TY - JOUR
T1 - An enhanced single-layer variational formulation for the effect of transverse shear on laminated orthotropic plates
AU - Cosentino, Enzo
AU - Weaver, Paul
PY - 2010/7
Y1 - 2010/7
N2 - A novel mixed formulation is derived by means of Reissner's variational approach-based on Castigliano's principle of least work in conjunction with a Lagrange multiplier method for the calculus of variations. The governing equations present an alternative theory for modeling the important three-dimensional structural aspects of plates in a two-dimensional form. By integrating the classical Cauchy's equilibrium equations with respect to the thickness co-ordinate, and enforcing continuity of shear and normal stresses at each ply interface, condenses the effect of the thickness. A reduced system of partial differential equations of sixth-order in one variable, is also proposed, which contains differential correction factors that formally modify the classical constitutive equations for composite laminates. The theory degenerates to classical composite plate analysis for thin configurations. Significant deviations from classical plate theory are observed when the thickness becomes comparable with the in-plane dimensions. A variety of case studies are presented and solutions are compared with other models available in the literature and with finite element analysis.
AB - A novel mixed formulation is derived by means of Reissner's variational approach-based on Castigliano's principle of least work in conjunction with a Lagrange multiplier method for the calculus of variations. The governing equations present an alternative theory for modeling the important three-dimensional structural aspects of plates in a two-dimensional form. By integrating the classical Cauchy's equilibrium equations with respect to the thickness co-ordinate, and enforcing continuity of shear and normal stresses at each ply interface, condenses the effect of the thickness. A reduced system of partial differential equations of sixth-order in one variable, is also proposed, which contains differential correction factors that formally modify the classical constitutive equations for composite laminates. The theory degenerates to classical composite plate analysis for thin configurations. Significant deviations from classical plate theory are observed when the thickness becomes comparable with the in-plane dimensions. A variety of case studies are presented and solutions are compared with other models available in the literature and with finite element analysis.
KW - Castigliano's theorem
KW - Mixed formulatio
KW - Variational approach
UR - http://www.scopus.com/inward/record.url?scp=77955330874&partnerID=8YFLogxK
U2 - 10.1016/j.euromechsol.2009.12.004
DO - 10.1016/j.euromechsol.2009.12.004
M3 - Article
AN - SCOPUS:77955330874
SN - 0997-7538
VL - 29
SP - 567
EP - 590
JO - European Journal of Mechanics, A/Solids
JF - European Journal of Mechanics, A/Solids
IS - 4
ER -