pp.669-76, 1977. ,
Vibration of thick laminated composite plates, J Sound Vib, vol.179, pp.475-98, 1995. ,
On the accuracy of recent global-local theories for bending and vibration of laminated plates, Compos Struct, vol.95, pp.163-72, 2013. ,
A generalisation of two-dimensional theories of laminated composite plates, Commun Appl Numer Methods, vol.3, pp.173-80, 1987. ,
Modeling of thick composites using a layerwise laminate theory, Int J Numer Meth Eng, vol.36, pp.655-77, 1993. ,
Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and multiquadrics discretizations, Eng Anal Bound Elem, vol.29, pp.1104-1118, 2005. ,
Exact 3d stress analysis of laminated composite plates by sampling surfaces method, Compos Struct, vol.94, pp.3654-63, 2012. ,
Dynamic analysis of laminated composite plates using a layer-wise mixed finite element model, Compos Struct, vol.59, pp.237-286, 2003. ,
Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking, Appl Mech Rev, vol.10, issue.3, pp.215-96, 2003. ,
? 3 plate theories for thick and thin plates: the generalized unified formulation, Compos Struct, vol.84, pp.256-70, 2008. ,
infty 6 mixed plate theories based on the generalized unified formulation. Part i: governing equations, Compos Struct, vol.87, issue.3, pp.1-11, 2009. ,
A sublaminate generalized unified formulation for the analysis of composite structures, Comput Struct, vol.142, pp.187-99, 2016. ,
Laminated composite plate theory with improved in-plane responses, J Appl Mech ASME, vol.53, pp.661-667, 1986. ,
Vibration of multilayered beams using sinus finite elements with transverse normal stress, Compos Struct, vol.92, pp.1524-1558, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-01366979
A consistent refinement of first-order shear deformation theory for laminated composite and sandwich plates using improved zigzag kinematics, J Mech Mater Struct, vol.5, pp.341-67, 2010. ,
An enhanced single-layer variational formulation for the effect of transverse shear on laminated orthotropic plates, Eur J Mech A Solids, vol.29, issue.4, pp.567-90, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00559139
A refined sinus plate finite element for laminated and sandwich structures under mechanical and thermomechanical loads, Comput Methods Appl Mech Eng, vol.253, pp.396-412, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-01366914
Historical review of zig-zag theories for multilayered plates and shells, Appl Mech Rev, vol.56, issue.3, pp.287-308, 2003. ,
Assessment of computational models for multilayered composite shells, Appl Mech Rev, vol.43, issue.4, pp.67-97, 1990. ,
Recent developments in finite elements analysis for laminated composite plates, Compos Struct, vol.88, pp.147-57, 2009. ,
A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates, Appl Mech Rev, vol.62, 2009. ,
On the free vibration analysis of laminated composite and sandwich plates: a review of recent literature with some numerical results, Compos Struct, vol.129, pp.177-201, 2015. ,
An extension of the kantorovich method, Quart Appl Math, vol.26, pp.219-248, 1968. ,
An extended kantorovich method for the solution of eigenvalue problems, Int J Solids Struct, vol.5, pp.559-72, 1969. ,
Stability and vibration of shear deformable plates first order and higher order analyses, Int J Solids Struct, vol.42, pp.1225-51, 2005. ,
Semi-analytical modeling of cutouts in rectangular plates with variable thickness -free vibration analysis, Appl Math Modell, vol.40, issue.15, pp.6983-7000, 2016. ,
The kantorovich method applied to bending, buckling, vibration, and 3d stress analyses of plates: a literature review, Mech Adv Mater Struct, 2005. ,
Nonlinear computational structural mechanics -new approaches and non-incremental methods of calculation, 1999. ,
An overview of the proper generalized decomposition with applications in computational rheology, J Non-Newton Fluid Mech, vol.166, issue.11, pp.578-92, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-01061441
Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models, Arch Comput Methods Eng, vol.17, issue.4, pp.327-50, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-01007235
A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids, J Non, vol.139, pp.153-76, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-01004909
A variational approach to three-dimensional elasticity solutions of laminated composite plates, J Appl Mech ASME, vol.59, pp.166-75, 1992. ,
Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity, Comput Methods Appl Mech Eng, vol.201, pp.1-12, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-01462825
Assessment of a composite beam finite element based on the proper generalized decomposition, Compos Struct, vol.94, issue.5, pp.1900-1910, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-01366922
Proper generalized decomposition and layer-wise approach for the modeling of composite plate structures, Int J Solids Struct, vol.50, pp.2239-50, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-01366917
Shell finite element based on the proper generalized decomposition for the modeling of cylindrical composite structures, Comput. Struct, vol.132, pp.1-11, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01366963
Circumventing the curse of dimensionality in the solution of highly multidimensional models encountered in quantum mechanics using meshfree finite sums decompositions, Lecture Notes Comput Sci Eng, vol.65, pp.1-17, 2006. ,
Greedy algorithms for high-dimensional eigenvalue problems, Constr Approx, vol.40, issue.3, pp.387-423, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00809855
Developments, ideas and evaluations based upon the reissner's mixed theorem in the modeling of multilayered plates and shells, Appl Mech Rev, vol.54, pp.301-330, 2001. ,
Considerations on higherorder finite elements for multilayered plates based on a unified formulation, Comput Struct, vol.84, pp.1222-1257, 2006. ,
Free vibration analysis of composite and sandwich plates using an improved discrete kirchhoff quadrilateral element based on third-order zigzag theory, Comput Mech, vol.42, issue.6, pp.803-827, 2008. ,
Natural vibrations of laminated and sandwich plates, J Eng Mech ASCE, vol.130, pp.1268-78, 2004. ,
Free vibrations of multilayered composite plates, AIAA J, vol.11, pp.1038-1047, 1973. ,
Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory, Compos Struct, vol.53, pp.73-85, 2001. ,
An accurate higher-order theory and c0 finite element for free vibration analysis of laminated composite and sadwich plates, Compos Struct, vol.92, pp.1299-307, 2010. ,